Deconstructing Convolutional Neural Networks with Tensorflow and Keras

I have been very fascinated by how Convolution Neural  Networks have been able to, so efficiently,  do image classification and image recognition CNN’s have been very successful in in both these tasks. A good paper that explores the workings of a CNN Visualizing and Understanding Convolutional Networks  by Matthew D Zeiler and Rob Fergus. They show how through a reverse process of convolution using a deconvnet.

In their paper they show how by passing the feature map through a deconvnet ,which does the reverse process of the convnet, they can reconstruct what input pattern originally caused a given activation in the feature map

In the paper they say “A deconvnet can be thought of as a convnet model that uses the same components (filtering, pooling) but in reverse, so instead of mapping pixels to features, it does the opposite. An input image is presented to the CNN and features  activation computed throughout the layers. To examine a given convnet activation, we set all other activations in the layer to zero and pass the feature maps as input to the attached deconvnet layer. Then we successively (i) unpool, (ii) rectify and (iii) filter to reconstruct the activity in the layer beneath that gave rise to the chosen activation. This is then repeated until input pixel space is reached.”

I started to scout the internet to see how I can implement this reverse process of Convolution to understand what really happens under the hood of a CNN.  There are a lot of good articles and blogs, but I found this post Applied Deep Learning – Part 4: Convolutional Neural Networks take the visualization of the CNN one step further.

This post takes VGG16 as the pre-trained network and then uses this network to display the intermediate visualizations.  While this post was very informative and also the visualizations of the various images were very clear, I wanted to simplify the problem for my own understanding.

Hence I decided to take the MNIST digit classification as my base problem. I created a simple 3 layer CNN which gives close to 99.1% accuracy and decided to see if I could do the visualization.

As mentioned in the above post, there are 3 major visualisations

  1. Feature activations at the layer
  2. Visualisation of the filters
  3. Visualisation of the class outputs

Feature Activation – This visualization the feature activation at the 3 different layers for a given input image. It can be seen that first layer  activates based on the edge of the image. Deeper layers activate in a more abstract way.

Visualization of the filters: This visualization shows what patterns the filters respond maximally to. This is implemented in Keras here

To do this the following is repeated in a loop

  • Choose a loss function that maximizes the value of a convnet filter activation
  • Do gradient ascent (maximization) in input space that increases the filter activation

Visualizing Class Outputs of the MNIST Convnet: This process is similar to determining the filter activation. Here the convnet is made to generate an image that represents the category maximally.

You can access the Google colab notebook here – Deconstructing Convolutional Neural Networks in Tensoflow and Keras

import numpy as np
import pandas as pd
import os
import tensorflow as tf
import matplotlib.pyplot as plt
from keras.layers import Dense, Dropout, Flatten
from keras.layers import Conv2D, MaxPooling2D, Input
from keras.models import Model
from sklearn.model_selection import train_test_split
from keras.utils import np_utils
Using TensorFlow backend.
In [0]:
mnist=tf.keras.datasets.mnist
# Set training and test data and labels
(training_images,training_labels),(test_images,test_labels)=mnist.load_data()
In [0]:
#Normalize training data
X =np.array(training_images).reshape(training_images.shape[0],28,28,1) 
# Normalize the images by dividing by 255.0
X = X/255.0
X.shape
# Use one hot encoding for the labels
Y = np_utils.to_categorical(training_labels, 10)
Y.shape
# Split training data into training and validation data in the ratio of 80:20
X_train, X_validation, y_train, y_validation = train_test_split(X,Y,test_size=0.20, random_state=42)
In [4]:
# Normalize test data
X_test =np.array(test_images).reshape(test_images.shape[0],28,28,1) 
X_test=X_test/255.0
#Use OHE for the test labels
Y_test = np_utils.to_categorical(test_labels, 10)
X_test.shape
Out[4]:
(10000, 28, 28, 1)

Display data

Display the training data and the corresponding labels

In [5]:
print(training_labels[0:10])
f, axes = plt.subplots(1, 10, sharey=True,figsize=(10,10))
for i,ax in enumerate(axes.flat):
    ax.axis('off')
    ax.imshow(X[i,:,:,0],cmap="gray")

Create a Convolutional Neural Network

The CNN consists of 3 layers

  • Conv2D of size 28 x 28 with 24 filters
  • Perform Max pooling
  • Conv2D of size 14 x 14 with 48 filters
  • Perform max pooling
  • Conv2d of size 7 x 7 with 64 filters
  • Flatten
  • Use Dense layer with 128 units
  • Perform 25% dropout
  • Perform categorical cross entropy with softmax activation function
In [0]:
num_classes=10
inputs = Input(shape=(28,28,1))
x = Conv2D(24,kernel_size=(3,3),padding='same',activation="relu")(inputs)
x = MaxPooling2D(pool_size=(2, 2))(x)
x = Conv2D(48, (3, 3), padding='same',activation='relu')(x)
x = MaxPooling2D(pool_size=(2, 2))(x)
x = Conv2D(64, (3, 3), padding='same',activation='relu')(x)
x = MaxPooling2D(pool_size=(2, 2))(x)
x = Flatten()(x)
x = Dense(128, activation='relu')(x)
x = Dropout(0.25)(x)
output = Dense(num_classes,activation="softmax")(x)

model = Model(inputs,output)

model.compile(loss='categorical_crossentropy', 
          optimizer='adam', 
          metrics=['accuracy'])

Summary of CNN

Display the summary of CNN

In [7]:
model.summary()
Model: "model_1"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_1 (InputLayer)         (None, 28, 28, 1)         0         
_________________________________________________________________
conv2d_1 (Conv2D)            (None, 28, 28, 24)        240       
_________________________________________________________________
max_pooling2d_1 (MaxPooling2 (None, 14, 14, 24)        0         
_________________________________________________________________
conv2d_2 (Conv2D)            (None, 14, 14, 48)        10416     
_________________________________________________________________
max_pooling2d_2 (MaxPooling2 (None, 7, 7, 48)          0         
_________________________________________________________________
conv2d_3 (Conv2D)            (None, 7, 7, 64)          27712     
_________________________________________________________________
max_pooling2d_3 (MaxPooling2 (None, 3, 3, 64)          0         
_________________________________________________________________
flatten_1 (Flatten)          (None, 576)               0         
_________________________________________________________________
dense_1 (Dense)              (None, 128)               73856     
_________________________________________________________________
dropout_1 (Dropout)          (None, 128)               0         
_________________________________________________________________
dense_2 (Dense)              (None, 10)                1290      
=================================================================
Total params: 113,514
Trainable params: 113,514
Non-trainable params: 0
_________________________________________________________________

Perform Gradient descent and validate with the validation data

In [8]:
epochs = 20
batch_size=256
history = model.fit(X_train,y_train,
         epochs=epochs,
         batch_size=batch_size,
         validation_data=(X_validation,y_validation))
————————————————
acc = history.history[ ‘accuracy’ ]
val_acc = history.history[ ‘val_accuracy’ ]
loss = history.history[ ‘loss’ ]
val_loss = history.history[‘val_loss’ ]
epochs = range(len(acc)) # Get number of epochs
#————————————————
# Plot training and validation accuracy per epoch
#————————————————
plt.plot ( epochs, acc,label=”training accuracy” )
plt.plot ( epochs, val_acc, label=’validation acuracy’ )
plt.title (‘Training and validation accuracy’)
plt.legend()
plt.figure()
#————————————————
# Plot training and validation loss per epoch
#————————————————
plt.plot ( epochs, loss , label=”training loss”)
plt.plot ( epochs, val_loss,label=”validation loss” )
plt.title (‘Training and validation loss’ )
plt.legend()
Test model on test data
f, axes = plt.subplots(1, 10, sharey=True,figsize=(10,10))
for i,ax in enumerate(axes.flat):
ax.axis(‘off’)
ax.imshow(X_test[i,:,:,0],cmap=”gray”)
l=[]
for i in range(10):
  x=X_test[i].reshape(1,28,28,1)
  y=model.predict(x)
  m = np.argmax(y, axis=1)
  print(m)
[7]
[2]
[1]
[0]
[4]
[1]
[4]
[9]
[5]
[9]

Generate the filter activations at the intermediate CNN layers

In [12]:
img = test_images[51].reshape(1,28,28,1)
fig = plt.figure(figsize=(5,5))
print(img.shape)
plt.imshow(img[0,:,:,0],cmap="gray")
plt.axis('off')

Display the activations at the intermediate layers

This displays the intermediate activations as the image passes through the filters and generates these feature maps

In [13]:
layer_names = ['conv2d_4', 'conv2d_5', 'conv2d_6']

layer_outputs = [layer.output for layer in model.layers if 'conv2d' in layer.name]
activation_model = Model(inputs=model.input,outputs=layer_outputs)
intermediate_activations = activation_model.predict(img)
images_per_row = 8
max_images = 8

for layer_name, layer_activation in zip(layer_names, intermediate_activations):
    print(layer_name,layer_activation.shape)
    n_features = layer_activation.shape[-1]
    print("features=",n_features)
    n_features = min(n_features, max_images)
    print(n_features)

    size = layer_activation.shape[1]
    print("size=",size)
    n_cols = n_features // images_per_row
    display_grid = np.zeros((size * n_cols, images_per_row * size))


    for col in range(n_cols):
      for row in range(images_per_row):
          channel_image = layer_activation[0,:, :, col * images_per_row + row]

          channel_image -= channel_image.mean()
          channel_image /= channel_image.std()
          channel_image *= 64
          channel_image += 128
          channel_image = np.clip(channel_image, 0, 255).astype('uint8')
          display_grid[col * size : (col + 1) * size,
                         row * size : (row + 1) * size] = channel_image
    scale = 2. / size
    plt.figure(figsize=(scale * display_grid.shape[1],
                        scale * display_grid.shape[0]))
    plt.axis('off')
    plt.title(layer_name)
    plt.grid(False)
    plt.imshow(display_grid, aspect='auto', cmap='viridis')
    
plt.show()

It can be seen that at the higher layers only abstract features of the input image are captured
# To fix the ImportError: cannot import name 'imresize' in the next cell. Run this cell. Then comment and restart and run all
#!pip install scipy==1.1.0

Visualize the pattern that the filters respond to maximally

  • Choose a loss function that maximizes the value of the CNN filter in a given layer
  • Start from a blank input image.
  • Do gradient ascent in input space. Modify input values so that the filter activates more
  • Repeat this in a loop.
In [14]:
from vis.visualization import visualize_activation, get_num_filters
from vis.utils import utils
from vis.input_modifiers import Jitter

max_filters = 24
selected_indices = []
vis_images = [[], [], [], [], []]
i = 0
selected_filters = [[0, 3, 11, 15, 16, 17, 18, 22], 
    [8, 21, 23, 25, 31, 32, 35, 41], 
    [2, 7, 11, 14, 19, 26, 35, 48]]

