Big Data-2: Move into the big league:Graduate from R to SparkR


This post is a continuation of my earlier post Big Data-1: Move into the big league:Graduate from Python to Pyspark. While the earlier post discussed parallel constructs in Python and Pyspark, this post elaborates similar and key constructs in R and SparkR. While this post just focuses on the programming part of R and SparkR it is essential to understand and fully grasp the concept of Spark, RDD and how data is distributed across the clusters. This post like the earlier post shows how if you already have a good handle of R, you can easily graduate to Big Data with SparkR

Note 1: This notebook has also been published at Databricks community site Big Data-2: Move into the big league:Graduate from R to SparkR

Note 2: You can download this RMarkdown file from Github at Big Data- Python to Pyspark and R to SparkR
1a. Read CSV- R

Note: To upload the CSV to databricks see the video Upload Flat File to Databricks Table

# Read CSV file
tendulkar= read.csv("/dbfs/FileStore/tables/tendulkar.csv",stringsAsFactors = FALSE,na.strings=c(NA,"-"))
#Check the dimensions of the dataframe
dim(tendulkar)
[1] 347  12
1b. Read CSV – SparkR
# Load the SparkR library
library(SparkR)
# Initiate a SparkR session
sparkR.session()
tendulkar1 <- read.df("/FileStore/tables/tendulkar.csv", 
                header = "true", 
                delimiter = ",", 
                source = "csv", 
                inferSchema = "true", 
                na.strings = "")

# Check the dimensions of the dataframe
dim(tendulkar1)
[1] 347  12
2a. Data frame shape – R
# Get the shape of the dataframe in R
dim(tendulkar)
[1] 347  12
2b. Dataframe shape – SparkR

The same ‘dim’ command works in SparkR too!

