jupyter
jupytext kernelspec formats text_representation ipynb,md extension format_name format_version jupytext_version .md markdown 1.3 1.14.4 display_name language name Python 3 (ipykernel) python python3

Fisher Linear Discriminant Analysis (LDA)

LDA is a widely used dimensionality reduction technique built on Fisher’s linear discriminant.

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import pandas as pd
import seaborn as sns
from sklearn.preprocessing import MinMaxScaler
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis

Dataset

raw_data = pd.read_csv('data/A_multivariate_study_of_variation_in_two_species_of_rock_crab_of_genus_Leptograpsus.csv')

data = raw_data.rename(columns={
    'sp': 'Species',
    'sex': 'Sex',
    'index': 'Index',
    'FL': 'Frontal Lobe',
    'RW': 'Rear Width',
    'CL': 'Carapace Midline',
    'CW': 'Maximum Width',
    'BD': 'Body Depth'})

data['Species'] = data['Species'].map({'B':'Blue', 'O':'Orange'})
data['Sex'] = data['Sex'].map({'M':'Male', 'F':'Female'})
data['Class'] = data.Species + data.Sex

data_columns = ['Frontal Lobe',
                'Rear Width',
                'Carapace Midline',
                'Maximum Width',
                'Body Depth']

# generate a class variable for all 4 classes
data['Class'] = data.Species + data.Sex

print(data['Class'].value_counts())
data.head(5)

# normalize data columns
data_norm = data.copy()
data_norm[data_columns] = MinMaxScaler().fit_transform(data[data_columns])

data_norm.describe().T

2-Dimensional Plot

no_components = 2

lda = LinearDiscriminantAnalysis(n_components = no_components)
data_lda = lda.fit_transform(data_norm[data_columns].values , y=data_norm['Class'])

data_norm[['LDA1', 'LDA2']] = data_lda

data_norm.head(1)

	Species	Sex	Index	Frontal Lobe	Rear Width	Carapace Midline	Maximum Width	Body Depth	Class	LDA1	LDA2
0	Blue	Male	1	0.056604	0.014599	0.042553	0.050667	0.058065	BlueMale	1.538869	-0.808137

fig = plt.figure(figsize=(10, 8))
sns.scatterplot(x='LDA1', y='LDA2', hue='Class', data=data_norm)

3-Dimensional Plot

no_components = 3

lda = LinearDiscriminantAnalysis(n_components = no_components)
data_lda = lda.fit_transform(data_norm[data_columns].values , y=data_norm['Class'])

data_norm[['LDA1', 'LDA2', 'LDA3']] = data_lda

data_norm.head(1)

	Species	Sex	Index	Frontal Lobe	Rear Width	Carapace Midline	Maximum Width	Body Depth	Class	LDA1	LDA2	LDA3
0	Blue	Male	1	0.056604	0.014599	0.042553	0.050667	0.058065	BlueMale	1.538869	-0.808137	1.18642

class_colours = {
    'BlueMale': '#0027c4', #blue
    'BlueFemale': '#f18b0a', #orange
    'OrangeMale': '#0af10a', # green
    'OrangeFemale': '#ff1500', #red
}

colours = data_norm['Class'].apply(lambda x: class_colours[x])

x=data_norm.LDA1
y=data_norm.LDA2
z=data_norm.LDA3

fig = plt.figure(figsize=(10,10))
plt.title('Linear Discriminant Analysis')
ax = fig.add_subplot(projection='3d')

ax.scatter(xs=x, ys=y, zs=z, s=50, c=colours)