# Set the layers
layer_name = ['conv2d_4', 'conv2d_5', 'conv2d_6']
# Set the layer indices
layer_idx = [1,3,5]
for layer_name,layer_idx in zip(layer_name,layer_idx):


    # Visualize all filters in this layer.
    if selected_filters:
        filters = selected_filters[i]
    else:
        # Randomly select filters
        filters = sorted(np.random.permutation(get_num_filters(model.layers[layer_idx]))[:max_filters])
    selected_indices.append(filters)

    # Generate input image for each filter.
    # Loop through the selected filters in each layer and generate the activation of these filters
    for idx in filters:
        img = visualize_activation(model, layer_idx, filter_indices=idx, tv_weight=0., 
                                   input_modifiers=[Jitter(0.05)], max_iter=300) 
        vis_images[i].append(img)

    # Generate stitched image palette with 4 cols so we get 2 rows.
    stitched = utils.stitch_images(vis_images[i], cols=4)    
    plt.figure(figsize=(20, 30))
    plt.title(layer_name)
    plt.axis('off')
    stitched = stitched.reshape(1,61,127,1)
    plt.imshow(stitched[0,:,:,0])
    plt.show()
    i += 1
from vis.utils import utils
new_vis_images = [[], [], [], [], []]
i = 0
layer_name = ['conv2d_4', 'conv2d_5', 'conv2d_6']
layer_idx = [1,3,5]
for layer_name,layer_idx in zip(layer_name,layer_idx):
   
    # Generate input image for each filter.
    for j, idx in enumerate(selected_indices[i]):
        img = visualize_activation(model, layer_idx, filter_indices=idx, 
                                   seed_input=vis_images[i][j], input_modifiers=[Jitter(0.05)], max_iter=300) 
        #img = utils.draw_text(img, 'Filter {}'.format(idx))  
        new_vis_images[i].append(img)

    stitched = utils.stitch_images(new_vis_images[i], cols=4)   
    plt.figure(figsize=(20, 30))
    plt.title(layer_name)
    plt.axis('off')
    print(stitched.shape)
    stitched = stitched.reshape(1,61,127,1)
    plt.imshow(stitched[0,:,:,0])
    plt.show()
    i += 1

Visualizing Class Outputs

Here the CNN will generate the image that maximally represents the category. Each of the output represents one of the digits as can be seen below

In [16]:
from vis.utils import utils
from keras import activations
codes = '''
zero 0
one 1
two 2
three 3
four 4
five 5
six 6
seven 7
eight 8
nine 9
'''
layer_idx=10
initial = []
images = []
tuples = []
# Swap softmax with linear for better visualization
model.layers[layer_idx].activation = activations.linear
model = utils.apply_modifications(model)
for line in codes.split('\n'):
    if not line:
        continue
    name, idx = line.rsplit(' ', 1)
    idx = int(idx)
    img = visualize_activation(model, layer_idx, filter_indices=idx, 
                               tv_weight=0., max_iter=300, input_modifiers=[Jitter(0.05)])

    initial.append(img)
    tuples.append((name, idx))

i = 0
for name, idx in tuples:
    img = visualize_activation(model, layer_idx, filter_indices=idx,
                               seed_input = initial[i], max_iter=300, input_modifiers=[Jitter(0.05)])
    #img = utils.draw_text(img, name) # Unable to display text on gray scale image
    i += 1
    images.append(img)

stitched = utils.stitch_images(images, cols=4)
plt.figure(figsize=(20, 20))
plt.axis('off')
stitched = stitched.reshape(1,94,127,1)
plt.imshow(stitched[0,:,:,0])

plt.show()

In the grid below the class outputs show the MNIST digits to which output responds to maximally. We can see the ghostly outline
of digits 0 – 9. We can clearly see the outline if 0,1, 2,3,4,5 (yes, it is there!),6,7, 8 and 9. If you look at this from a little distance the digits are clearly visible. Isn’t that really cool!!


 

Conclusion:


It is really interesting to see the class outputs which show the image to which the class output responds to maximally. In the
post Applied Deep Learning – Part 4: Convolutional Neural Networks the class output show much more complicated images and is worth a look. It is really interesting to note that the model has adjusted the filter values and the weights of the fully connected network to maximally respond to the MNIST digits

References

1. Visualizing and Understanding Convolutional Networks
2. Applied Deep Learning – Part 4: Convolutional Neural Networks
3. Visualizing Intermediate Activations of a CNN trained on the MNIST Dataset
4. How convolutional neural networks see the world
5. Keras – Activation_maximization

Also see

1. Using Reinforcement Learning to solve Gridworld
2. Deep Learning from first principles in Python, R and Octave – Part 8
3. Cricketr learns new tricks : Performs fine-grained analysis of players
4. Video presentation on Machine Learning, Data Science, NLP and Big Data – Part 1
5. Big Data-2: Move into the big league:Graduate from R to SparkR
6. OpenCV: Fun with filters and convolution
7. Powershell GUI – Adding bells and whistles

To see all posts click Index of posts

Understanding Neural Style Transfer with Tensorflow and Keras

Neural Style Transfer (NST)  is a fascinating area of Deep Learning and Convolutional Neural Networks. NST is an interesting technique, in which the style from an image, known as the ‘style image’ is transferred to another image ‘content image’ and we get a third a image which is a generated image which has the content of the original image and the style of another image.

NST can be used to reimagine how famous painters like Van Gogh, Claude Monet or a Picasso would have visualised a scenery or architecture. NST uses Convolutional Neural Networks (CNNs) to achieve this artistic style transfer from one image to another. NST was originally implemented by Gati et al., in their paper Neural Algorithm of Artistic Style. Convolutional Neural Networks have been very successful in image classification image recognition et cetera. CNN networks have also been have also generated very interesting pictures using Neural Style Transfer which will be shown in this post. An interesting aspect of CNN’s is that the first couple of layers in the CNN capture basic features of the image like edges and  pixel values. But as we go deeper into the CNN, the network captures higher level features of the input image.

To get started with Neural Style transfer  we will be using the VGG19 pre-trained network. The VGG19 CNN is a compact pre-trained your network which can be used for performing the NST. However, we could have also used Resnet or InceptionV3 networks for this purpose but these are very large networks. The idea of using a network trained on a different task and applying it to a new task is called transfer learning.

What needs to be done to transfer the style from one of the image to another image. This brings us to the question – What is ‘style’? What is it that distinguishes Van Gogh’s painting or Picasso’s cubist art. Convolutional Neural Networks capture basic features in the lower layers and much more complex features in the deeper layers.  Style can be computed by taking the correlation of the feature maps in a layer L. This is my interpretation of how style is captured.  Since style  is intrinsic to  the image, it  implies that the style feature would exist across all the filters in a layer. Hence, to pick up this style we would need to get the correlation of the filters across channels of a lawyer. This is computed mathematically, using the Gram matrix which calculates the correlation of the activation of a the filter by the style image and generated image

To transfer the style from one image to the content image we need to do two parallel operations while doing forward propagation
– Compute the content loss between the source image and the generated image
– Compute the style loss between the style image and the generated image
– Finally we need to compute the total loss

In order to get transfer the style from the ‘style’ image to the ‘content ‘image resulting in a  ‘generated’  image  the total loss has to be minimised. Therefore backward propagation with gradient descent  is done to minimise the total loss comprising of the content and style loss.

Initially we make the Generated Image ‘G’ the same as the source image ‘S’

The content loss at layer ‘l’

L_{content} = 1/2 \sum_{i}^{j} ( F^{l}_{i,j} - P^{l}_{i,j})^{2}

where F^{l}_{i,j} and P^{l}_{i,j} represent the activations at layer ‘l’ in a filter i, at position ‘j’. The intuition is that the activations will be same for similar source and generated image. We need to minimise the content loss so that the generated stylized image is as close to the original image as possible. An intermediate layer of VGG19 block5_conv2 is used

The Style layers that are are used are

style_layers = [‘block1_conv1’,
‘block2_conv1’,
‘block3_conv1’,
‘block4_conv1’,
‘block5_conv1’]
To compute the Style Loss the Gram matrix needs to be computed. The Gram Matrix is computed by unrolling the filters as shown below (source: Convolutional Neural Networks by Prof Andrew Ng, Coursera). The result is a matrix of size n_{c} x n_{c} where n_{c} is the number of channels
The above diagram shows the filters of height n_{H} and width n_{W} with n_{C} channels
The contribution of layer ‘l’ to style loss is given by
L^{'}_{style} = \frac{\sum_{i}^{j} (G^{2}_{i,j} - A^l{i,j})^2}{4N^{2}_{l}M^{2}_{l}}
where G_{i,j}  and A_{i,j} are the Gram matrices of the style and generated images respectively. By minimising the distance in the gram matrices of the style and generated image we can ensure that generated image is a stylized version of the original image similar to the style image
The total loss is given by
L_{total} = \alpha L_{content} + \beta L_{style}
Back propagation with gradient descent works to minimise the content loss between the source and generated image, while the style loss tries to minimise the discrepancies in the style of the style image and generated image. Running through forward and backpropagation through several epochs successfully transfers the style from the style image to the source image.
You can check the Notebook at Neural Style Transfer

Note: The code in this notebook is largely based on the Neural Style Transfer tutorial from Tensorflow, though I may have taken some changes from other blogs. I also made a few changes to the code in this tutorial, like removing the scaling factor, or the class definition (Personally, I belong to the old school (C language) and am not much in love with the ‘self.”..All references are included below

Note: Here is a interesting thought. Could we do a Neural Style Transfer in music? Imagine Carlos Santana playing ‘Hotel California’ or Brian May style in ‘Another brick in the wall’. While our first reaction would be that it may not sound good as we are used to style of these songs, we may be surprised by a possible style transfer. This is definitely music to the ears!

 

Here are few runs from this

A) Run 1

1. Neural Style Transfer – a) Content Image – My portrait.  b) Style Image – Wassily Kadinsky Oil on canvas, 1913, Vassily Kadinsky’s composition

 

2. Result of Neural Style Transfer

 

 

2) Run 2

a) Content Image – Portrait of my parents b) Style Image –  Vincent Van Gogh’s ,Starry Night Oil on canvas 1889

 

2. Result of Neural Style Transfer

 

 

Run 3

1.  Content Image – Caesar 2 (Masai Mara- 20 Jun 2018).  Style Image – The Great Wave at Kanagawa – Katsushika Hokosai, 1826-1833

 

Screenshot 2020-04-12 at 12.40.44 PM

2. Result of Neural Style Transfer

lkg

 

 

Run 4

1.   Content Image – Junagarh Fort , Rajasthan   Sep 2016              b) Style Image – Le Pont Japonais by Claude Monet, Oil on canvas, 1920

 

 

2. Result of Neural Style Transfer

 

Neural Style Transfer is a very ingenious idea which shows that we can segregate the style of a painting and transfer to another image.