dim(tendulkar1)
[1] 347  12
3a . Dataframe columns – R
# Get the names
names(tendulkar) # Also colnames(tendulkar)
 [1] "Runs"       "Mins"       "BF"         "X4s"        "X6s"       
 [6] "SR"         "Pos"        "Dismissal"  "Inns"       "Opposition"
[11] "Ground"     "Start.Date"
3b. Dataframe columns – SparkR
names(tendulkar1)
 [1] "Runs"       "Mins"       "BF"         "4s"         "6s"        
 [6] "SR"         "Pos"        "Dismissal"  "Inns"       "Opposition"
[11] "Ground"     "Start Date"
4a. Rename columns – R
names(tendulkar)=c('Runs','Minutes','BallsFaced','Fours','Sixes','StrikeRate','Position','Dismissal','Innings','Opposition','Ground','StartDate')
names(tendulkar)
 [1] "Runs"       "Minutes"    "BallsFaced" "Fours"      "Sixes"     
 [6] "StrikeRate" "Position"   "Dismissal"  "Innings"    "Opposition"
[11] "Ground"     "StartDate"
4b. Rename columns – SparkR
names(tendulkar1)=c('Runs','Minutes','BallsFaced','Fours','Sixes','StrikeRate','Position','Dismissal','Innings','Opposition','Ground','StartDate')
names(tendulkar1)
 [1] "Runs"       "Minutes"    "BallsFaced" "Fours"      "Sixes"     
 [6] "StrikeRate" "Position"   "Dismissal"  "Innings"    "Opposition"
[11] "Ground"     "StartDate"
5a. Summary – R
summary(tendulkar)
     Runs              Minutes        BallsFaced         Fours       
 Length:347         Min.   :  1.0   Min.   :  0.00   Min.   : 0.000  
 Class :character   1st Qu.: 33.0   1st Qu.: 22.00   1st Qu.: 1.000  
 Mode  :character   Median : 82.0   Median : 58.50   Median : 4.000  
                    Mean   :125.5   Mean   : 89.75   Mean   : 6.274  
                    3rd Qu.:181.0   3rd Qu.:133.25   3rd Qu.: 9.000  
                    Max.   :613.0   Max.   :436.00   Max.   :35.000  
                    NA's   :18      NA's   :19       NA's   :19      
     Sixes          StrikeRate        Position     Dismissal        
 Min.   :0.0000   Min.   :  0.00   Min.   :2.00   Length:347        
 1st Qu.:0.0000   1st Qu.: 38.09   1st Qu.:4.00   Class :character  
 Median :0.0000   Median : 52.25   Median :4.00   Mode  :character  
 Mean   :0.2097   Mean   : 51.79   Mean   :4.24                     
 3rd Qu.:0.0000   3rd Qu.: 65.09   3rd Qu.:4.00                     
 Max.   :4.0000   Max.   :166.66   Max.   :7.00                     
 NA's   :18       NA's   :20       NA's   :18                       
    Innings       Opposition           Ground           StartDate        
 Min.   :1.000   Length:347         Length:347         Length:347        
 1st Qu.:1.000   Class :character   Class :character   Class :character  
 Median :2.000   Mode  :character   Mode  :character   Mode  :character  
 Mean   :2.376                                                           
 3rd Qu.:3.000                                                           
 Max.   :4.000                                                           
 NA's   :1
5b. Summary – SparkR
summary(tendulkar1)
SparkDataFrame[summary:string, Runs:string, Minutes:string, BallsFaced:string, Fours:string, Sixes:string, StrikeRate:string, Position:string, Dismissal:string, Innings:string, Opposition:string, Ground:string, StartDate:string]
6a. Displaying details of dataframe with str() – R
str(tendulkar)
'data.frame':	347 obs. of  12 variables:
 $ Runs      : chr  "15" "DNB" "59" "8" ...
 $ Minutes   : int  28 NA 254 24 124 74 193 1 50 324 ...
 $ BallsFaced: int  24 NA 172 16 90 51 134 1 44 266 ...
 $ Fours     : int  2 NA 4 1 5 5 6 0 3 5 ...
 $ Sixes     : int  0 NA 0 0 0 0 0 0 0 0 ...
 $ StrikeRate: num  62.5 NA 34.3 50 45.5 ...
 $ Position  : int  6 NA 6 6 7 6 6 6 6 6 ...
 $ Dismissal : chr  "bowled" NA "lbw" "run out" ...
 $ Innings   : int  2 4 1 3 1 1 3 2 3 1 ...
 $ Opposition: chr  "v Pakistan" "v Pakistan" "v Pakistan" "v Pakistan" ...
 $ Ground    : chr  "Karachi" "Karachi" "Faisalabad" "Faisalabad" ...
 $ StartDate : chr  "15-Nov-89" "15-Nov-89" "23-Nov-89" "23-Nov-89" ...
6b. Displaying details of dataframe with str() – SparkR
str(tendulkar1)
'SparkDataFrame': 12 variables:
 $ Runs      : chr "15" "DNB" "59" "8" "41" "35"
 $ Minutes   : chr "28" "-" "254" "24" "124" "74"
 $ BallsFaced: chr "24" "-" "172" "16" "90" "51"
 $ Fours     : chr "2" "-" "4" "1" "5" "5"
 $ Sixes     : chr "0" "-" "0" "0" "0" "0"
 $ StrikeRate: chr "62.5" "-" "34.3" "50" "45.55" "68.62"
 $ Position  : chr "6" "-" "6" "6" "7" "6"
 $ Dismissal : chr "bowled" "-" "lbw" "run out" "bowled" "lbw"
 $ Innings   : chr "2" "4" "1" "3" "1" "1"
 $ Opposition: chr "v Pakistan" "v Pakistan" "v Pakistan" "v Pakistan" "v Pakistan" "v Pakistan"
 $ Ground    : chr "Karachi" "Karachi" "Faisalabad" "Faisalabad" "Lahore" "Sialkot"
 $ StartDate : chr "15-Nov-89" "15-Nov-89" "23-Nov-89" "23-Nov-89" "1-Dec-89" "9-Dec-89"
7a. Head & tail -R
print(head(tendulkar),3)
print(tail(tendulkar),3)
 Runs Minutes BallsFaced Fours Sixes StrikeRate Position Dismissal Innings
1   15      28         24     2     0      62.50        6    bowled       2
2  DNB      NA         NA    NA    NA         NA       NA             4
3   59     254        172     4     0      34.30        6       lbw       1
4    8      24         16     1     0      50.00        6   run out       3
5   41     124         90     5     0      45.55        7    bowled       1
6   35      74         51     5     0      68.62        6       lbw       1
  Opposition     Ground StartDate
1 v Pakistan    Karachi 15-Nov-89
2 v Pakistan    Karachi 15-Nov-89
3 v Pakistan Faisalabad 23-Nov-89
4 v Pakistan Faisalabad 23-Nov-89
5 v Pakistan     Lahore  1-Dec-89
6 v Pakistan    Sialkot  9-Dec-89
    Runs Minutes BallsFaced Fours Sixes StrikeRate Position Dismissal Innings
342   37     125         81     5     0      45.67        4    caught       2
343   21      71         23     2     0      91.30        4   run out       4
344   32      99         53     5     0      60.37        4       lbw       2
345    1       8          5     0     0      20.00        4       lbw       4
346   10      41         24     2     0      41.66        4       lbw       2
347   74     150        118    12     0      62.71        4    caught       2
       Opposition  Ground StartDate
342   v Australia  Mohali 14-Mar-13
343   v Australia  Mohali 14-Mar-13
344   v Australia   Delhi 22-Mar-13
345   v Australia   Delhi 22-Mar-13
346 v West Indies Kolkata  6-Nov-13
347 v West Indies  Mumbai 14-Nov-13
7b. Head – SparkR
head(tendulkar1,3)
  Runs Minutes BallsFaced Fours Sixes StrikeRate Position Dismissal Innings
1   15      28         24     2     0       62.5        6    bowled       2
2  DNB       -          -     -     -          -        -         -       4
3   59     254        172     4     0       34.3        6       lbw       1
  Opposition     Ground StartDate
1 v Pakistan    Karachi 15-Nov-89
2 v Pakistan    Karachi 15-Nov-89
3 v Pakistan Faisalabad 23-Nov-89
8a. Determining the column types with sapply -R
sapply(tendulkar,class)
       Runs     Minutes  BallsFaced       Fours       Sixes  StrikeRate 
"character"   "integer"   "integer"   "integer"   "integer"   "numeric" 
   Position   Dismissal     Innings  Opposition      Ground   StartDate 
  "integer" "character"   "integer" "character" "character" "character"
8b. Determining the column types with printSchema – SparkR
printSchema(tendulkar1)
root
 |-- Runs: string (nullable = true)
 |-- Minutes: string (nullable = true)
 |-- BallsFaced: string (nullable = true)
 |-- Fours: string (nullable = true)
 |-- Sixes: string (nullable = true)
 |-- StrikeRate: string (nullable = true)
 |-- Position: string (nullable = true)
 |-- Dismissal: string (nullable = true)
 |-- Innings: string (nullable = true)
 |-- Opposition: string (nullable = true)
 |-- Ground: string (nullable = true)
 |-- StartDate: string (nullable = true)
9a. Selecting columns – R
library(dplyr)
df=select(tendulkar,Runs,BallsFaced,Minutes)
head(df,5)
  Runs BallsFaced Minutes
1   15         24      28
2  DNB         NA      NA
3   59        172     254
4    8         16      24
5   41         90     124
9b. Selecting columns – SparkR
library(SparkR)
Sys.setenv(SPARK_HOME="/usr/hdp/2.6.0.3-8/spark")
.libPaths(c(file.path(Sys.getenv("SPARK_HOME"), "R", "lib"), .libPaths()))
# Initiate a SparkR session
sparkR.session()
tendulkar1 <- read.df("/FileStore/tables/tendulkar.csv", 
                header = "true", 
                delimiter = ",", 
                source = "csv", 
                inferSchema = "true", 
                na.strings = "")
df=SparkR::select(tendulkar1, "Runs", "BF","Mins")
head(SparkR::collect(df))
  Runs  BF Mins
1   15  24   28
2  DNB   -    -
3   59 172  254
4    8  16   24
5   41  90  124
6   35  51   74
10a. Filter rows by criteria – R
library(dplyr)
df=tendulkar %>% filter(Runs > 50)
head(df,5)
  Runs Minutes BallsFaced Fours Sixes StrikeRate Position Dismissal Innings
1  DNB      NA         NA    NA    NA         NA       NA             4
2   59     254        172     4     0      34.30        6       lbw       1
3    8      24         16     1     0      50.00        6   run out       3
4   57     193        134     6     0      42.53        6    caught       3
5   88     324        266     5     0      33.08        6    caught       1
     Opposition     Ground StartDate
1    v Pakistan    Karachi 15-Nov-89
2    v Pakistan Faisalabad 23-Nov-89
3    v Pakistan Faisalabad 23-Nov-89
4    v Pakistan    Sialkot  9-Dec-89
5 v New Zealand     Napier  9-Feb-90
10b. Filter rows by criteria – SparkR
df=SparkR::filter(tendulkar1, tendulkar1$Runs > 50)
head(SparkR::collect(df))
  Runs Mins  BF 4s 6s    SR Pos Dismissal Inns     Opposition       Ground
1   59  254 172  4  0  34.3   6       lbw    1     v Pakistan   Faisalabad
2   57  193 134  6  0 42.53   6    caught    3     v Pakistan      Sialkot
3   88  324 266  5  0 33.08   6    caught    1  v New Zealand       Napier
4   68  216 136  8  0    50   6    caught    2      v England   Manchester
5  114  228 161 16  0  70.8   4    caught    2    v Australia        Perth
6  111  373 270 19  0 41.11   4    caught    2 v South Africa Johannesburg
  Start Date
1  23-Nov-89
2   9-Dec-89
3   9-Feb-90
4   9-Aug-90
5   1-Feb-92
6  26-Nov-92
11a. Unique values -R
unique(tendulkar$Runs)
  [1] "15"   "DNB"  "59"   "8"    "41"   "35"   "57"   "0"    "24"   "88"  
 [11] "5"    "10"   "27"   "68"   "119*" "21"   "11"   "16"   "7"    "40"  
 [21] "148*" "6"    "17"   "114"  "111"  "1"    "73"   "50"   "9*"   "165" 
 [31] "78"   "62"   "TDNB" "28"   "104*" "71"   "142"  "96"   "43"   "11*" 
 [41] "34"   "85"   "179"  "54"   "4"    "0*"   "52*"  "2"    "122"  "31"  
 [51] "177"  "74"   "42"   "18"   "61"   "36"   "169"  "9"    "15*"  "92"  
 [61] "83"   "143"  "139"  "23"   "148"  "13"   "155*" "79"   "47"   "113" 
 [71] "67"   "136"  "29"   "53"   "124*" "126*" "44*"  "217"  "116"  "52"  
 [81] "45"   "97"   "20"   "39"   "201*" "76"   "65"   "126"  "36*"  "69"  
 [91] "155"  "22*"  "103"  "26"   "90"   "176"  "117"  "86"   "12"   "193" 
[101] "16*"  "51"   "32"   "55"   "37"   "44"   "241*" "60*"  "194*" "3"   
[111] "32*"  "248*" "94"   "22"   "109"  "19"   "14"   "28*"  "63"   "64"  
[121] "101"  "122*" "91"   "82"   "56*"  "154*" "153"  "49"   "10*"  "103*"
[131] "160"  "100*" "105*" "100"  "106"  "84"   "203"  "98"   "38"   "214" 
[141] "53*"  "111*" "146"  "14*"  "56"   "80"   "25"   "81"   "13*"
11b. Unique values – SparkR
head(SparkR::distinct(tendulkar1[,"Runs"]),5)
  Runs
1 119*
2    7
3   51
4  169
5  32*
12a. Aggregate – Mean, min and max – R
library(dplyr)
library(magrittr)
a <- tendulkar$Runs != "DNB"
tendulkar <- tendulkar[a,]
dim(tendulkar)

