232 lines
6.1 KiB
Python
232 lines
6.1 KiB
Python
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import numpy as np
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import numpy.typing as npt
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from matplotlib import pyplot as plt
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import cv2
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import uz_framework.image as uz_image
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import uz_framework.text as uz_text
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import os
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def one_a() -> None:
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print('Hello')
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def one_b() -> None:
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points = np.loadtxt('./data/points.txt')
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uz_image.compute_PCA(points)
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def one_d() -> None:
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points = np.loadtxt('./data/points.txt')
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U, S, VT = uz_image.compute_PCA(points)
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uz_image.plot_histogram_pca(U, S, VT)
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# U is the matrix of eigenvectors
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# S is the vector of eigenvalues
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# VT is the matrix of eigenvectors
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def one_e() -> None:
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"""
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Now remove the direction of the lowest variance from the input data. This means
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we will project the data into the subspace of the first eigenvector. We can do this
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by transforming the data into the PCA space then setting to 0 the components
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corresponding to the eigenvectors we want to remove. The resulting points can
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then be transformed back to the original space. Project each of the input points to
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PCA space, then project them back to Cartesian space by multiplying them by the
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diminished matrix U.
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"""
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points = np.loadtxt('./data/points.txt')
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U, S, VT, mean = uz_image.compute_PCA(points)
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# Drop all but first eigenvector
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U = U[:, 0:1]
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# Project points into PCA subspace
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y_i = np.matmul(points - mean, U)
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# Project points back into original subspace
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x_i = np.matmul(y_i, U.T) + mean
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# Plot the original points and the projected points
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plt.scatter(points[:, 0], points[:, 1], c='b', label='Original')
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plt.scatter(x_i[:, 0], x_i[:, 1], c='r', label='Projected')
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plt.show()
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def two_a():
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points = np.loadtxt('./data/points.txt')
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def two_b():
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points = np.loadtxt('./data/points.txt')
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U, S, VT, mean = dual_PCA(points)
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print(U)
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y_i = np.matmul(points - mean, U)
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# Project points back into original subspace
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x_i = np.matmul(y_i, U.T) + mean
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# Plot the original points and the projected points
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plt.scatter(points[:, 0], points[:, 1], c='b', label='Original')
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plt.scatter(x_i[:, 0], x_i[:, 1], c='r', label='Projected')
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plt.show()
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def dual_PCA(points):
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X = points.T.copy()
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mean = np.mean(X, axis=1)
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X = X - mean[:, np.newaxis]
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# Compute the covariance matrix
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C = (1/(X.shape[1]-1)) * X.T @ X
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# Compute the eigenvalues and eigenvectors
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U, S, VT = np.linalg.svd(C)
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S += 1e-15
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U = X @ U @ np.sqrt(np.diag(1/(S * (X.shape[1]-1))))
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return U, S, VT, mean
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def three_a():
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imgs = read_images('./data/faces/1')
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def three_b():
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imgs = read_images('./data/faces/1')
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U, S, VT, mean = dual_PCA(imgs)
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# Plot those eigenvectors
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fig, axs = plt.subplots(1, 5)
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for i in range(5):
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axs[i].imshow(U[:, i].reshape((96, 84)), cmap='gray')
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plt.show()
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# Project images into PCA subspace
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y_i = np.matmul(imgs - mean, U)
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# Project images back into original subspace
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x_i = np.matmul(y_i, U.T) + mean
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# Plot the original images and the projected images
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fig, axs = plt.subplots(1, 5)
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for i in range(5):
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axs[i].imshow(imgs[i].reshape((96, 84)), cmap='gray')
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plt.show()
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img = imgs[0].copy()
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# Add noise to index 4074
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img[4074] = 0
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# Project image into PCA subspace
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y_i = np.matmul(img - mean, U)
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# Project image back into original subspace
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x_i = np.matmul(y_i, U.T) + mean
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# Plot the original image and the projected image
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fig, axs = plt.subplots(1, 2)
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axs[0].imshow(img.reshape((96, 84)), cmap='gray')
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axs[1].imshow(x_i.reshape((96, 84)), cmap='gray')
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plt.show()
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# Count the difference in pixels
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print(np.sum(np.abs(img - x_i)))
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img2 = imgs[0].copy()
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# Project image into PCA subspace
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y_i = np.matmul(img2 - mean, U)
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y_i[0] = 0
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# Project image back into original subspace
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x_i = np.matmul(y_i, U.T) + mean
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# Plot the original image and the projected images
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fig, axs = plt.subplots(1, 2)
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axs[0].imshow(img2.reshape((96, 84)), cmap='gray')
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axs[1].imshow(x_i.reshape((96, 84)), cmap='gray')
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plt.show()
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# Count the number of pixels that are different
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print(np.sum(np.abs(img - x_i)))
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def read_images(data_path):
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imgs = np.array([])
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for filename in os.listdir(data_path):
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img = uz_image.imread_gray(os.path.join(data_path, filename), uz_image.ImageType.float64)
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# Reshape image into a vector
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img = img.reshape((img.shape[0] * img.shape[1], 1))
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if imgs.size == 0:
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imgs = img
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else:
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imgs = np.hstack((imgs, img))
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return imgs.T
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def three_c():
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imgs = read_images('./data/faces/1')
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U, S, VT, mean = dual_PCA(imgs)
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img = imgs[0].copy()
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values = [32, 16, 8, 4, 2, 1]
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for value in values:
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# Projcet image into PCA subspace
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y_i = np.matmul(img - mean, U)
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y_i[value:] = 0
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# Project image back into original subspace
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x_i = np.matmul(y_i, U.T) + mean
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# Plot the original image and the projected images
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fig, axs = plt.subplots(1, 2)
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axs[0].imshow(img.reshape((96, 84)), cmap='gray')
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axs[1].imshow(x_i.reshape((96, 84)), cmap='gray')
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plt.show()
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# Count the number of pixels that are different
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print(np.sum(np.abs(img - x_i)))
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def three_e():
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imgs = read_images('./data/faces/1')
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U, S, VT, mean = dual_PCA(imgs)
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elephant = uz_image.imread_gray('./data/elephant.jpg', uz_image.ImageType.float64)
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elephant = elephant.reshape((elephant.shape[0] * elephant.shape[1], 1)).T
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# Project image into PCA subspace
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y_i = np.matmul(elephant - mean, U)
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# Project image back into original subspace
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x_i = np.matmul(y_i, U.T) + mean
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# Plot the original image and the projected images
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fig, axs = plt.subplots(1, 2)
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axs[0].imshow(elephant.reshape((96, 84)), cmap='gray')
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axs[1].imshow(x_i.reshape((96, 84)), cmap='gray')
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plt.show()
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# ######## #
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# SOLUTION #
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# ######## #
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def main():
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#one_b()
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#one_d()
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#one_e()
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#two_b()
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#three_a()
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#three_c()
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three_e()
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#two_c()
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#ex2()
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#ex3()
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if __name__ == '__main__':
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main()
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