References

1. A Neural Algorithm of Artistic Style, Leon A. Gatys, Alexander S. Ecker, Matthias Bethge
2. Neural style transfer
3. Neural Style Transfer: Creating Art with Deep Learning using tf.keras and eager execution
4. Convolutional Neural Network, DeepLearning.AI Specialization, Prof Andrew Ng
5. Intuitive Guide to Neural Style Transfer

See also

1. Big Data-5: kNiFi-ing through cricket data with yorkpy
2. Cricketr adds team analytics to its repertoire
3. Cricpy performs granular analysis of players
4. My book ‘Deep Learning from first principles:Second Edition’ now on Amazon
5. Programming Zen and now – Some essential tips-2
6. The Anomaly
7. Practical Machine Learning with R and Python – Part 5
8. Literacy in India – A deepR dive
9. “Is it an animal? Is it an insect?” in Android

To see all posts click Index of posts

The mechanics of Convolutional Neural Networks in Tensorflow and Keras

Convolutional Neural Networks (CNNs), have been very popular in the last decade or so. CNNs have been used in multiple applications like image recognition, image classification, facial recognition, neural style transfer etc. CNN’s have been extremely successful in handling these kind of problems. How do they work? What makes them so successful? What is the principle behind CNN’s ?

Note: this post is based on two Coursera courses I did, namely namely Deep Learning specialisation by Prof Andrew Ng and Tensorflow Specialisation by  Laurence Moroney.

In this post I show you how CNN’s work. To understand how CNNs work, we need to understand the concept behind machine learning algorithms. If you take a simple machine learning algorithm in which you are trying to do multi-class classification using softmax or binary classification with the sigmoid function, for a set of for a set of input features against a target variable we need to create an objective function of the input features versus the target variable. Then we need to minimise this objective function, while performing gradient descent, such that the cost  is the lowest. This will give the set of weights for the different variables in the objective function.

The central problem in ML algorithms is to do feature selection, i.e.  we need to find the set of features that actually influence the target.  There are various methods for doing features selection – best fit, forward fit, backward fit, ridge and lasso regression. All these methods try to pick out the predictors that influence the output most, by making the weights of the other features close to zero. Please look at my post – Practical Machine Learning in R and Python – Part 3, where I show you the different methods for doing features selection.

In image classification or Image recognition we need to find the important features in the image. How do we do that? Many years back, have played around with OpenCV.  While working with OpenCV I came across are numerous filters like the Sobel ,the Laplacian, Canny, Gaussian filter et cetera which can be used to identify key features of the image. For example the Canny filter feature can be used for edge detection, Gaussian for smoothing, Sobel for determining the derivative and we have other filters for detecting vertical or horizontal edges. Take a look at my post Computer Vision: Ramblings on derivatives, histograms and contours So for handling images we need to apply these filters to pick  out the key features of the image namely the edges and other features. So rather than using the entire image’s pixels against the target class we can pick out the features from the image and use that as predictors of the target output.

Note: that in Convolutional Neural Network, fixed filter values like the those shown above  are not used directly. Rather the filter values are learned through back propagation and gradient descent as shown below.

In CNNs the filter values are considered to be weights which are then learned and updated in each forward/backward propagation cycle much like the way a fully connected Deep Learning Network learns the weights of the network.

Here is a short derivation of the most important parts of how a CNNs work

The convolution of a filter F with the input X can be represented as.

 

 

Convolving we get

 

This the forward propagation as it passes through a non-linear function like Relu

 

To go through back propagation we need to compute the \partial L  at every node of Convolutional Neural network

 

The loss with respect to the output is \partial L/\partial O. \partial O/\partial X & \partial O/\partial F are the local derivatives

We need these local derivatives because we can learn the filter values using gradient descent

where \alpha is the learning rate. Also \partial L/\partial X is the loss which is back propagated to the previous layers. You can see the detailed derivation of back propagation in my post Deep Learning from first principles in Python, R and Octave – Part 3 in a L-layer, multi-unit Deep Learning network.

In the fully connected layers the weights associated with each connection is computed in every cycle of forward and backward propagation using gradient descent. Similarly, the filter values are also computed and updated in each forward and backward propagation cycle. This is done so as to minimize the loss at the output layer.

By using the chain rule and simplifying the back propagation for the Convolutional layers we get these 2 equations. The first equation is used to learn the filter values and the second is used pass the loss to layers before

(for the detailed derivation see Convolutions and Backpropagations

An important aspect of performing convolutions is to reduce the size of  the flattened image that is passed into the fully connected DL network. Successively convolving with 2D filters and doing a max pooling helps to reduce the size of the features that we can use for learning the images. Convolutions also enable a sparsity of connections  as you can see in the diagram below. In the LeNet-5 Convolution Neural Network of Yann Le Cunn, successive convolutions reduce the image size from 28 x 28=784 to 120 flattened values.

Here is an interesting Deep Learning problem. Convolutions help in picking out important features of images and help in image classification/ detection. What would be its equivalent if we wanted to identify the Carnatic ragam of a song? A Carnatic ragam is roughly similar to Western scales (major, natural, melodic, blues) with all its modes Lydian, Aeolion, Phyrgian etc. Except in the case of the ragams, it is more nuanced, complex and involved. Personally, I can rarely identify a ragam on which a carnatic song is based (I am tone deaf when it comes to identifying ragams). I have come to understand that each Carnatic ragam has its own character, which is made up of several melodic phrases which are unique to that flavor of a ragam. What operation like convolution would be needed so that we can pick out these unique phrases in a Carnatic ragam? Of course, we would need to use it in Recurrent Neural Networks with LSTMs as a song is a time sequence of notes to identify sequences. Nevertheless, if there was some operation with which we can pick up the distinct, unique phrases from a song and then run it through a classifier, maybe we would be able to identify the ragam of the song.

Below I implement 3 simple CNN using the Dogs vs Cats Dataset from Kaggle. The first CNN uses regular Convolutions a Fully connected network to classify the images. The second approach uses Image Augmentation. For some reason, I did not get a better performance with Image Augumentation. Thirdly I use the pre-trained Inception v3 network.

 

1. Basic Convolutional Neural Network in Tensorflow & Keras

You can view the Colab notebook here – Cats_vs_dogs_1.ipynb

Here some important parts of the notebook

Create CNN Model

  • Use 3 Convolution + Max pooling layers with 32,64 and 128 filters respectively
  • Flatten the data
  • Have 2 Fully connected layers with 128, 512 neurons with relu activation
  • Use sigmoid for binary classification
In [0]:
model = tf.keras.models.Sequential([
    tf.keras.layers.Conv2D(32,(3,3),activation='relu',input_shape=(150,150,3)),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Conv2D(64,(3,3),activation='relu'),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Conv2D(128,(3,3),activation='relu'),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Flatten(),
    tf.keras.layers.Dense(128,activation='relu'),
    tf.keras.layers.Dense(512,activation='relu'),
    tf.keras.layers.Dense(1,activation='sigmoid')
])

Print model summary

In [13]:
model.summary()
Model: "sequential"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d (Conv2D)              (None, 148, 148, 32)      896       
_________________________________________________________________
max_pooling2d (MaxPooling2D) (None, 74, 74, 32)        0         
_________________________________________________________________
conv2d_1 (Conv2D)            (None, 72, 72, 64)        18496     
_________________________________________________________________
max_pooling2d_1 (MaxPooling2 (None, 36, 36, 64)        0         
_________________________________________________________________
conv2d_2 (Conv2D)            (None, 34, 34, 128)       73856     
_________________________________________________________________
max_pooling2d_2 (MaxPooling2 (None, 17, 17, 128)       0         
_________________________________________________________________
flatten (Flatten)            (None, 36992)             0         
_________________________________________________________________
dense (Dense)                (None, 128)               4735104   
_________________________________________________________________
dense_1 (Dense)              (None, 512)               66048     
_________________________________________________________________
dense_2 (Dense)              (None, 1)                 513       
=================================================================
Total params: 4,894,913
Trainable params: 4,894,913
Non-trainable params: 0
_________________________________________________________________

Use the Adam Optimizer with binary cross entropy

model.compile(optimizer='adam',
             loss='binary_crossentropy',
             metrics=['accuracy'])

Perform Gradient Descent

  • Do Gradient Descent for 15 epochs
history=model.fit(train_generator,
                 validation_data=validation_generator,
                 steps_per_epoch=100,
                 epochs=15,
                 validation_steps=50,
                 verbose=2)
Epoch 1/15
100/100 - 13s - loss: 0.6821 - accuracy: 0.5425 - val_loss: 0.6484 - val_accuracy: 0.6131
Epoch 2/15
100/100 - 13s - loss: 0.6227 - accuracy: 0.6456 - val_loss: 0.6161 - val_accuracy: 0.6394
Epoch 3/15
100/100 - 13s - loss: 0.5975 - accuracy: 0.6719 - val_loss: 0.5558 - val_accuracy: 0.7206
Epoch 4/15
100/100 - 13s - loss: 0.5480 - accuracy: 0.7241 - val_loss: 0.5431 - val_accuracy: 0.7138
Epoch 5/15
100/100 - 13s - loss: 0.5182 - accuracy: 0.7447 - val_loss: 0.4839 - val_accuracy: 0.7606
Epoch 6/15
100/100 - 13s - loss: 0.4773 - accuracy: 0.7781 - val_loss: 0.5029 - val_accuracy: 0.7506
Epoch 7/15
100/100 - 13s - loss: 0.4466 - accuracy: 0.7972 - val_loss: 0.4573 - val_accuracy: 0.7912
Epoch 8/15
100/100 - 13s - loss: 0.4395 - accuracy: 0.7997 - val_loss: 0.4252 - val_accuracy: 0.8119
Epoch 9/15
100/100 - 13s - loss: 0.4314 - accuracy: 0.8019 - val_loss: 0.4931 - val_accuracy: 0.7481
Epoch 10/15
100/100 - 13s - loss: 0.4309 - accuracy: 0.7969 - val_loss: 0.4203 - val_accuracy: 0.8109
Epoch 11/15
100/100 - 13s - loss: 0.4329 - accuracy: 0.7916 - val_loss: 0.4189 - val_accuracy: 0.8069
Epoch 12/15
100/100 - 13s - loss: 0.4248 - accuracy: 0.8050 - val_loss: 0.4476 - val_accuracy: 0.7925
Epoch 13/15
100/100 - 13s - loss: 0.3868 - accuracy: 0.8306 - val_loss: 0.3900 - val_accuracy: 0.8236
Epoch 14/15
100/100 - 13s - loss: 0.3710 - accuracy: 0.8328 - val_loss: 0.4520 - val_accuracy: 0.7900
Epoch 15/15
100/100 - 13s - loss: 0.3654 - accuracy: 0.8353 - val_loss: 0.3999 - val_accuracy: 0.8100