# Remove rows with 'TDNB'
c <- tendulkar$Runs != "TDNB"
tendulkar <- tendulkar[c,]

# Remove rows with absent
d <- tendulkar$Runs != "absent"
tendulkar <- tendulkar[d,]
dim(tendulkar)

# Remove the "* indicating not out
tendulkar$Runs <- as.numeric(gsub("\\*","",tendulkar$Runs))
c <- complete.cases(tendulkar)

#Subset the rows which are complete
tendulkar <- tendulkar[c,]
print(dim(tendulkar))
df <-tendulkar %>%  group_by(Ground) %>% summarise(meanRuns= mean(Runs), minRuns=min(Runs), maxRuns=max(Runs)) 
#names(tendulkar)
head(df)
[1] 327  12
# A tibble: 6 x 4
  Ground       meanRuns minRuns maxRuns
                   
1 Adelaide        32.6       0.    153.
2 Ahmedabad       40.1       4.    217.
3 Auckland         5.00      5.      5.
4 Bangalore       57.9       4.    214.
5 Birmingham      46.8       1.    122.
6 Bloemfontein    85.0      15.    155.
12b. Aggregate- Mean, Min, Max – SparkR
sparkR.session()

tendulkar1 <- read.df("/FileStore/tables/tendulkar.csv", 
                header = "true", 
                delimiter = ",", 
                source = "csv", 
                inferSchema = "true", 
                na.strings = "")

print(dim(tendulkar1))
tendulkar1 <-SparkR::filter(tendulkar1,tendulkar1$Runs != "DNB")
print(dim(tendulkar1))
tendulkar1<-SparkR::filter(tendulkar1,tendulkar1$Runs != "TDNB")
print(dim(tendulkar1))
tendulkar1<-SparkR::filter(tendulkar1,tendulkar1$Runs != "absent")
print(dim(tendulkar1))

