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How to implement Linear Discriminant Analysis (LDA) using sklearn in python?

Description

To implement LDA using python.

Process

Linear Discriminant Analysis:

  • LDA is used mainly for dimension reduction of a data set.
  • LDA tries to reduce dimensions of the feature set while retaining the information that discriminates output classes.
  • LDA is a supervised dimensionality reduction technique.
  • Its used to avoid overfitting.

Data Re scaling:

  • Standardization is one of the data re scaling method.
  • Data re scaling is an important part of data preparation before applying machine learning algorithms.
  • Standardization refers to shifting the distribution of each attribute to have a mean of zero and a standard deviation of one (unit variance).

Eigen Values:

  • Eigenvalue is a number, it gives how much variance there is in the data in that direction related to output classes.
  • Each feature has own eigen vectors and eigen values.
  • The eigen vector with the highest eigenvalue is therefore the principal component.

Explained Variance:

  • It contains variance ratio for each linear discriminant.
  • First discriminant having more variance data points.
  • Second discriminant having less variance data points.
Sample Code

#import libraries
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
import warnings
warnings.filterwarnings(“ignore”)

#load data set URL
url = “https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data”
names = [‘sepal-length’, ‘sepal-width’, ‘petal-length’, ‘petal-width’, ‘class’]
data = pd.read_csv(url, names=names)

X = data.drop(‘class’,1)

print(“Actual Features before standardizing\n\n”,X.head())

y = data[‘class’]

# Standardizing the features
X_trans = StandardScaler().fit_transform(X)

print(“\n”)
print(“After standardizing the features\n\n”,X_trans)
print(“\n”)

#covariance matrix
covar_matrix = LDA(n_components = 4)

covar_matrix.fit(X_trans,y)

variance = covar_matrix.explained_variance_ratio_

#Cumulative sum of variance
var=np.cumsum(np.round(variance, decimals=3)*100)
print(“Eigen values\n\n”,var)

#plot for variance explained
plt.ylabel(‘% Variance Explained’)
plt.xlabel(‘# of Features’)
plt.title(‘LDA Analysis’)
plt.ylim(30,100.5)
plt.style.context(‘seaborn-whitegrid’)
plt.plot(var)
plt.show()

#Fit LDA for two components
lda = LDA(n_components = 2)
LinearComponents = lda.fit_transform(X_trans, y)

#make it as data frame
finalDf = pd.DataFrame(data = LinearComponents
, columns = [‘linear discriminant 1’, ‘linear discriminant 2’])

print(“After transform X, the linear discriminants are\n\n”,finalDf.head())
print(“\n”)

#data visualizations
print(“2D LDA Visualization\n”)

def visual(df):
np.random.seed(1)
sample_size = 5
df = df.sample(sample_size)
plt.figure(figsize=(8,5))
sns.distplot(finalDf[‘linear discriminant 1’], hist = True, kde = False,kde_kws = {‘linewidth’: 3})
plt.show()
visual(finalDf)
print(“\n”)

def visual1(df):
np.random.seed(1)
sample_size = 5
plt.figure(figsize=(8,5))
sns.distplot(finalDf[‘linear discriminant 2’], hist = True, kde=False,
bins=int(180/5), color = ‘blue’,
hist_kws={‘edgecolor’:’black’})
plt.show()

visual1(finalDf)
print(“\n”)

#scatter plot
ax = sns.scatterplot(x=”linear discriminant 1″, y=”linear discriminant 2″, data=finalDf)
plt.show()
print(“\n”)

print(“The explained variance percentage is:”,lda.explained_variance_ratio_*100)

Screenshots
implement Linear Discriminant Analysis (LDA) using sklearn in python
import seaborn as sns
avoid overfitting
Data re scalling
Actual Features before standardizing
Standardizing the features
Explained Variance
plot for variance explained
Fit LDA for two components
First discriminant having more variance data points