 

 

 

 

 

 

Plot results

    • Plot training and validation accuracy

 

  • Plot training and validation loss

 

 

 

 

 

 

#-----------------------------------------------------------
# Retrieve a list of list results on training and test data
# sets for each training epoch
#-----------------------------------------------------------
acc      = history.history[     'accuracy' ]
val_acc  = history.history[ 'val_accuracy' ]
loss     = history.history[    'loss' ]
val_loss = history.history['val_loss' ]

epochs   = range(len(acc)) # Get number of epochs

#------------------------------------------------
# Plot training and validation accuracy per epoch
#------------------------------------------------
plt.plot  ( epochs,     acc,label="training accuracy" )
plt.plot  ( epochs, val_acc, label='validation acuracy' )
plt.title ('Training and validation accuracy')
plt.legend()

plt.figure()

#------------------------------------------------
# Plot training and validation loss per epoch
#------------------------------------------------
plt.plot  ( epochs,     loss , label="training loss")
plt.plot  ( epochs, val_loss,label="validation loss" )
plt.title ('Training and validation loss'   )
plt.legend()



 

2. CNN with Image Augmentation

You can check the Cats_vs_Dogs_2.ipynb

Including the important parts of this implementation below

Use Image Augumentation

Use Image Augumentation to improve performance

  • Use the same model parameters as before
  • Perform the following image augmentation
    • width, height shift
    • shear and zoom

    Note: Adding rotation made the performance worse

import tensorflow as tf
from tensorflow import keras
from tensorflow.keras.optimizers import RMSprop
from tensorflow.keras.preprocessing.image import ImageDataGenerator
model = tf.keras.models.Sequential([
    tf.keras.layers.Conv2D(32,(3,3),activation='relu',input_shape=(150,150,3)),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Conv2D(64,(3,3),activation='relu'),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Conv2D(128,(3,3),activation='relu'),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Flatten(),
    tf.keras.layers.Dense(128,activation='relu'),
    tf.keras.layers.Dense(512,activation='relu'),
    tf.keras.layers.Dense(1,activation='sigmoid')
])


train_datagen = ImageDataGenerator(
      rescale=1./255,
      #rotation_range=90,
      width_shift_range=0.2,
      height_shift_range=0.2,
      shear_range=0.2,
      zoom_range=0.2)
      #horizontal_flip=True,
      #fill_mode='nearest')

validation_datagen = ImageDataGenerator(rescale=1./255)
#
train_generator = train_datagen.flow_from_directory(train_dir,
                                                    batch_size=32,
                                                    class_mode='binary',
                                                    target_size=(150, 150))     
# --------------------
# Flow validation images in batches of 20 using test_datagen generator
# --------------------
validation_generator =  validation_datagen.flow_from_directory(validation_dir,
                                                         batch_size=32,
                                                         class_mode  = 'binary',
                                                         target_size = (150, 150))

# Use Adam Optmizer 
model.compile(optimizer='adam',
             loss='binary_crossentropy',
             metrics=['accuracy'])
Found 20000 images belonging to 2 classes.
Found 5000 images belonging to 2 classes.

Perform Gradient Descent

history=model.fit(train_generator,
                 validation_data=validation_generator,
                 steps_per_epoch=100,
                 epochs=15,
                 validation_steps=50,
                 verbose=2)
Epoch 1/15
100/100 - 27s - loss: 0.5716 - accuracy: 0.6922 - val_loss: 0.4843 - val_accuracy: 0.7744
Epoch 2/15
100/100 - 27s - loss: 0.5575 - accuracy: 0.7084 - val_loss: 0.4683 - val_accuracy: 0.7750
Epoch 3/15
100/100 - 26s - loss: 0.5452 - accuracy: 0.7228 - val_loss: 0.4856 - val_accuracy: 0.7665
Epoch 4/15
100/100 - 27s - loss: 0.5294 - accuracy: 0.7347 - val_loss: 0.4654 - val_accuracy: 0.7812
Epoch 5/15
100/100 - 27s - loss: 0.5352 - accuracy: 0.7350 - val_loss: 0.4557 - val_accuracy: 0.7981
Epoch 6/15
100/100 - 26s - loss: 0.5136 - accuracy: 0.7453 - val_loss: 0.4964 - val_accuracy: 0.7621
Epoch 7/15
100/100 - 27s - loss: 0.5249 - accuracy: 0.7334 - val_loss: 0.4959 - val_accuracy: 0.7556
Epoch 8/15
100/100 - 26s - loss: 0.5035 - accuracy: 0.7497 - val_loss: 0.4555 - val_accuracy: 0.7969
Epoch 9/15
100/100 - 26s - loss: 0.5024 - accuracy: 0.7487 - val_loss: 0.4675 - val_accuracy: 0.7728
Epoch 10/15
100/100 - 27s - loss: 0.5015 - accuracy: 0.7500 - val_loss: 0.4276 - val_accuracy: 0.8075
Epoch 11/15
100/100 - 26s - loss: 0.5002 - accuracy: 0.7581 - val_loss: 0.4193 - val_accuracy: 0.8131
Epoch 12/15
100/100 - 27s - loss: 0.4733 - accuracy: 0.7706 - val_loss: 0.5209 - val_accuracy: 0.7398
Epoch 13/15
100/100 - 27s - loss: 0.4999 - accuracy: 0.7538 - val_loss: 0.4109 - val_accuracy: 0.8075
Epoch 14/15
100/100 - 27s - loss: 0.4550 - accuracy: 0.7859 - val_loss: 0.3770 - val_accuracy: 0.8288
Epoch 15/15
100/100 - 26s - loss: 0.4688 - accuracy: 0.7688 - val_loss: 0.4764 - val_accuracy: 0.7786

Plot results

  • Plot training and validation accuracy
  • Plot training and validation loss
In [15]:
import matplotlib.pyplot as plt
#-----------------------------------------------------------
# Retrieve a list of list results on training and test data
# sets for each training epoch
#-----------------------------------------------------------
acc      = history.history[     'accuracy' ]
val_acc  = history.history[ 'val_accuracy' ]
loss     = history.history[    'loss' ]
val_loss = history.history['val_loss' ]

epochs   = range(len(acc)) # Get number of epochs

#------------------------------------------------
# Plot training and validation accuracy per epoch
#------------------------------------------------
plt.plot  ( epochs,     acc,label="training accuracy" )
plt.plot  ( epochs, val_acc, label='validation acuracy' )
plt.title ('Training and validation accuracy')
plt.legend()

plt.figure()

#------------------------------------------------
# Plot training and validation loss per epoch
#------------------------------------------------
plt.plot  ( epochs,     loss , label="training loss")
plt.plot  ( epochs, val_loss,label="validation loss" )
plt.title ('Training and validation loss'   )
plt.legend()
 


Implementation using Inception Network V3

The implementation is in the Colab notebook Cats_vs_Dog_3.ipynb

This is implemented as below

Use Inception V3

import os

from tensorflow.keras import layers
from tensorflow.keras import Model

  
from tensorflow.keras.applications.inception_v3 import InceptionV3
pre_trained_model = InceptionV3(input_shape = (150, 150, 3), 
                                include_top = False, 
                                weights = 'imagenet')


for layer in pre_trained_model.layers:
  layer.trainable = False
  
# pre_trained_model.summary()

last_layer = pre_trained_model.get_layer('mixed7')
print('last layer output shape: ', last_layer.output_shape)
last_output = last_layer.output
Downloading data from https://storage.googleapis.com/tensorflow/keras-applications/inception_v3/inception_v3_weights_tf_dim_ordering_tf_kernels_notop.h5
87916544/87910968 [==============================] - 1s 0us/step
last layer output shape:  (None, 7, 7, 768)

Use Layer 7 of Inception Network

  • Use Image Augumentation
  • Use Adam Optimizer
In [0]:
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras.optimizers import RMSprop
from tensorflow.keras.preprocessing.image import ImageDataGenerator
# Flatten the output layer to 1 dimension
x = layers.Flatten()(last_output)
# Add a fully connected layer with 1,024 hidden units and ReLU activation
x = layers.Dense(1024, activation='relu')(x)
# Add a dropout rate of 0.2
x = layers.Dropout(0.2)(x)                  
# Add a final sigmoid layer for classification
x = layers.Dense  (1, activation='sigmoid')(x)           

model = Model( pre_trained_model.input, x) 
#train_datagen = ImageDataGenerator( rescale = 1.0/255. )
#validation_datagen = ImageDataGenerator( rescale = 1.0/255. )

train_datagen = ImageDataGenerator(
      rescale=1./255,
      #rotation_range=90,
      width_shift_range=0.2,
      height_shift_range=0.2,
      shear_range=0.2,
      zoom_range=0.2)
      #horizontal_flip=True,
      #fill_mode='nearest')

validation_datagen = ImageDataGenerator(rescale=1./255)
#
train_generator = train_datagen.flow_from_directory(train_dir,
                                                    batch_size=32,
                                                    class_mode='binary',
                                                    target_size=(150, 150))     
# --------------------
# Flow validation images in batches of 20 using test_datagen generator
# --------------------
validation_generator =  validation_datagen.flow_from_directory(validation_dir,
                                                         batch_size=32,
                                                         class_mode  = 'binary',
                                                         target_size = (150, 150))


model.compile(optimizer='adam',
             loss='binary_crossentropy',
             metrics=['accuracy'])
Found 20000 images belonging to 2 classes.
Found 5000 images belonging to 2 classes.