# Cast the string type Runs to double
withColumn(tendulkar1, "Runs", cast(tendulkar1$Runs, "double"))
head(SparkR::distinct(tendulkar1[,"Runs"]),20)
# Remove the "* indicating not out
tendulkar1$Runs=SparkR::regexp_replace(tendulkar1$Runs, "\\*", "")
head(SparkR::distinct(tendulkar1[,"Runs"]),20)
df=SparkR::summarize(SparkR::groupBy(tendulkar1, tendulkar1$Ground), mean = mean(tendulkar1$Runs), minRuns=min(tendulkar1$Runs),maxRuns=max(tendulkar1$Runs))
head(df,20)
[1] 347  12
[1] 330  12
[1] 329  12
[1] 329  12
          Ground       mean minRuns maxRuns
1      Bangalore  54.312500       0      96
2       Adelaide  32.600000       0      61
3  Colombo (PSS)  37.200000      14      71
4   Christchurch  12.000000       0      24
5       Auckland   5.000000       5       5
6        Chennai  60.625000       0      81
7      Centurion  73.500000     111      36
8       Brisbane   7.666667       0       7
9     Birmingham  46.750000       1      40
10     Ahmedabad  40.125000     100       8
11 Colombo (RPS) 143.000000     143     143
12    Chittagong  57.800000     101      36
13     Cape Town  69.857143      14       9
14    Bridgetown  26.000000       0      92
15      Bulawayo  55.000000      36      74
16         Delhi  39.947368       0      76
17    Chandigarh  11.000000      11      11
18  Bloemfontein  85.000000      15     155
19 Colombo (SSC)  77.555556     104       8
20       Cuttack   2.000000       2       2
13a Using SQL with SparkR
sparkR.session()
tendulkar1 <- read.df("/FileStore/tables/tendulkar.csv", 
                header = "true", 
                delimiter = ",", 
                source = "csv", 
                inferSchema = "true", 
                na.strings = "")

# Register this SparkDataFrame as a temporary view.
createOrReplaceTempView(tendulkar1, "tendulkar2")

# SQL statements can be run by using the sql method
df=SparkR::sql("SELECT * FROM tendulkar2 WHERE Ground='Karachi'")

head(df)

  Runs Mins BF 4s 6s    SR Pos Dismissal Inns Opposition  Ground Start Date
1   15   28 24  2  0  62.5   6    bowled    2 v Pakistan Karachi  15-Nov-89
2  DNB    -  -  -  -     -   -         -    4 v Pakistan Karachi  15-Nov-89
3   23   49 29  5  0 79.31   4    bowled    2 v Pakistan Karachi  29-Jan-06
4   26   74 47  5  0 55.31   4    bowled    4 v Pakistan Karachi  29-Jan-06
Conclusion

This post discusses some of the key constructs in R and SparkR and how one can transition from R to SparkR fairly easily. I will be adding more constructs later. Do check back!

You may also like
1. Exploring Quantum Gate operations with QCSimulator
2. Deep Learning from first principles in Python, R and Octave – Part 4
3. A Bluemix recipe with MongoDB and Node.js
4. Practical Machine Learning with R and Python – Part 5
5. Introducing cricketr! : An R package to analyze performances of cricketers

To see all posts click Index of posts

My book ‘Practical Machine Learning in R and Python: Second edition’ on Amazon


Note: The 3rd edition of this book is now available My book ‘Practical Machine Learning in R and Python: Third edition’ on Amazon

The third edition of my book ‘Practical Machine Learning with R and Python – Machine Learning in stereo’ is now available in both paperback ($12.99) and kindle ($9.99/Rs449) versions.  This second edition includes more content,  extensive comments and formatting for better readability.

In this book I implement some of the most common, but important Machine Learning algorithms in R and equivalent Python code.
1. Practical machine with R and Python: Third Edition – Machine Learning in Stereo(Paperback-$12.99)
2. Practical machine with R and Third Edition – Machine Learning in Stereo(Kindle- $9.99/Rs449)

This book is ideal both for beginners and the experts in R and/or Python. Those starting their journey into datascience and ML will find the first 3 chapters useful, as they touch upon the most important programming constructs in R and Python and also deal with equivalent statements in R and Python. Those who are expert in either of the languages, R or Python, will find the equivalent code ideal for brushing up on the other language. And finally,those who are proficient in both languages, can use the R and Python implementations to internalize the ML algorithms better.

Here is a look at the topics covered

Table of Contents
Preface …………………………………………………………………………….4
Introduction ………………………………………………………………………6
1. Essential R ………………………………………………………………… 8
2. Essential Python for Datascience ……………………………………………57
3. R vs Python …………………………………………………………………81
4. Regression of a continuous variable ……………………………………….101
5. Classification and Cross Validation ………………………………………..121
6. Regression techniques and regularization ………………………………….146
7. SVMs, Decision Trees and Validation curves ………………………………191
8. Splines, GAMs, Random Forests and Boosting ……………………………222
9. PCA, K-Means and Hierarchical Clustering ………………………………258
References ……………………………………………………………………..269

Pick up your copy today!!
Hope you have a great time learning as I did while implementing these algorithms!

Deep Learning from first principles in Python, R and Octave – Part 1


“You don’t perceive objects as they are. You perceive them as you are.”
“Your interpretation of physical objects has everything to do with the historical trajectory of your brain – and little to do with the objects themselves.”
“The brain generates its own reality, even before it receives information coming in from the eyes and the other senses. This is known as the internal model”

                          David Eagleman - The Brain: The Story of You

This is the first in the series of posts, I intend to write on Deep Learning. This post is inspired by the Deep Learning Specialization by Prof Andrew Ng on Coursera and Neural Networks for Machine Learning by Prof Geoffrey Hinton also on Coursera. In this post I implement Logistic regression with a 2 layer Neural Network i.e. a Neural Network that just has an input layer and an output layer and with no hidden layer.I am certain that any self-respecting Deep Learning/Neural Network would consider a Neural Network without hidden layers as no Neural Network at all!

