**Introduction**

This is the final and concluding part of my series on ‘Practical Machine Learning with R and Python’. In this series I included the implementations of the most common Machine Learning algorithms in R and Python. The algorithms implemented were

1. Practical Machine Learning with R and Python – Part 1 In this initial post, I touch upon regression of a continuous target variable. Specifically I touch upon Univariate, Multivariate, Polynomial regression and KNN regression in both R and Python

2. Practical Machine Learning with R and Python – Part 2 In this post, I discuss Logistic Regression, KNN classification and Cross Validation error for both LOOCV and K-Fold in both R and Python

3. Practical Machine Learning with R and Python – Part 3 This 3rd part included feature selection in Machine Learning. Specifically I touch best fit, forward fit, backward fit, ridge(L2 regularization) & lasso (L1 regularization). The post includes equivalent code in R and Python.

4. Practical Machine Learning with R and Python – Part 4 In this part I discussed SVMs, Decision Trees, Validation, Precision-Recall, AUC and ROC curves

5. Practical Machine Learning with R and Python – Part 5 In this penultimate part, I touch upon B-splines, natural splines, smoothing spline, Generalized Additive Models(GAMs), Decision Trees, Random Forests and Gradient Boosted Treess.

In this last part I cover Unsupervised Learning. Specifically I cover the implementations of Principal Component Analysis (PCA). K-Means and Heirarchical Clustering. You can download this R Markdown file from Github at MachineLearning-RandPython-Part6

## 1.1a Principal Component Analysis (PCA) – R code

Principal Component Analysis is used to reduce the dimensionality of the input. In the code below 8 x 8 pixel of handwritten digits is reduced into its principal components. Then a scatter plot of the first 2 principal components give a very good visial representation of the data

`library(dplyr)`

```
library(ggplot2)
#Note: This example is adapted from an the example in the book Python Datascience handbook by
# Jake VanderPlas (https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html)
# Read the digits data (From sklearn datasets)
digits= read.csv("digits.csv")
# Create a digits classes target variable
digitClasses <- factor(digits$X0.000000000000000000e.00.29)
#Invoke the Principal Componsent analysis on columns 1-64
digitsPCA=prcomp(digits[,1:64])
# Create a dataframe of PCA
df <- data.frame(digitsPCA$x)
# Bind the digit classes
df1 <- cbind(df,digitClasses)
# Plot only the first 2 Principal components as a scatter plot. This plot uses only the
# first 2 principal components
ggplot(df1,aes(x=PC1,y=PC2,col=digitClasses)) + geom_point() +
ggtitle("Top 2 Principal Components")
```

## 1.1 b Variance explained vs no principal components – R code

In the code below the variance explained vs the number of principal components is plotted. It can be seen that with 20 Principal components almost 90% of the variance is explained by this reduced dimensional model.

```
# Read the digits data (from sklearn datasets)
digits= read.csv("digits.csv")
# Digits target
digitClasses <- factor(digits$X0.000000000000000000e.00.29)
digitsPCA=prcomp(digits[,1:64])
# Get the Standard Deviation
sd=digitsPCA$sdev
```

```
# Compute the variance
digitsVar=digitsPCA$sdev^2
#Compute the percent variance explained
percentVarExp=digitsVar/sum(digitsVar)
# Plot the percent variance exlained as a function of the number of principal components
#plot(cumsum(percentVarExp), xlab="Principal Component",
# ylab="Cumulative Proportion of Variance Explained",
# main="Principal Components vs % Variance explained",ylim=c(0,1),type='l',lwd=2,
# col="blue")
```

## 1.1c Principal Component Analysis (PCA) – Python code

```
import numpy as np
from sklearn.decomposition import PCA
from sklearn import decomposition
from sklearn import datasets
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits
# Load the digits data
digits = load_digits()
# Select only the first 2 principal components
pca = PCA(2) # project from 64 to 2 dimensions
#Compute the first 2 PCA
projected = pca.fit_transform(digits.data)
# Plot a scatter plot of the first 2 principal components
plt.scatter(projected[:, 0], projected[:, 1],
c=digits.target, edgecolor='none', alpha=0.5,
cmap=plt.cm.get_cmap('spectral', 10))
plt.xlabel('PCA 1')
plt.ylabel('PCA 2')
plt.colorbar();
plt.title("Top 2 Principal Components")
plt.savefig('fig1.png', bbox_inches='tight')
```

## 1.1 b Variance vs no principal components

## – Python code

```
import numpy as np
from sklearn.decomposition import PCA
from sklearn import decomposition
from sklearn import datasets
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits
digits = load_digits()
# Select all 64 principal components
pca = PCA(64) # project from 64 to 2 dimensions
projected = pca.fit_transform(digits.data)
# Obtain the explained variance for each principal component
varianceExp= pca.explained_variance_ratio_
# Compute the total sum of variance
totVarExp=np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)
# Plot the variance explained as a function of the number of principal components
plt.plot(totVarExp)
plt.xlabel('No of principal components')
plt.ylabel('% variance explained')
plt.title('No of Principal Components vs Total Variance explained')
plt.savefig('fig2.png', bbox_inches='tight')
```