Fit model

history=model.fit(train_generator,
                 validation_data=validation_generator,
                 steps_per_epoch=100,
                 epochs=15,
                 validation_steps=50,
                 verbose=2)
Epoch 1/15
100/100 - 31s - loss: 0.5961 - accuracy: 0.8909 - val_loss: 0.1919 - val_accuracy: 0.9456
Epoch 2/15
100/100 - 30s - loss: 0.2002 - accuracy: 0.9259 - val_loss: 0.1025 - val_accuracy: 0.9550
Epoch 3/15
100/100 - 30s - loss: 0.1618 - accuracy: 0.9366 - val_loss: 0.0920 - val_accuracy: 0.9581
Epoch 4/15
100/100 - 29s - loss: 0.1442 - accuracy: 0.9381 - val_loss: 0.0960 - val_accuracy: 0.9600
Epoch 5/15
100/100 - 30s - loss: 0.1402 - accuracy: 0.9381 - val_loss: 0.0703 - val_accuracy: 0.9794
Epoch 6/15
100/100 - 30s - loss: 0.1437 - accuracy: 0.9413 - val_loss: 0.1090 - val_accuracy: 0.9531
Epoch 7/15
100/100 - 30s - loss: 0.1325 - accuracy: 0.9428 - val_loss: 0.0756 - val_accuracy: 0.9670
Epoch 8/15
100/100 - 29s - loss: 0.1341 - accuracy: 0.9491 - val_loss: 0.0625 - val_accuracy: 0.9737
Epoch 9/15
100/100 - 29s - loss: 0.1186 - accuracy: 0.9513 - val_loss: 0.0934 - val_accuracy: 0.9581
Epoch 10/15
100/100 - 29s - loss: 0.1171 - accuracy: 0.9513 - val_loss: 0.0642 - val_accuracy: 0.9727
Epoch 11/15
100/100 - 29s - loss: 0.1018 - accuracy: 0.9591 - val_loss: 0.0930 - val_accuracy: 0.9606
Epoch 12/15
100/100 - 29s - loss: 0.1190 - accuracy: 0.9541 - val_loss: 0.0737 - val_accuracy: 0.9719
Epoch 13/15
100/100 - 29s - loss: 0.1223 - accuracy: 0.9494 - val_loss: 0.0740 - val_accuracy: 0.9695
Epoch 14/15
100/100 - 29s - loss: 0.1158 - accuracy: 0.9516 - val_loss: 0.0659 - val_accuracy: 0.9744
Epoch 15/15
100/100 - 29s - loss: 0.1168 - accuracy: 0.9591 - val_loss: 0.0788 - val_accuracy: 0.9669

Plot results

  • Plot training and validation accuracy
  • Plot training and validation loss
In [14]:
import matplotlib.pyplot as plt
#-----------------------------------------------------------
# Retrieve a list of list results on training and test data
# sets for each training epoch
#-----------------------------------------------------------
acc      = history.history[     'accuracy' ]
val_acc  = history.history[ 'val_accuracy' ]
loss     = history.history[    'loss' ]
val_loss = history.history['val_loss' ]

epochs   = range(len(acc)) # Get number of epochs

#------------------------------------------------
# Plot training and validation accuracy per epoch
#------------------------------------------------
plt.plot  ( epochs,     acc,label="training accuracy" )
plt.plot  ( epochs, val_acc, label='validation acuracy' )
plt.title ('Training and validation accuracy')
plt.legend()

plt.figure()

#------------------------------------------------
# Plot training and validation loss per epoch
#------------------------------------------------
plt.plot  ( epochs,     loss , label="training loss")
plt.plot  ( epochs, val_loss,label="validation loss" )
plt.title ('Training and validation loss'   )
plt.legend()

 

I intend to do some interesting stuff with Convolutional Neural Networks.

Watch this space!

See also
1. Architecting a cloud based IP Multimedia System (IMS)
2. Exploring Quantum Gate operations with QCSimulator
3. Big Data 6: The T20 Dance of Apache NiFi and yorkpy
4. The Many Faces of Latency
5. The Clash of the Titans in Test and ODI cricket

To see all posts click Index of posts

Getting started with Tensorflow, Keras in Python and R

The Pale Blue Dot

“From this distant vantage point, the Earth might not seem of any particular interest. But for us, it’s different. Consider again that dot. That’s here, that’s home, that’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every “superstar,” every “supreme leader,” every saint and sinner in the history of our species lived there—on the mote of dust suspended in a sunbeam.”

Carl Sagan

Tensorflow and Keras are Deep Learning frameworks that really simplify a lot of things to the user. If you are familiar with Machine Learning and Deep Learning concepts then Tensorflow and Keras are really a playground to realize your ideas.  In this post I show how you can get started with Tensorflow in both Python and R

 

Tensorflow in Python

For tensorflow in Python, I found Google’s Colab an ideal environment for running your Deep Learning code. This is an Google’s research project  where you can execute your code  on GPUs, TPUs etc

Tensorflow in R (RStudio)

To execute tensorflow in R (RStudio) you need to install tensorflow and keras as shown below
In this post I show how to get started with Tensorflow and Keras in R.

# Install Tensorflow in RStudio
#install_tensorflow()
# Install Keras
#install_packages("keras")
library(tensorflow)
libary(keras)

This post takes 3 different Machine Learning problems and uses the
Tensorflow/Keras framework to solve it

Note:
You can view the Google Colab notebook at Tensorflow in Python
The RMarkdown file has been published at RPubs and can be accessed
at Getting started with Tensorflow in R

Checkout my book ‘Deep Learning from first principles: Second Edition – In vectorized Python, R and Octave’. My book starts with the implementation of a simple 2-layer Neural Network and works its way to a generic L-Layer Deep Learning Network, with all the bells and whistles. The derivations have been discussed in detail. The code has been extensively commented and included in its entirety in the Appendix sections. My book is available on Amazon as paperback ($14.99) and in kindle version($9.99/Rs449).

1. Multivariate regression with Tensorflow – Python

This code performs multivariate regression using Tensorflow and keras on the advent of Parkinson disease through sound recordings see Parkinson Speech Dataset with Multiple Types of Sound Recordings Data Set . The clinician’s motorUPDRS score has to be predicted from the set of features

In [0]:
# Import tensorflow
import tensorflow as tf
from tensorflow import keras
In [2]:
#Get the data rom the UCI Machine Learning repository
dataset = keras.utils.get_file("parkinsons_updrs.data", "https://archive.ics.uci.edu/ml/machine-learning-databases/parkinsons/telemonitoring/parkinsons_updrs.data")
Downloading data from https://archive.ics.uci.edu/ml/machine-learning-databases/parkinsons/telemonitoring/parkinsons_updrs.data
917504/911261 [==============================] - 0s 0us/step
In [3]:
# Read the CSV file 
import pandas as pd
parkinsons = pd.read_csv(dataset, na_values = "?", comment='\t',
                      sep=",", skipinitialspace=True)
print(parkinsons.shape)
print(parkinsons.columns)
#Check if there are any NAs in the rows
parkinsons.isna().sum()
(5875, 22)
Index(['subject#', 'age', 'sex', 'test_time', 'motor_UPDRS', 'total_UPDRS',
       'Jitter(%)', 'Jitter(Abs)', 'Jitter:RAP', 'Jitter:PPQ5', 'Jitter:DDP',
       'Shimmer', 'Shimmer(dB)', 'Shimmer:APQ3', 'Shimmer:APQ5',
       'Shimmer:APQ11', 'Shimmer:DDA', 'NHR', 'HNR', 'RPDE', 'DFA', 'PPE'],
      dtype='object')
Out[3]:
subject#         0
age              0
sex              0
test_time        0
motor_UPDRS      0
total_UPDRS      0
Jitter(%)        0
Jitter(Abs)      0
Jitter:RAP       0
Jitter:PPQ5      0
Jitter:DDP       0
Shimmer          0
Shimmer(dB)      0
Shimmer:APQ3     0
Shimmer:APQ5     0
Shimmer:APQ11    0
Shimmer:DDA      0
NHR              0
HNR              0
RPDE             0
DFA              0
PPE              0
dtype: int64
Note: To see how to create dummy variables see my post Practical Machine Learning with R and Python – Part 2
In [4]:
# Drop the columns subject number as it is not relevant
parkinsons1=parkinsons.drop(['subject#'],axis=1)

# Create dummy variables for sex (M/F)
parkinsons2=pd.get_dummies(parkinsons1,columns=['sex'])
parkinsons2.head()

Out[4]
age test_time motor_UPDRS total_UPDRS Jitter(%) Jitter(Abs) Jitter:RAP Jitter:PPQ5 Jitter:DDP Shimmer Shimmer(dB) Shimmer:APQ3 Shimmer:APQ5 Shimmer:APQ11 Shimmer:DDA NHR HNR RPDE DFA PPE sex_0 sex_1
0 72 5.6431 28.199 34.398 0.00662 0.000034 0.00401 0.00317 0.01204 0.02565 0.230 0.01438 0.01309 0.01662 0.04314 0.014290 21.640 0.41888 0.54842 0.16006 1 0
1 72 12.6660 28.447 34.894 0.00300 0.000017 0.00132 0.00150 0.00395 0.02024 0.179 0.00994 0.01072 0.01689 0.02982 0.011112 27.183 0.43493 0.56477 0.10810 1 0
2 72 19.6810 28.695 35.389 0.00481 0.000025 0.00205 0.00208 0.00616 0.01675 0.181 0.00734 0.00844 0.01458 0.02202 0.020220 23.047 0.46222 0.54405 0.21014 1 0
3 72 25.6470 28.905 35.810 0.00528 0.000027 0.00191 0.00264 0.00573 0.02309 0.327 0.01106 0.01265 0.01963 0.03317 0.027837 24.445 0.48730 0.57794 0.33277 1 0
4 72 33.6420 29.187 36.375 0.00335 0.000020 0.00093 0.00130 0.00278 0.01703 0.176 0.00679 0.00929 0.01819 0.02036 0.011625 26.126 0.47188 0.56122 0.19361 1 0

# Create a training and test data set with 80%/20%
train_dataset = parkinsons2.sample(frac=0.8,random_state=0)
test_dataset = parkinsons2.drop(train_dataset.index)