This 2 layer network is implemented in Python, R and Octave languages. I have included Octave, into the mix, as Octave is a close cousin of Matlab. These implementations in Python, R and Octave are equivalent vectorized implementations. So, if you are familiar in any one of the languages, you should be able to look at the corresponding code in the other two. You can download this R Markdown file and Octave code from DeepLearning -Part 1

Check out my video presentation which discusses the derivations in detail
1. Elements of Neural Networks and Deep Le- Part 1
2. Elements of Neural Networks and Deep Learning – Part 2

To start with, Logistic Regression is performed using sklearn’s logistic regression package for the cancer data set also from sklearn. This is shown below

1. Logistic Regression

import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn.datasets import make_classification, make_blobs

from sklearn.metrics import confusion_matrix
from matplotlib.colors import ListedColormap
from sklearn.datasets import load_breast_cancer
# Load the cancer data
(X_cancer, y_cancer) = load_breast_cancer(return_X_y = True)
X_train, X_test, y_train, y_test = train_test_split(X_cancer, y_cancer,
                                                   random_state = 0)
# Call the Logisitic Regression function
clf = LogisticRegression().fit(X_train, y_train)
print('Accuracy of Logistic regression classifier on training set: {:.2f}'
     .format(clf.score(X_train, y_train)))
print('Accuracy of Logistic regression classifier on test set: {:.2f}'
     .format(clf.score(X_test, y_test)))
## Accuracy of Logistic regression classifier on training set: 0.96
## Accuracy of Logistic regression classifier on test set: 0.96

To check on other classification algorithms, check my post Practical Machine Learning with R and Python – Part 2.

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).

You may also like my companion book “Practical Machine Learning with R and Python:Second Edition- Machine Learning in stereo” available in Amazon in paperback($10.99) and Kindle($7.99/Rs449) versions. This book is ideal for a quick reference of the various ML functions and associated measurements in both R and Python which are essential to delve deep into Deep Learning.

2. Logistic Regression as a 2 layer Neural Network

In the following section Logistic Regression is implemented as a 2 layer Neural Network in Python, R and Octave. The same cancer data set from sklearn will be used to train and test the Neural Network in Python, R and Octave. This can be represented diagrammatically as below

 

The cancer data set has 30 input features, and the target variable ‘output’ is either 0 or 1. Hence the sigmoid activation function will be used in the output layer for classification.

This simple 2 layer Neural Network is shown below
At the input layer there are 30 features and the corresponding weights of these inputs which are initialized to small random values.
Z= w_{1}x_{1} +w_{2}x_{2} +..+ w_{30}x_{30} + b
where ‘b’ is the bias term

The Activation function is the sigmoid function which is a= 1/(1+e^{-z})
The Loss, when the sigmoid function is used in the output layer, is given by
L=-(ylog(a) + (1-y)log(1-a)) (1)

Gradient Descent

Forward propagation

In forward propagation cycle of the Neural Network the output Z and the output of activation function, the sigmoid function, is first computed. Then using the output ‘y’ for the given features, the ‘Loss’ is computed using equation (1) above.

Backward propagation

The backward propagation cycle determines how the ‘Loss’ is impacted for small variations from the previous layers upto the input layer. In other words, backward propagation computes the changes in the weights at the input layer, which will minimize the loss. Several cycles of gradient descent are performed in the path of steepest descent to find the local minima. In other words the set of weights and biases, at the input layer, which will result in the lowest loss is computed by gradient descent. The weights at the input layer are decreased by a parameter known as the ‘learning rate’. Too big a ‘learning rate’ can overshoot the local minima, and too small a ‘learning rate’ can take a long time to reach the local minima. This is done for ‘m’ training examples.

Chain rule of differentiation
Let y=f(u)
and u=g(x) then
\partial y/\partial x = \partial y/\partial u * \partial u/\partial x

Derivative of sigmoid
\sigma=1/(1+e^{-z})
Let x= 1 + e^{-z}  then
\sigma = 1/x
\partial \sigma/\partial x = -1/x^{2}
\partial x/\partial z = -e^{-z}
Using the chain rule of differentiation we get
\partial \sigma/\partial z = \partial \sigma/\partial x * \partial x/\partial z
=-1/(1+e^{-z})^{2}* -e^{-z} = e^{-z}/(1+e^{-z})^{2}
Therefore \partial \sigma/\partial z = \sigma(1-\sigma)        -(2)

The 3 equations for the 2 layer Neural Network representation of Logistic Regression are
L=-(y*log(a) + (1-y)*log(1-a))      -(a)
a=1/(1+e^{-Z})      -(b)
Z= w_{1}x_{1} +w_{2}x_{2} +...+ w_{30}x_{30} +b = Z = \sum_{i} w_{i}*x_{i} + b -(c)

The back propagation step requires the computation of dL/dw_{i} and dL/db_{i}. In the case of regression it would be dE/dw_{i} and dE/db_{i} where dE is the Mean Squared Error function.
Computing the derivatives for back propagation we have
dL/da = -(y/a + (1-y)/(1-a))          -(d)
because d/dx(logx) = 1/x
Also from equation (2) we get
da/dZ = a (1-a)                                  – (e)
By chain rule
\partial L/\partial Z = \partial L/\partial a * \partial a/\partial Z
therefore substituting the results of (d) & (e) we get
\partial L/\partial Z = -(y/a + (1-y)/(1-a)) * a(1-a) = a-y         (f)
Finally
\partial L/\partial w_{i}= \partial L/\partial a * \partial a/\partial Z * \partial Z/\partial w_{i}                                                           -(g)
\partial Z/\partial w_{i} = x_{i}            – (h)
and from (f) we have  \partial L/\partial Z =a-y
Therefore  (g) reduces to
\partial L/\partial w_{i} = x_{i}* (a-y) -(i)
Also
\partial L/\partial b = \partial L/\partial a * \partial a/\partial Z * \partial Z/\partial b -(j)
Since
\partial Z/\partial b = 1 and using (f) in (j)
\partial L/\partial b = a-y

