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from __future__ import print_function, division
import matplotlib.pyplot as plt
import numpy as np
from mlfromscratch.utils import calculate_covariance_matrix, normalize, standardize
class MultiClassLDA():
"""Enables dimensionality reduction for multiple
class distributions. It transforms the features space into a space where
the between class scatter is maximized and the within class scatter is
minimized.
Parameters:
-----------
solver: str
If 'svd' we use the pseudo-inverse to calculate the inverse of matrices
when doing the transformation.
"""
def __init__(self, solver="svd"):
self.solver = solver
def _calculate_scatter_matrices(self, X, y):
n_features = np.shape(X)[1]
labels = np.unique(y)
# Within class scatter matrix:
# SW = sum{ (X_for_class - mean_of_X_for_class)^2 }
# <=> (n_samples_X_for_class - 1) * covar(X_for_class)
SW = np.empty((n_features, n_features))
for label in labels:
_X = X[y == label]
SW += (len(_X) - 1) * calculate_covariance_matrix(_X)
# Between class scatter:
# SB = sum{ n_samples_for_class * (mean_for_class - total_mean)^2 }
total_mean = np.mean(X, axis=0)
SB = np.empty((n_features, n_features))
for label in labels:
_X = X[y == label]
_mean = np.mean(_X, axis=0)
SB += len(_X) * (_mean - total_mean).dot((_mean - total_mean).T)
return SW, SB
def transform(self, X, y, n_components):
SW, SB = self._calculate_scatter_matrices(X, y)
# Determine SW^-1 * SB by calculating inverse of SW
A = np.linalg.inv(SW).dot(SB)
# Get eigenvalues and eigenvectors of SW^-1 * SB
eigenvalues, eigenvectors = np.linalg.eigh(A)
# Sort the eigenvalues and corresponding eigenvectors from largest
# to smallest eigenvalue and select the first n_components
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx][:n_components]
eigenvectors = eigenvectors[:, idx][:, :n_components]
# Project the data onto eigenvectors
X_transformed = X.dot(eigenvectors)
return X_transformed
def plot_in_2d(self, X, y, title=None):
""" Plot the dataset X and the corresponding labels y in 2D using the LDA
transformation."""
X_transformed = self.transform(X, y, n_components=2)
x1 = X_transformed[:, 0]
x2 = X_transformed[:, 1]
plt.scatter(x1, x2, c=y)
if title: plt.title(title)
plt.show()
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