Principal Component Analysis

Class Reference

class pykitml.PCA(data_points, no_components)

This class implements Principle Component Analysis.

__init__(data_points, no_components)

This class implements Principle Component Analysis, used for dimensionality reduction.

Parameters:

data_points (numpy.array) – The dataset to perform PCA i.e. dimensionality reduction on.
no_components (int) – Number of principle components to use.

transform(data_points)

Transforms the input dataset to lower dimensions.

Parameters:: data_points (numpy.array) – The input dataset.
Returns:: transformed_data_points – The transformed input.
Return type:: numpy.array

inverse_transform(pca_points)

Gets the original dataset from transformed points.

Parameters:: pca_points (numpy.array) – The transformed points.

retention: Returns the amount of variance retained, between 0 and 1.

Example: Compressing Fashion MNIST dataset

import os.path
import random

import matplotlib.pyplot as plt
import pykitml as pk
from pykitml.datasets import mnist

# Download dataset
if not os.path.exists('mnist.pkl'):
    mnist.get()

# Load dataset
training_data, _, _, _ = mnist.load()

# Train PCA, reduce 784 dimensions to 250 dimensions
pca = pk.PCA(training_data, 250)
print('Variance retention:', pca.retention)

# Pick random datapoints
indices = random.sample(range(1, 1000), 16)
examples = training_data[indices]

# Show the original images
plt.figure('Original', figsize=(10, 7))
for i in range(1, 17):
    plt.subplot(4, 4, i)
    plt.imshow(examples[i-1].reshape((28, 28)), cmap='gray')

# Transform the example and compress
transformed_examples = pca.transform(examples)

# Inverse transform and recover the examples
recovered_examples = pca.inverse_transform(transformed_examples)

# Show the inverse transformed examples
plt.figure('Recovered', figsize=(10, 7))
for i in range(1, 17):
    plt.subplot(4, 4, i)
    plt.imshow(recovered_examples[i-1].reshape((28, 28)), cmap='gray')

# Show results
plt.show()

Original/Uncompressed

Recovered/Compressed