The gradient computes the weights at the input layer and the corresponding bias by using the values
of dw_{i} and db
w_{i} := w_{i} -\alpha * dw_{i}
b := b -\alpha * db
I found the computation graph representation in the book Deep Learning: Ian Goodfellow, Yoshua Bengio, Aaron Courville, very useful to visualize and also compute the backward propagation. For the 2 layer Neural Network of Logistic Regression the computation graph is shown below

3. Neural Network for Logistic Regression -Python code (vectorized)

import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split

# Define the sigmoid function
def sigmoid(z):  
    a=1/(1+np.exp(-z))    
    return a

# Initialize
def initialize(dim):
    w = np.zeros(dim).reshape(dim,1)
    b = 0   
    return w

# Compute the loss
def computeLoss(numTraining,Y,A):
    loss=-1/numTraining *np.sum(Y*np.log(A) + (1-Y)*(np.log(1-A)))
    return(loss)

# Execute the forward propagation
def forwardPropagation(w,b,X,Y):
    # Compute Z
    Z=np.dot(w.T,X)+b
    # Determine the number of training samples
    numTraining=float(len(X))
    # Compute the output of the sigmoid activation function 
    A=sigmoid(Z)
    #Compute the loss
    loss = computeLoss(numTraining,Y,A)
    # Compute the gradients dZ, dw and db
    dZ=A-Y
    dw=1/numTraining*np.dot(X,dZ.T)
    db=1/numTraining*np.sum(dZ)
    
    # Return the results as a dictionary
    gradients = {"dw": dw,
             "db": db}
    loss = np.squeeze(loss)
    return gradients,loss

# Compute Gradient Descent    
def gradientDescent(w, b, X, Y, numIerations, learningRate):
    losses=[]
    idx =[]
    # Iterate 
    for i in range(numIerations):
        gradients,loss=forwardPropagation(w,b,X,Y)
        #Get the derivates
        dw = gradients["dw"]
        db = gradients["db"]
        w = w-learningRate*dw
        b = b-learningRate*db

        # Store the loss
        if i % 100 == 0:
            idx.append(i)
            losses.append(loss)      
        # Set params and grads
        params = {"w": w,
                  "b": b}  
        grads = {"dw": dw,
                 "db": db}
    
    return params, grads, losses,idx

# Predict the output for a training set 
def predict(w,b,X):
    size=X.shape[1]
    yPredicted=np.zeros((1,size))
    Z=np.dot(w.T,X)
    # Compute the sigmoid
    A=sigmoid(Z)
    for i in range(A.shape[1]):
        #If the value is > 0.5 then set as 1
        if(A[0][i] > 0.5):
            yPredicted[0][i]=1
        else:
        # Else set as 0
            yPredicted[0][i]=0

    return yPredicted

#Normalize the data   
def normalize(x):
    x_norm = None
    x_norm = np.linalg.norm(x,axis=1,keepdims=True)
    x= x/x_norm
    return x

   
# Run the 2 layer Neural Network on the cancer data set

from sklearn.datasets import load_breast_cancer
# Load the cancer data
(X_cancer, y_cancer) = load_breast_cancer(return_X_y = True)
# Create train and test sets
X_train, X_test, y_train, y_test = train_test_split(X_cancer, y_cancer,
                                                   random_state = 0)
# Normalize the data for better performance
X_train1=normalize(X_train)


# Create weight vectors of zeros. The size is the number of features in the data set=30
w=np.zeros((X_train.shape[1],1))
#w=np.zeros((30,1))
b=0

#Normalize the training data so that gradient descent performs better
X_train1=normalize(X_train)
#Transpose X_train so that we have a matrix as (features, numSamples)
X_train2=X_train1.T

# Reshape to remove the rank 1 array and then transpose
y_train1=y_train.reshape(len(y_train),1)
y_train2=y_train1.T

# Run gradient descent for 4000 times and compute the weights
parameters, grads, costs,idx = gradientDescent(w, b, X_train2, y_train2, numIerations=4000, learningRate=0.75)
w = parameters["w"]
b = parameters["b"]
   

# Normalize X_test
X_test1=normalize(X_test)
#Transpose X_train so that we have a matrix as (features, numSamples)
X_test2=X_test1.T

#Reshape y_test
y_test1=y_test.reshape(len(y_test),1)
y_test2=y_test1.T

# Predict the values for 
yPredictionTest = predict(w, b, X_test2)
yPredictionTrain = predict(w, b, X_train2)

# Print the accuracy
print("train accuracy: {} %".format(100 - np.mean(np.abs(yPredictionTrain - y_train2)) * 100))
print("test accuracy: {} %".format(100 - np.mean(np.abs(yPredictionTest - y_test)) * 100))

# Plot the Costs vs the number of iterations
fig1=plt.plot(idx,costs)
fig1=plt.title("Gradient descent-Cost vs No of iterations")
fig1=plt.xlabel("No of iterations")
fig1=plt.ylabel("Cost")
fig1.figure.savefig("fig1", bbox_inches='tight')
## train accuracy: 90.3755868545 %
## test accuracy: 89.5104895105 %

Note: It can be seen that the Accuracy on the training and test set is 90.37% and 89.51%. This is comparatively poorer than the 96% which the logistic regression of sklearn achieves! But this is mainly because of the absence of hidden layers which is the real power of neural networks.