# Select columns
train_dataset1= train_dataset[['age', 'test_time', 'Jitter(%)', 'Jitter(Abs)',
       'Jitter:RAP', 'Jitter:PPQ5', 'Jitter:DDP', 'Shimmer', 'Shimmer(dB)',
       'Shimmer:APQ3', 'Shimmer:APQ5', 'Shimmer:APQ11', 'Shimmer:DDA', 'NHR',
       'HNR', 'RPDE', 'DFA', 'PPE', 'sex_0', 'sex_1']]
test_dataset1= test_dataset[['age','test_time', 'Jitter(%)', 'Jitter(Abs)',
       'Jitter:RAP', 'Jitter:PPQ5', 'Jitter:DDP', 'Shimmer', 'Shimmer(dB)',
       'Shimmer:APQ3', 'Shimmer:APQ5', 'Shimmer:APQ11', 'Shimmer:DDA', 'NHR',
       'HNR', 'RPDE', 'DFA', 'PPE', 'sex_0', 'sex_1']]
In [7]:
# Generate the statistics of the columns for use in normalization of the data
train_stats = train_dataset1.describe()
train_stats = train_stats.transpose()
train_stats
Out[7]:
count mean std min 25% 50% 75% max
age 4700.0 64.792766 8.870401 36.000000 58.000000 65.000000 72.000000 85.000000
test_time 4700.0 93.399490 53.630411 -4.262500 46.852250 93.405000 139.367500 215.490000
Jitter(%) 4700.0 0.006136 0.005612 0.000830 0.003560 0.004900 0.006770 0.099990
Jitter(Abs) 4700.0 0.000044 0.000036 0.000002 0.000022 0.000034 0.000053 0.000396
Jitter:RAP 4700.0 0.002969 0.003089 0.000330 0.001570 0.002235 0.003260 0.057540
Jitter:PPQ5 4700.0 0.003271 0.003760 0.000430 0.001810 0.002480 0.003460 0.069560
Jitter:DDP 4700.0 0.008908 0.009267 0.000980 0.004710 0.006705 0.009790 0.172630
Shimmer 4700.0 0.033992 0.025922 0.003060 0.019020 0.027385 0.039810 0.268630
Shimmer(dB) 4700.0 0.310487 0.231016 0.026000 0.175000 0.251000 0.363250 2.107000
Shimmer:APQ3 4700.0 0.017125 0.013275 0.001610 0.009190 0.013615 0.020562 0.162670
Shimmer:APQ5 4700.0 0.020151 0.016848 0.001940 0.010750 0.015785 0.023733 0.167020
Shimmer:APQ11 4700.0 0.027508 0.020270 0.002490 0.015630 0.022685 0.032713 0.275460
Shimmer:DDA 4700.0 0.051375 0.039826 0.004840 0.027567 0.040845 0.061683 0.488020
NHR 4700.0 0.032116 0.060206 0.000304 0.010827 0.018403 0.031452 0.748260
HNR 4700.0 21.704631 4.288853 1.659000 19.447750 21.973000 24.445250 37.187000
RPDE 4700.0 0.542549 0.100212 0.151020 0.471235 0.543490 0.614335 0.966080
DFA 4700.0 0.653015 0.070446 0.514040 0.596470 0.643285 0.710618 0.865600
PPE 4700.0 0.219559 0.091506 0.021983 0.156470 0.205340 0.264017 0.731730
sex_0 4700.0 0.681489 0.465948 0.000000 0.000000 1.000000 1.000000 1.000000
sex_1 4700.0 0.318511 0.465948 0.000000 0.000000 0.000000 1.000000 1.000000
In [0]:
# Create the target variable
train_labels = train_dataset.pop('motor_UPDRS')
test_labels = test_dataset.pop('motor_UPDRS')
In [0]:
# Normalize the data by subtracting the mean and dividing by the standard deviation
def normalize(x):
  return (x - train_stats['mean']) / train_stats['std']

# Create normalized training and test data
normalized_train_data = normalize(train_dataset1)
normalized_test_data = normalize(test_dataset1)
In [0]:
# Create a Deep Learning model with keras
model = tf.keras.Sequential([
    keras.layers.Dense(6, activation=tf.nn.relu, input_shape=[len(train_dataset1.keys())]),
    keras.layers.Dense(9, activation=tf.nn.relu),
    keras.layers.Dense(6,activation=tf.nn.relu),
    keras.layers.Dense(1)
  ])

# Use the Adam optimizer with a learning rate of 0.01
optimizer=keras.optimizers.Adam(lr=.01, beta_1=0.9, beta_2=0.999, epsilon=None, decay=0.0, amsgrad=False)

# Set the metrics required to be Mean Absolute Error and Mean Squared Error.For regression, the loss is mean_squared_error
model.compile(loss='mean_squared_error',
                optimizer=optimizer,
                metrics=['mean_absolute_error', 'mean_squared_error'])
In [0]:
# Create a model
history=model.fit(
  normalized_train_data, train_labels,
  epochs=1000, validation_data = (normalized_test_data,test_labels), verbose=0)
In [26]:
hist = pd.DataFrame(history.history)
hist['epoch'] = history.epoch
hist.tail()
Out[26]:
loss mean_absolute_error mean_squared_error val_loss val_mean_absolute_error val_mean_squared_error epoch
995 15.773989 2.936990 15.773988 16.980803 3.028168 16.980803 995
996 15.238623 2.873420 15.238622 17.458752 3.101033 17.458752 996
997 15.437594 2.895500 15.437593 16.926016 2.971508 16.926018 997
998 15.867891 2.943521 15.867892 16.950249 2.985036 16.950249 998
999 15.846878 2.938914 15.846880 17.095623 3.014504 17.095625 999
In [30]:
def plot_history(history):
  hist = pd.DataFrame(history.history)
  hist['epoch'] = history.epoch

  plt.figure()
  plt.xlabel('Epoch')
  plt.ylabel('Mean Abs Error')
  plt.plot(hist['epoch'], hist['mean_absolute_error'],
           label='Train Error')
  plt.plot(hist['epoch'], hist['val_mean_absolute_error'],
           label = 'Val Error')
  plt.ylim([2,5])
  plt.legend()

  plt.figure()
  plt.xlabel('Epoch')
  plt.ylabel('Mean Square Error ')
  plt.plot(hist['epoch'], hist['mean_squared_error'],
           label='Train Error')
  plt.plot(hist['epoch'], hist['val_mean_squared_error'],
           label = 'Val Error')
  plt.ylim([10,40])
  plt.legend()
  plt.show()


plot_history(history)

Observation

It can be seen that the mean absolute error is on an average about +/- 4.0. The validation error also is about the same. This can be reduced by playing around with the hyperparamaters and increasing the number of iterations

1a. Multivariate Regression in Tensorflow – R

# Install Tensorflow in RStudio
#install_tensorflow()
# Install Keras
#install_packages("keras")
library(tensorflow)
library(keras)
library(dplyr)
library(dummies)
## dummies-1.5.6 provided by Decision Patterns
library(tensorflow)
library(keras)

Multivariate regression

This code performs multivariate regression using Tensorflow and keras on the advent of Parkinson disease through sound recordings see Parkinson Speech Dataset with Multiple Types of Sound Recordings Data Set. The clinician’s motorUPDRS score has to be predicted from the set of features.

Read the data

# Download the Parkinson's data from UCI Machine Learning repository
dataset <- read.csv("https://archive.ics.uci.edu/ml/machine-learning-databases/parkinsons/telemonitoring/parkinsons_updrs.data")

# Set the column names
names(dataset) <- c("subject","age", "sex", "test_time","motor_UPDRS","total_UPDRS","Jitter","Jitter.Abs",
                 "Jitter.RAP","Jitter.PPQ5","Jitter.DDP","Shimmer", "Shimmer.dB", "Shimmer.APQ3",
                 "Shimmer.APQ5","Shimmer.APQ11","Shimmer.DDA", "NHR","HNR", "RPDE", "DFA","PPE")

# Remove the column 'subject' as it is not relevant to analysis
dataset1 <- subset(dataset, select = -c(subject))

# Make the column 'sex' as a factor for using dummies
dataset1$sex=as.factor(dataset1$sex)
# Add dummy variables for categorical cariable 'sex'
dataset2 <- dummy.data.frame(dataset1, sep = ".")
## Warning in model.matrix.default(~x - 1, model.frame(~x - 1), contrasts =
## FALSE): non-list contrasts argument ignored
dataset3 <- na.omit(dataset2)

Split the data as training and test in 80/20

## Split data 80% training and 20% test
sample_size <- floor(0.8 * nrow(dataset3))

## set the seed to make your partition reproducible
set.seed(12)
train_index <- sample(seq_len(nrow(dataset3)), size = sample_size)

train_dataset <- dataset3[train_index, ]
test_dataset <- dataset3[-train_index, ]

train_data <- train_dataset %>% select(sex.0,sex.1,age, test_time,Jitter,Jitter.Abs,Jitter.PPQ5,Jitter.DDP,
                              Shimmer, Shimmer.dB,Shimmer.APQ3,Shimmer.APQ11,
                              Shimmer.DDA,NHR,HNR,RPDE,DFA,PPE)

train_labels <- select(train_dataset,motor_UPDRS)
test_data <- test_dataset %>% select(sex.0,sex.1,age, test_time,Jitter,Jitter.Abs,Jitter.PPQ5,Jitter.DDP,
                              Shimmer, Shimmer.dB,Shimmer.APQ3,Shimmer.APQ11,
                              Shimmer.DDA,NHR,HNR,RPDE,DFA,PPE)
test_labels <- select(test_dataset,motor_UPDRS)

Normalize the data

 # Normalize the data by subtracting the mean and dividing by the standard deviation
normalize<-function(x) {
  y<-(x - mean(x)) / sd(x)
  return(y)
}

normalized_train_data <-apply(train_data,2,normalize)
# Convert to matrix
train_labels <- as.matrix(train_labels)
normalized_test_data <- apply(test_data,2,normalize)
test_labels <- as.matrix(test_labels)

Create the Deep Learning Model

model <- keras_model_sequential()
model %>% 
  layer_dense(units = 6, activation = 'relu', input_shape = dim(normalized_train_data)[2]) %>% 
  layer_dense(units = 9, activation = 'relu') %>%
  layer_dense(units = 6, activation = 'relu') %>%
  layer_dense(units = 1)

# Set the metrics required to be Mean Absolute Error and Mean Squared Error.For regression, the loss is 
# mean_squared_error
model %>% compile(
  loss = 'mean_squared_error',
  optimizer = optimizer_rmsprop(),
  metrics = c('mean_absolute_error','mean_squared_error')
)

# Fit the model
# Use the test data for validation
history <- model %>% fit(
  normalized_train_data, train_labels, 
  epochs = 30, batch_size = 128, 
  validation_data = list(normalized_test_data,test_labels)
)

Plot mean squared error, mean absolute error and loss for training data and test data

plot(history)

Fig1

2. Binary classification in Tensorflow – Python

This is a simple binary classification problem from UCI Machine Learning repository and deals with data on Breast cancer from the Univ. of Wisconsin Breast Cancer Wisconsin (Diagnostic) Data Set bold text

In [31]:
import tensorflow as tf
from tensorflow import keras
import pandas as pd
# Read the data set from UCI ML site
dataset_path = keras.utils.get_file("breast-cancer-wisconsin.data", "https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data")
raw_dataset = pd.read_csv(dataset_path, sep=",", na_values = "?", skipinitialspace=True,)
dataset = raw_dataset.copy()

#Check for Null and drop
dataset.isna().sum()
dataset = dataset.dropna()
dataset.isna().sum()

# Set the column names
dataset.columns = ["id","thickness",	"cellsize",	"cellshape","adhesion","epicellsize",
                    "barenuclei","chromatin","normalnucleoli","mitoses","class"]
dataset.head()
Downloading data from https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data
24576/19889 [=====================================] - 0s 1us/step
id	thickness	cellsize	cellshape	adhesion	epicellsize	barenuclei	chromatin	normalnucleoli	mitoses	class
0	1002945	5	4	4	5	7	10.0	3	2	1	2
1	1015425	3	1	1	1	2	2.0	3	1	1	2
2	1016277	6	8	8	1	3	4.0	3	7	1	2
3	1017023	4	1	1	3	2	1.0	3	1	1	2
4	1017122	8	10	10	8	7	10.0	9	7	1	4
# Create a training/test set in the ratio 80/20
train_dataset = dataset.sample(frac=0.8,random_state=0)
test_dataset = dataset.drop(train_dataset.index)