## 1.2a K-Means – R code

In the code first the scatter plot of the first 2 Principal Components of the handwritten digits is plotted as a scatter plot. Over this plot 10 centroids of the 10 different clusters corresponding the 10 diferent digits is plotted over the original scatter plot.

```
library(ggplot2)
# Read the digits data
digits= read.csv("digits.csv")
# Create digit classes target variable
digitClasses <- factor(digits$X0.000000000000000000e.00.29)
# Compute the Principal COmponents
digitsPCA=prcomp(digits[,1:64])
# Create a data frame of Principal components and the digit classes
df <- data.frame(digitsPCA$x)
df1 <- cbind(df,digitClasses)
# Pick only the first 2 principal components
a<- df[,1:2]
# Compute K Means of 10 clusters and allow for 1000 iterations
k<-kmeans(a,10,1000)
# Create a dataframe of the centroids of the clusters
df2<-data.frame(k$centers)
#Plot the first 2 principal components with the K Means centroids
ggplot(df1,aes(x=PC1,y=PC2,col=digitClasses)) + geom_point() +
geom_point(data=df2,aes(x=PC1,y=PC2),col="black",size = 4) +
ggtitle("Top 2 Principal Components with KMeans clustering")
```

## 1.2b K-Means – Python code

The centroids of the 10 different handwritten digits is plotted over the scatter plot of the first 2 principal components.

```
import numpy as np
from sklearn.decomposition import PCA
from sklearn import decomposition
from sklearn import datasets
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits
from sklearn.cluster import KMeans
digits = load_digits()
# Select only the 1st 2 principal components
pca = PCA(2) # project from 64 to 2 dimensions
projected = pca.fit_transform(digits.data)
# Create 10 different clusters
kmeans = KMeans(n_clusters=10)
# Compute the clusters
kmeans.fit(projected)
y_kmeans = kmeans.predict(projected)
# Get the cluster centroids
centers = kmeans.cluster_centers_
centers
#Create a scatter plot of the first 2 principal components
plt.scatter(projected[:, 0], projected[:, 1],
c=digits.target, edgecolor='none', alpha=0.5,
cmap=plt.cm.get_cmap('spectral', 10))
plt.xlabel('PCA 1')
plt.ylabel('PCA 2')
plt.colorbar();
# Overlay the centroids on the scatter plot
plt.scatter(centers[:, 0], centers[:, 1], c='darkblue', s=100)
plt.savefig('fig3.png', bbox_inches='tight')
```

## 1.3a Heirarchical clusters – R code

Herirachical clusters is another type of unsupervised learning. It successively joins the closest pair of objects (points or clusters) in succession based on some ‘distance’ metric. In this type of clustering we do not have choose the number of centroids. We can cut the created dendrogram mat an appropriate height to get a desired and reasonable number of clusters These are the following ‘distance’ metrics used while combining successive objects

- Ward
- Complete
- Single
- Average
- Centroid

```
# Read the IRIS dataset
iris <- datasets::iris
iris2 <- iris[,-5]
species <- iris[,5]
#Compute the distance matrix
d_iris <- dist(iris2)
# Use the 'average' method to for the clsuters
hc_iris <- hclust(d_iris, method = "average")
# Plot the clusters
plot(hc_iris)
# Cut tree into 3 groups
sub_grp <- cutree(hc_iris, k = 3)
# Number of members in each cluster
table(sub_grp)
```

```
## sub_grp
## 1 2 3
## 50 64 36
```

```
# Draw rectangles around the clusters
rect.hclust(hc_iris, k = 3, border = 2:5)
```

## 1.3a Heirarchical clusters – Python code

```
from sklearn.datasets import load_iris
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import dendrogram, linkage
# Load the IRIS data set
iris = load_iris()
# Generate the linkage matrix using the average method
Z = linkage(iris.data, 'average')
#Plot the dendrogram
#dendrogram(Z)
#plt.xlabel('Data')
#plt.ylabel('Distance')
#plt.suptitle('Samples clustering', fontweight='bold', fontsize=14);
#plt.savefig('fig4.png', bbox_inches='tight')
```

# Conclusion

This is the last and concluding part of my series on Practical Machine Learning with R and Python. These parallel implementations of R and Python can be used as a quick reference while working on a large project. A person who is adept in one of the languages R or Python, can quickly absorb code in the other language.

Hope you find this series useful!

More interesting things to come. Watch this space!

**References**

- Statistical Learning, Prof Trevor Hastie & Prof Robert Tibesherani, Online Stanford
- Applied Machine Learning in Python Prof Kevyn-Collin Thomson, University Of Michigan, Coursera

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5. Bend it like Bluemix, MongoDB using Auto-scale – Part 1!

To see all posts see ‘Index of posts‘