Day 35: 60 days of Data Science and Machine Learning Series

Principal Component Analysis with a project..

Dimensionality is the number of input variables or features for a dataset and dimensionality reduction is the process through which we reduce the number of input variables in a dataset. A lot of input features makes predictive modeling a more challenging task.

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Principal Component Analysis is a dimensionality-reduction technique used to reduce the dimensionality of large data sets to smaller one, by transforming a large set of variables while preserving the information all along.

In this post, we are going to demonstrate PCA. Data for this project can be found here:

https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data

Let’s dive in!

Import necessary libraries

%matplotlib inline
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
from sklearn.preprocessing import StandardScaler
plt.style.use("ggplot")
plt.rcParams["figure.figsize"] = (15,10)

Load the Data

iris = pd.read_csv('Path to data",header= None)
iris.info()

Output —

<class 'pandas.core.frame.DataFrame'>
Int64Index: 150 entries, 0 to 149
Data columns (total 5 columns):
sepal_length    150 non-null float64
sepal_width     150 non-null float64
petal_length    150 non-null float64
petal_width     150 non-null float64
species         150 non-null object
dtypes: float64(4), object(1)
memory usage: 7.0+ KB

Data Visualization

sns.scatterplot(x=iris.sepal_length,y=iris.sepal_width,hue=iris.species,style=iris.species)

Output —

Data Standardization

X = iris.iloc[:,0:4].values
y=iris.species.values

X= StandardScaler().fit_transform(X)

Compute the Eigenvectors and Eigenvalues

covariance_matrix = np.cov(X.T)
eigen_values, eigen_vectors = np.linalg.eig(covariance_matrix)
print("Eigen Values:",eigen_values)

print("Eigen Vectors:", eigen_vectors)

Output —

Eigen Values: [2.93035378 0.92740362 0.14834223 0.02074601]
Eigen Vectors: [[ 0.52237162 -0.37231836 -0.72101681  0.26199559]
 [-0.26335492 -0.92555649  0.24203288 -0.12413481]
 [ 0.58125401 -0.02109478  0.14089226 -0.80115427]
 [ 0.56561105 -0.06541577  0.6338014   0.52354627]]

Singular Value Decomposition (SVD)

eigen_svd, s, v = np.linalg.svd(X.T)
eigen_svd

Output —

array([[-0.52237162, -0.37231836,  0.72101681,  0.26199559],
       [ 0.26335492, -0.92555649, -0.24203288, -0.12413481],
       [-0.58125401, -0.02109478, -0.14089226, -0.80115427],
       [-0.56561105, -0.06541577, -0.6338014 ,  0.52354627]])

Principal Components

var_e = [(i/sum(eigen_values))*100 for i in eigen_values]
sns.lineplot(x=[1,2,3,4],y=np.cumsum(var_e))
plt.xlabel("No of Components")
plt.show()

Output —

Plot Data

p_m = (eigen_vectors.T[:][:])[:2].T
X_pca = X.dot(p_m)

for species in ('Iris-setosa','Iris-versicolor','Iris-virginica'):
    sns.scatterplot(X_pca[y==species,0],
                   X_pca[y==species,1])

Output —

Day 36 : Coming soon

Follow and Stay tuned. Keep coding :)

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That’s it fellas. Peace out and keep coding :)

Stay Tuned and of-course let me end this post with a quote by Steve Jobs ;)

“You have to be burning with an idea, or a problem, or a wrong that you want to right. If you’re not passionate enough from the start, you’ll never stick it out.”