# Set the training and test set
train_dataset1= train_dataset[['thickness','cellsize','cellshape','adhesion',
                'epicellsize', 'barenuclei', 'chromatin', 'normalnucleoli','mitoses']]
test_dataset1=test_dataset[['thickness','cellsize','cellshape','adhesion',
                'epicellsize', 'barenuclei', 'chromatin', 'normalnucleoli','mitoses']]
In [34]:
# Generate the stats for each column to be used for normalization
train_stats = train_dataset1.describe()
train_stats = train_stats.transpose()
train_stats
Out[34]:
count mean std min 25% 50% 75% max
thickness 546.0 4.430403 2.812768 1.0 2.0 4.0 6.0 10.0
cellsize 546.0 3.179487 3.083668 1.0 1.0 1.0 5.0 10.0
cellshape 546.0 3.225275 3.005588 1.0 1.0 1.0 5.0 10.0
adhesion 546.0 2.921245 2.937144 1.0 1.0 1.0 4.0 10.0
epicellsize 546.0 3.261905 2.252643 1.0 2.0 2.0 4.0 10.0
barenuclei 546.0 3.560440 3.651946 1.0 1.0 1.0 7.0 10.0
chromatin 546.0 3.483516 2.492687 1.0 2.0 3.0 5.0 10.0
normalnucleoli 546.0 2.875458 3.064305 1.0 1.0 1.0 4.0 10.0
mitoses 546.0 1.609890 1.736762 1.0 1.0 1.0 1.0 10.0
In [0]:
# Create target variables
train_labels = train_dataset.pop('class')
test_labels = test_dataset.pop('class')
In [0]:
# Set the target variables as 0 or 1
train_labels[train_labels==2] =0 # benign
train_labels[train_labels==4] =1 # malignant

test_labels[test_labels==2] =0 # benign
test_labels[test_labels==4] =1 # malignant
In [0]:
# Normalize by subtracting mean and dividing by standard deviation
def normalize(x):
  return (x - train_stats['mean']) / train_stats['std']

# Convert columns to numeric
train_dataset1 = train_dataset1.apply(pd.to_numeric)
test_dataset1 = test_dataset1.apply(pd.to_numeric)

# Normalize
normalized_train_data = normalize(train_dataset1)
normalized_test_data = normalize(test_dataset1)
In [0]:
# Create a model
model = tf.keras.Sequential([
    keras.layers.Dense(6, activation=tf.nn.relu, input_shape=[len(train_dataset1.keys())]),
    keras.layers.Dense(9, activation=tf.nn.relu),
    keras.layers.Dense(6,activation=tf.nn.relu),
    keras.layers.Dense(1)
  ])

# Use the RMSProp optimizer
optimizer = tf.keras.optimizers.RMSprop(0.01)

# Since this is binary classification use binary_crossentropy
model.compile(loss='binary_crossentropy',
                optimizer=optimizer,
                metrics=['acc'])


# Fit a model
history=model.fit(
  normalized_train_data, train_labels,
  epochs=1000, validation_data=(normalized_test_data,test_labels), verbose=0)
In [55]:
hist = pd.DataFrame(history.history)
hist['epoch'] = history.epoch
hist.tail()
loss acc val_loss val_acc epoch
995 0.112499 0.992674 0.454739 0.970588 995
996 0.112499 0.992674 0.454739 0.970588 996
997 0.112499 0.992674 0.454739 0.970588 997
998 0.112499 0.992674 0.454739 0.970588 998
999 0.112499 0.992674 0.454739 0.970588 999
In [58]:
# Plot training and test accuracy 
plt.plot(history.history['acc'])
plt.plot(history.history['val_acc'])
plt.title('model accuracy')
plt.ylabel('accuracy')
plt.xlabel('epoch')
plt.legend(['train', 'test'], loc='upper left')
plt.ylim([0.9,1])
plt.show()












# Plot training and test loss
plt.plot(history.history['loss'])
plt.plot(history.history['val_loss'])
plt.title('model loss')
plt.ylabel('loss')
plt.xlabel('epoch')
plt.legend(['train', 'test'], loc='upper left')
plt.ylim([0,0.5])
plt.show()


2a. Binary classification in Tensorflow -R

This is a simple binary classification problem from UCI Machine Learning repository and deals with data on Breast cancer from the Univ. of Wisconsin Breast Cancer Wisconsin (Diagnostic) Data Set

# Read the data for Breast cancer (Wisconsin)
dataset <- read.csv("https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data")

# Rename the columns
names(dataset) <- c("id","thickness",   "cellsize", "cellshape","adhesion","epicellsize",
                    "barenuclei","chromatin","normalnucleoli","mitoses","class")

# Remove the columns id and class
dataset1 <- subset(dataset, select = -c(id, class))
dataset2 <- na.omit(dataset1)

# Convert the column to numeric
dataset2$barenuclei <- as.numeric(dataset2$barenuclei)

Normalize the data

train_data <-apply(dataset2,2,normalize)
train_labels <- as.matrix(select(dataset,class))

# Set the target variables as 0 or 1 as it binary classification
train_labels[train_labels==2,]=0
train_labels[train_labels==4,]=1

Create the Deep Learning model

model <- keras_model_sequential()
model %>% 
  layer_dense(units = 6, activation = 'relu', input_shape = dim(train_data)[2]) %>% 
  layer_dense(units = 9, activation = 'relu') %>%
  layer_dense(units = 6, activation = 'relu') %>%
  layer_dense(units = 1)

# Since this is a binary classification we use binary cross entropy
model %>% compile(
  loss = 'binary_crossentropy',
  optimizer = optimizer_rmsprop(),
  metrics = c('accuracy')  # Metrics is accuracy
)

Fit the model. Use 20% of data for validation

history <- model %>% fit(
  train_data, train_labels, 
  epochs = 30, batch_size = 128, 
  validation_split = 0.2
)

Plot the accuracy and loss for training and validation data

plot(history)

3. MNIST in Tensorflow – Python

This takes the famous MNIST handwritten digits . It ca be seen that Tensorflow and Keras make short work of this famous problem of the late 1980s

# Download MNIST data
mnist=tf.keras.datasets.mnist
# Set training and test data and labels
(training_images,training_labels),(test_images,test_labels)=mnist.load_data()

print(training_images.shape)
print(test_images.shape)
(60000, 28, 28)
(10000, 28, 28)
In [61]:
# Plot a sample image from MNIST and show contents
import matplotlib.pyplot as plt
plt.imshow(training_images[1])
print(training_images[1])
[[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 51 159 253
159 50 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 48 238 252 252
252 237 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 54 227 253 252 239
233 252 57 6 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 10 60 224 252 253 252 202
84 252 253 122 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 163 252 252 252 253 252 252
96 189 253 167 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 51 238 253 253 190 114 253 228
47 79 255 168 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 48 238 252 252 179 12 75 121 21
0 0 253 243 50 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 38 165 253 233 208 84 0 0 0 0
0 0 253 252 165 0 0 0 0 0]
[ 0 0 0 0 0 0 0 7 178 252 240 71 19 28 0 0 0 0
0 0 253 252 195 0 0 0 0 0]
[ 0 0 0 0 0 0 0 57 252 252 63 0 0 0 0 0 0 0
0 0 253 252 195 0 0 0 0 0]
[ 0 0 0 0 0 0 0 198 253 190 0 0 0 0 0 0 0 0
0 0 255 253 196 0 0 0 0 0]
[ 0 0 0 0 0 0 76 246 252 112 0 0 0 0 0 0 0 0
0 0 253 252 148 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 230 25 0 0 0 0 0 0 0 0
7 135 253 186 12 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 223 0 0 0 0 0 0 0 0 7
131 252 225 71 0 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 145 0 0 0 0 0 0 0 48 165
252 173 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 86 253 225 0 0 0 0 0 0 114 238 253
162 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 249 146 48 29 85 178 225 253 223 167
56 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 252 252 229 215 252 252 252 196 130 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 28 199 252 252 253 252 252 233 145 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 25 128 252 253 252 141 37 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]]


# Normalize the images by dividing by 255.0
training_images = training_images/255.0
test_images = test_images/255.0

# Create a Sequential Keras model
model = tf.keras.models.Sequential([tf.keras.layers.Flatten(),
                                   tf.keras.layers.Dense(1024,activation=tf.nn.relu),
                                   tf.keras.layers.Dense(10,activation=tf.nn.softmax)])
model.compile(optimizer='adam',loss='sparse_categorical_crossentropy',metrics=['accuracy'])
In [68]:
history=model.fit(training_images,training_labels,validation_data=(test_images, test_labels), epochs=5, verbose=1)
Train on 60000 samples, validate on 10000 samples
Epoch 1/5
60000/60000 [==============================] - 17s 291us/sample - loss: 0.0020 - acc: 0.9999 - val_loss: 0.0719 - val_acc: 0.9810
Epoch 2/5
60000/60000 [==============================] - 17s 284us/sample - loss: 0.0021 - acc: 0.9998 - val_loss: 0.0705 - val_acc: 0.9821
Epoch 3/5
60000/60000 [==============================] - 17s 286us/sample - loss: 0.0017 - acc: 0.9999 - val_loss: 0.0729 - val_acc: 0.9805
Epoch 4/5
60000/60000 [==============================] - 17s 284us/sample - loss: 0.0014 - acc: 0.9999 - val_loss: 0.0762 - val_acc: 0.9804
Epoch 5/5
60000/60000 [==============================] - 17s 280us/sample - loss: 0.0015 - acc: 0.9999 - val_loss: 0.0735 - val_acc: 0.9812

Fig 1

Fig 2

 

 

 

 

 

 

 

 

MNIST in Tensorflow – R

The following code uses Tensorflow to learn MNIST’s handwritten digits ### Load MNIST data

mnist <- dataset_mnist()
x_train <- mnist$train$x
y_train <- mnist$train$y
x_test <- mnist$test$x
y_test <- mnist$test$y

Reshape and rescale

# Reshape the array
x_train <- array_reshape(x_train, c(nrow(x_train), 784))
x_test <- array_reshape(x_test, c(nrow(x_test), 784))
# Rescale
x_train <- x_train / 255
x_test <- x_test / 255

Convert out put to One Hot encoded format

y_train <- to_categorical(y_train, 10)
y_test <- to_categorical(y_test, 10)

Fit the model

Use the softmax activation for recognizing 10 digits and categorical cross entropy for loss

model <- keras_model_sequential() 
model %>% 
  layer_dense(units = 256, activation = 'relu', input_shape = c(784)) %>% 
  layer_dense(units = 128, activation = 'relu') %>%
  layer_dense(units = 10, activation = 'softmax') # Use softmax

model %>% compile(
  loss = 'categorical_crossentropy',
  optimizer = optimizer_rmsprop(),
  metrics = c('accuracy')
)

Fit the model

Note: A smaller number of epochs has been used. For better performance increase number of epochs

history <- model %>% fit(
  x_train, y_train, 
  epochs = 5, batch_size = 128, 
  validation_data = list(x_test,y_test)
)

Take 4+: Presentations on ‘Elements of Neural Networks and Deep Learning’ – Parts 1-8

“Lights, camera and … action – Take 4+!”