4. Neural Network for Logistic Regression -R code (vectorized)

source("RFunctions-1.R")
# Define the sigmoid function
sigmoid <- function(z){
    a <- 1/(1+ exp(-z))
    a
}

# Compute the loss
computeLoss <- function(numTraining,Y,A){
    loss <- -1/numTraining* sum(Y*log(A) + (1-Y)*log(1-A))
    return(loss)
}

# Compute forward propagation
forwardPropagation <- function(w,b,X,Y){
    # Compute Z
    Z <- t(w) %*% X +b
    #Set the number of samples
    numTraining <- ncol(X)
    # Compute the activation function
    A=sigmoid(Z) 
    
    #Compute the loss
    loss <- computeLoss(numTraining,Y,A)
    
    # Compute the gradients dZ, dw and db
    dZ<-A-Y
    dw<-1/numTraining * X %*% t(dZ)
    db<-1/numTraining*sum(dZ)
    
    fwdProp <- list("loss" = loss, "dw" = dw, "db" = db)
    return(fwdProp)
}

# Perform one cycle of Gradient descent
gradientDescent <- function(w, b, X, Y, numIerations, learningRate){
    losses <- NULL
    idx <- NULL
    # Loop through the number of iterations
    for(i in 1:numIerations){
        fwdProp <-forwardPropagation(w,b,X,Y)
        #Get the derivatives
        dw <- fwdProp$dw
        db <- fwdProp$db
        #Perform gradient descent
        w = w-learningRate*dw
        b = b-learningRate*db
        l <- fwdProp$loss
        # Stoe the loss
        if(i %% 100 == 0){
            idx <- c(idx,i)
            losses <- c(losses,l)  
        }
    }
    
    # Return the weights and losses
    gradDescnt <- list("w"=w,"b"=b,"dw"=dw,"db"=db,"losses"=losses,"idx"=idx)
   
    return(gradDescnt)
}

# Compute the predicted value for input
predict <- function(w,b,X){
    m=dim(X)[2]
    # Create a ector of 0's
    yPredicted=matrix(rep(0,m),nrow=1,ncol=m)
    Z <- t(w) %*% X +b
    # Compute sigmoid
    A=sigmoid(Z)
    for(i in 1:dim(A)[2]){
        # If A > 0.5 set value as 1
        if(A[1,i] > 0.5)
        yPredicted[1,i]=1
       else
        # Else set as 0
        yPredicted[1,i]=0
    }

    return(yPredicted)
}

# Normalize the matrix
normalize <- function(x){
    #Create the norm of the matrix.Perform the Frobenius norm of the matrix 
    n<-as.matrix(sqrt(rowSums(x^2)))
    #Sweep by rows by norm. Note '1' in the function which performing on every row
    normalized<-sweep(x, 1, n, FUN="/")
    return(normalized)
}

# Run the 2 layer Neural Network on the cancer data set
# Read the data (from sklearn)
cancer <- read.csv("cancer.csv")
# Rename the target variable
names(cancer) <- c(seq(1,30),"output")
# Split as training and test sets
train_idx <- trainTestSplit(cancer,trainPercent=75,seed=5)
train <- cancer[train_idx, ]
test <- cancer[-train_idx, ]

# Set the features
X_train <-train[,1:30]
y_train <- train[,31]
X_test <- test[,1:30]
y_test <- test[,31]
# Create a matrix of 0's with the number of features
w <-matrix(rep(0,dim(X_train)[2]))
b <-0
X_train1 <- normalize(X_train)
X_train2=t(X_train1)

# Reshape  then transpose
y_train1=as.matrix(y_train)
y_train2=t(y_train1)

# Perform gradient descent
gradDescent= gradientDescent(w, b, X_train2, y_train2, numIerations=3000, learningRate=0.77)


# Normalize X_test
X_test1=normalize(X_test)
#Transpose X_train so that we have a matrix as (features, numSamples)
X_test2=t(X_test1)

#Reshape y_test and take transpose
y_test1=as.matrix(y_test)
y_test2=t(y_test1)

# Use the values of the weights generated from Gradient Descent
yPredictionTest = predict(gradDescent$w, gradDescent$b, X_test2)
yPredictionTrain = predict(gradDescent$w, gradDescent$b, X_train2)

sprintf("Train accuracy: %f",(100 - mean(abs(yPredictionTrain - y_train2)) * 100))
## [1] "Train accuracy: 90.845070"
sprintf("test accuracy: %f",(100 - mean(abs(yPredictionTest - y_test)) * 100))
## [1] "test accuracy: 87.323944"
df <-data.frame(gradDescent$idx, gradDescent$losses)
names(df) <- c("iterations","losses")
ggplot(df,aes(x=iterations,y=losses)) + geom_point() + geom_line(col="blue") +
    ggtitle("Gradient Descent - Losses vs No of Iterations") +
    xlab("No of iterations") + ylab("Losses")

4. Neural Network for Logistic Regression -Octave code (vectorized)


1;
# Define sigmoid function
function a = sigmoid(z)
a = 1 ./ (1+ exp(-z));
end
# Compute the loss
function loss=computeLoss(numtraining,Y,A)
loss = -1/numtraining * sum((Y .* log(A)) + (1-Y) .* log(1-A));
end


# Perform forward propagation
function [loss,dw,db,dZ] = forwardPropagation(w,b,X,Y)
% Compute Z
Z = w' * X + b;
numtraining = size(X)(1,2);
# Compute sigmoid
A = sigmoid(Z);


#Compute loss. Note this is element wise product
loss =computeLoss(numtraining,Y,A);
# Compute the gradients dZ, dw and db
dZ = A-Y;
dw = 1/numtraining* X * dZ';
db =1/numtraining*sum(dZ);

end

# Compute Gradient Descent
function [w,b,dw,db,losses,index]=gradientDescent(w, b, X, Y, numIerations, learningRate)
#Initialize losses and idx
losses=[];
index=[];
# Loop through the number of iterations
for i=1:numIerations,
[loss,dw,db,dZ] = forwardPropagation(w,b,X,Y);
# Perform Gradient descent
w = w - learningRate*dw;
b = b - learningRate*db;
if(mod(i,100) ==0)
# Append index and loss
index = [index i];
losses = [losses loss];
endif

end
end

# Determine the predicted value for dataset
function yPredicted = predict(w,b,X)
m = size(X)(1,2);
yPredicted=zeros(1,m);
# Compute Z
Z = w' * X + b;
# Compute sigmoid
A = sigmoid(Z);
for i=1:size(X)(1,2),
# Set predicted as 1 if A > 0,5
if(A(1,i) >= 0.5)
yPredicted(1,i)=1;
else
yPredicted(1,i)=0;
endif
end
end


# Normalize by dividing each value by the sum of squares
function normalized = normalize(x)
# Compute Frobenius norm. Square the elements, sum rows and then find square root
a = sqrt(sum(x .^ 2,2));
# Perform element wise division
normalized = x ./ a;
end


# Split into train and test sets
function [X_train,y_train,X_test,y_test] = trainTestSplit(dataset,trainPercent)
# Create a random index
ix = randperm(length(dataset));
# Split into training
trainSize = floor(trainPercent/100 * length(dataset));
train=dataset(ix(1:trainSize),:);
# And test
test=dataset(ix(trainSize+1:length(dataset)),:);
X_train = train(:,1:30);
y_train = train(:,31);
X_test = test(:,1:30);
y_test = test(:,31);
end


cancer=csvread("cancer.csv");
[X_train,y_train,X_test,y_test] = trainTestSplit(cancer,75);
w=zeros(size(X_train)(1,2),1);
b=0;
X_train1=normalize(X_train);
X_train2=X_train1';
y_train1=y_train';
[w1,b1,dw,db,losses,idx]=gradientDescent(w, b, X_train2, y_train1, numIerations=3000, learningRate=0.75);
# Normalize X_test
X_test1=normalize(X_test);
#Transpose X_train so that we have a matrix as (features, numSamples)
X_test2=X_test1';
y_test1=y_test';
# Use the values of the weights generated from Gradient Descent
yPredictionTest = predict(w1, b1, X_test2);
yPredictionTrain = predict(w1, b1, X_train2);


trainAccuracy=100-mean(abs(yPredictionTrain - y_train1))*100
testAccuracy=100- mean(abs(yPredictionTest - y_test1))*100
trainAccuracy = 90.845
testAccuracy = 89.510
graphics_toolkit('gnuplot')
plot(idx,losses);
title ('Gradient descent- Cost vs No of iterations');
xlabel ("No of iterations");
ylabel ("Cost");

Conclusion
This post starts with a simple 2 layer Neural Network implementation of Logistic Regression. Clearly the performance of this simple Neural Network is comparatively poor to the highly optimized sklearn’s Logistic Regression. This is because the above neural network did not have any hidden layers. Deep Learning & Neural Networks achieve extraordinary performance because of the presence of deep hidden layers

The Deep Learning journey has begun… Don’t miss the bus!
Stay tuned for more interesting posts in Deep Learning!!

References
1. Deep Learning Specialization
2. Neural Networks for Machine Learning
3. Deep Learning, Ian Goodfellow, Yoshua Bengio and Aaron Courville
4. Neural Networks: The mechanics of backpropagation
5. Machine Learning

Also see
1. My book ‘Practical Machine Learning with R and Python’ on Amazon
2. Simplifying Machine Learning: Bias, Variance, regularization and odd facts – Part 4
3. The 3rd paperback & kindle editions of my books on Cricket, now on Amazon
4. Practical Machine Learning with R and Python – Part 4
5. Introducing QCSimulator: A 5-qubit quantum computing simulator in R
6. A Bluemix recipe with MongoDB and Node.js
7. My travels through the realms of Data Science, Machine Learning, Deep Learning and (AI)

To see all posts check Index of posts

My 3 video presentations on “Essential R”


In this post I include my  3 video presentations on the topic “Essential R”. In these 3 presentations I cover the entire landscape of R. I cover the following

  • R Language – The essentials
  • Key R Packages (dplyr, lubridate, ggplot2, etc.)
  • How to create R Markdown and share reports
  • A look at Shiny apps
  • How to create a simple R package

You can download the relevant slide deck and practice code at Essential R

Essential R – Part 1
This video cover basic R data types – character, numeric, vectors, matrices, lists and data frames. It also touches on how to subset these data types

Essential R – Part 2
This video continues on how to subset dataframes (the most important data type) and some important packages. It also presents one of the most important job of a Data Scientist – that of cleaning and shaping the data. This is done with an example unclean data frame. It also  touches on some  key operations of dplyr like select, filter, arrange, summarise and mutate. Other packages like lubridate, quantmod are also included. This presentation also shows how to use base plot and ggplot2

Essential R – Part 3
This final session covers R Markdown , and  touches on some of the key markdown elements. There is a brief overview of a simple Shiny app. Finally this presentation also shows the key steps to create an R package

These 3 R sessions cover most of the basic R topics that we tend to use in a our day-to-day R way of life. With this you should be able to hit the ground running!

Hope you enjoy these video presentation and also hope you have an even greater time with R!

Check out my 2 books on cricket, a) Cricket analytics with cricketr b) Beaten by sheer pace – Cricket analytics with yorkr, now available in both paperback & kindle versions on Amazon!!! Pick up your copies today!

Also see
1. Introducing QCSimulator: A 5-qubit quantum computing simulator in R
2. Computer Vision: Ramblings on derivatives, histograms and contours
3. Designing a Social Web Portal
4. Revisiting Whats up, Watson – Using Watson’s Question and Answer with Bluemix – Part 2
5. Re-introducing cricketr! : An R package to analyze performances of cricketers

To see all my posts click – Index of posts