This post includes  a rework of all presentation of ‘Elements of Neural Networks and Deep  Learning Parts 1-8 ‘ since my earlier presentations had some missing parts, omissions and some occasional errors. So I have re-recorded all the presentations.
This series of presentation will do a deep-dive  into Deep Learning networks starting from the fundamentals. The equations required for performing learning in a L-layer Deep Learning network  are derived in detail, starting from the basics. Further, the presentations also discuss multi-class classification, regularization techniques, and gradient descent optimization methods in deep networks methods. Finally the presentations also touch on how  Deep Learning Networks can be tuned.

The corresponding implementations are available in vectorized R, Python and Octave are available in my book ‘Deep Learning from first principles:Second edition- In vectorized Python, R and Octave

1. Elements of Neural Networks and Deep Learning – Part 1
This presentation introduces Neural Networks and Deep Learning. A look at history of Neural Networks, Perceptrons and why Deep Learning networks are required and concluding with a simple toy examples of a Neural Network and how they compute. This part also includes a small digression on the basics of Machine Learning and how the algorithm learns from a data set

2. Elements of Neural Networks and Deep Learning – Part 2
This presentation takes logistic regression as an example and creates an equivalent 2 layer Neural network. The presentation also takes a look at forward & backward propagation and how the cost is minimized using gradient descent


The implementation of the discussed 2 layer Neural Network in vectorized R, Python and Octave are available in my post ‘Deep Learning from first principles in Python, R and Octave – Part 1‘

3. Elements of Neural Networks and Deep Learning – Part 3
This 3rd part, discusses a primitive neural network with an input layer, output layer and a hidden layer. The neural network uses tanh activation in the hidden layer and a sigmoid activation in the output layer. The equations for forward and backward propagation are derived.


To see the implementations for the above discussed video see my post ‘Deep Learning from first principles in Python, R and Octave – Part 2

4. Elements of Neural Network and Deep Learning – Part 4
This presentation is a continuation of my 3rd presentation in which I derived the equations for a simple 3 layer Neural Network with 1 hidden layer. In this video presentation, I discuss step-by-step the derivations for a L-Layer, multi-unit Deep Learning Network, with any activation function g(z)


The implementations of L-Layer, multi-unit Deep Learning Network in vectorized R, Python and Octave are available in my post Deep Learning from first principles in Python, R and Octave – Part 3

5. Elements of Neural Network and Deep Learning – Part 5
This presentation discusses multi-class classification using the Softmax function. The detailed derivation for the Jacobian of the Softmax is discussed, and subsequently the derivative of cross-entropy loss is also discussed in detail. Finally the final set of equations for a Neural Network with multi-class classification is derived.


The corresponding implementations in vectorized R, Python and Octave are available in the following posts
a. Deep Learning from first principles in Python, R and Octave – Part 4
b. Deep Learning from first principles in Python, R and Octave – Part 5

6. Elements of Neural Networks and Deep Learning – Part 6
This part discusses initialization methods specifically like He and Xavier. The presentation also focuses on how to prevent over-fitting using regularization. Lastly the dropout method of regularization is also discussed


The corresponding implementations in vectorized R, Python and Octave of the above discussed methods are available in my post Deep Learning from first principles in Python, R and Octave – Part 6

7. Elements of Neural Networks and Deep Learning – Part 7
This presentation introduces exponentially weighted moving average and shows how this is used in different approaches to gradient descent optimization. The key techniques discussed are learning rate decay, momentum method, rmsprop and adam.

The equivalent implementations of the gradient descent optimization techniques in R, Python and Octave can be seen in my post Deep Learning from first principles in Python, R and Octave – Part 7

8. Elements of Neural Networks and Deep Learning – Part 8
This last part touches on the method to adopt while tuning hyper-parameters in Deep Learning networks

Checkout my book ‘Deep Learning from first principles: Second Edition – In vectorized Python, R and Octave’. My book starts with the implementation of a simple 2-layer Neural Network and works its way to a generic L-Layer Deep Learning Network, with all the bells and whistles. The derivations have been discussed in detail. The code has been extensively commented and included in its entirety in the Appendix sections. My book is available on Amazon as paperback ($18.99) and in kindle version($9.99/Rs449).

This concludes this series of presentations on “Elements of Neural Networks and Deep Learning’

Also
1. My book ‘Practical Machine Learning in R and Python: Third edition’ on Amazon
2. Introducing cricpy:A python package to analyze performances of cricketers
3. Natural language processing: What would Shakespeare say?
4. Big Data-2: Move into the big league:Graduate from R to SparkR
5. Presentation on Wireless Technologies – Part 1
6. Introducing cricketr! : An R package to analyze performances of cricketers

To see all posts click Index of posts

My presentations on ‘Elements of Neural Networks & Deep Learning’ -Parts 6,7,8

This is the final set of presentations in my series ‘Elements of Neural Networks and Deep Learning’. This set follows the earlier 2 sets of presentations namely
1. My presentations on ‘Elements of Neural Networks & Deep Learning’ -Part1,2,3
2. My presentations on ‘Elements of Neural Networks & Deep Learning’ -Parts 4,5

In this final set of presentations I discuss initialization methods, regularization techniques including dropout. Next I also discuss gradient descent optimization methods like momentum, rmsprop, adam etc. Lastly, I briefly also touch on hyper-parameter tuning approaches. The corresponding implementations are available in vectorized R, Python and Octave are available in my book ‘Deep Learning from first principles:Second edition- In vectorized Python, R and Octave

1. Elements of Neural Networks and Deep Learning – Part 6
This part discusses initialization methods specifically like He and Xavier. The presentation also focuses on how to prevent over-fitting using regularization. Lastly the dropout method of regularization is also discusses


The corresponding implementations in vectorized R, Python and Octave of the above discussed methods are available in my post Deep Learning from first principles in Python, R and Octave – Part 6

2. Elements of Neural Networks and Deep Learning – Part 7
This presentation introduces exponentially weighted moving average and shows how this is used in different approaches to gradient descent optimization. The key techniques discussed are learning rate decay, momentum method, rmsprop and adam.


The equivalent implementations of the gradient descent optimization techniques in R, Python and Octave can be seen in my post Deep Learning from first principles in Python, R and Octave – Part 7

3. Elements of Neural Networks and Deep Learning – Part 8
This last part touches upon hyper-parameter tuning in Deep Learning networks


This concludes this series of presentations on “Elements of Neural Networks and Deep Learning’

Important note: Do check out my later version of these videos at Take 4+: Presentations on ‘Elements of Neural Networks and Deep Learning’ – Parts 1-8 . These have more content and also include some corrections. Check it out!

Checkout my book ‘Deep Learning from first principles: Second Edition – In vectorized Python, R and Octave’. My book starts with the implementation of a simple 2-layer Neural Network and works its way to a generic L-Layer Deep Learning Network, with all the bells and whistles. The derivations have been discussed in detail. The code has been extensively commented and included in its entirety in the Appendix sections. My book is available on Amazon as paperback ($18.99) and and in kindle version($9.99/Rs449).

See also
1. My book ‘Practical Machine Learning in R and Python: Third edition’ on Amazon
2. Big Data-1: Move into the big league:Graduate from Python to Pyspark
3. My travels through the realms of Data Science, Machine Learning, Deep Learning and (AI)
4. Revisiting crimes against women in India
5. Introducing cricket package yorkr: Part 1- Beaten by sheer pace!
6. Deblurring with OpenCV: Weiner filter reloaded
7. Taking a closer look at Quantum gates and their operations

To see all posts click Index of posts

My presentations on ‘Elements of Neural Networks & Deep Learning’ -Parts 4,5

This is the next set of presentations on “Elements of Neural Networks and Deep Learning”.  In the 4th presentation I discuss and derive the generalized equations for a multi-unit, multi-layer Deep Learning network.  The 5th presentation derives the equations for a Deep Learning network when performing multi-class classification along with the derivations for cross-entropy loss. The corresponding implementations are available in vectorized R, Python and Octave are available in my book ‘Deep Learning from first principles:Second edition- In vectorized Python, R and Octave

Important note: Do check out my later version of these videos at Take 4+: Presentations on ‘Elements of Neural Networks and Deep Learning’ – Parts 1-8 . These have more content and also include some corrections. Check it out!

1. Elements of Neural Network and Deep Learning – Part 4
This presentation is a continuation of my 3rd presentation in which I derived the equations for a simple 3 layer Neural Network with 1 hidden layer. In this video presentation, I discuss step-by-step the derivations for a L-Layer, multi-unit Deep Learning Network, with any activation function g(z)


The implementations of L-Layer, multi-unit Deep Learning Network in vectorized R, Python and Octave are available in my post Deep Learning from first principles in Python, R and Octave – Part 3

2. Elements of Neural Network and Deep Learning – Part 5
This presentation discusses multi-class classification using the Softmax function. The detailed derivation for the Jacobian of the Softmax is discussed, and subsequently the derivative of cross-entropy loss is also discussed in detail. Finally the final set of equations for a Neural Network with multi-class classification is derived.


The corresponding implementations in vectorized R, Python and Octave are available in the following posts
a. Deep Learning from first principles in Python, R and Octave – Part 4
b. Deep Learning from first principles in Python, R and Octave – Part 5

To be continued. Watch this space!

Checkout my book ‘Deep Learning from first principles: Second Edition – In vectorized Python, R and Octave’. My book starts with the implementation of a simple 2-layer Neural Network and works its way to a generic L-Layer Deep Learning Network, with all the bells and whistles. The derivations have been discussed in detail. The code has been extensively commented and included in its entirety in the Appendix sections. My book is available on Amazon as paperback ($18.99) and in kindle version($9.99/Rs449).

Also see
1. My book ‘Practical Machine Learning in R and Python: Third edition’ on Amazon
2. Big Data-2: Move into the big league:Graduate from R to SparkR
3. Introducing QCSimulator: A 5-qubit quantum computing simulator in R
4. My TEDx talk on the “Internet of Things
5. Rock N’ Roll with Bluemix, Cloudant & NodeExpress
6. GooglyPlus: yorkr analyzes IPL players, teams, matches with plots and tables
7. Literacy in India – A deepR dive
8. Fun simulation of a Chain in Android

To see all posts click Index of Posts