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k-means.py
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k-means.py
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import numpy as np
import random
import cv2
random.seed(7)
np.random.seed(7)
def get_initial_centroids(X, k):
"""
Function picks k random data points from dataset X, recurring points are removed and replaced but new points
so a result we have array of k unique points. Founded points can be used as intial centroids for k means algorithm
Args:
X (numpy.ndarray) : dataset points array, size N:D
k (int): number of centroids
Returns:
(numpy.ndarray): array of k unique initial centroids, size K:D
"""
number_of_samples = X.shape[0]
sample_points_ids = random.sample(range(0, number_of_samples), k)
centroids = [tuple(X[id]) for id in sample_points_ids]
unique_centroids = list(set(centroids))
number_of_unique_centroids = len(unique_centroids)
while number_of_unique_centroids < k:
new_sample_points_ids = random.sample(range(0, number_of_samples), k - number_of_unique_centroids)
new_centroids = [tuple(X[id]) for id in new_sample_points_ids]
unique_centroids = list(set(unique_centroids + new_centroids))
number_of_unique_centroids = len(unique_centroids)
return np.array(unique_centroids)
def get_euclidean_distance(A_matrix, B_matrix):
"""
Function computes euclidean distance between matrix A and B.
E. g. C[2,15] is distance between point 2 from A (A[2]) matrix and point 15 from matrix B (B[15])
Args:
A_matrix (numpy.ndarray): Matrix size N1:D
B_matrix (numpy.ndarray): Matrix size N2:D
Returns:
numpy.ndarray: Matrix size N1:N2
"""
A_square = np.reshape(np.sum(A_matrix * A_matrix, axis=1), (A_matrix.shape[0], 1))
B_square = np.reshape(np.sum(B_matrix * B_matrix, axis=1), (1, B_matrix.shape[0]))
AB = A_matrix @ B_matrix.T
C = -2 * AB + B_square + A_square
return np.sqrt(C)
def get_clusters(X, centroids, distance_mesuring_method):
"""
Function finds k centroids and assigns each of the N points of array X to one centroid
Args:
X (numpy.ndarray): array of sample points, size N:D
centroids (numpy.ndarray): array of centroids, size K:D
distance_mesuring_method (function): function taking 2 Matrices A (N1:D) and B (N2:D) and returning distance
between all points from matrix A and all points from matrix B, size N1:N2
Returns:
dict {cluster_number: list_of_points_in_cluster}
"""
k = centroids.shape[0]
clusters = {}
distance_matrix = distance_mesuring_method(X, centroids)
closest_cluster_ids = np.argmin(distance_matrix, axis=1)
for i in range(k):
clusters[i] = []
for i, cluster_id in enumerate(closest_cluster_ids):
clusters[cluster_id].append(X[i])
return clusters
def has_centroids_covered(previous_centroids, new_centroids, distance_mesuring_method, movement_threshold_delta):
"""
Function checks if any of centroids moved more then MOVEMENT_THRESHOLD_DELTA if not we assume the centroids were founded
Args:
previous_centroids (numpy.ndarray): array of k old centroids, size K:D
new_centroids (numpy.ndarray): array of k new centroids, size K:D
distance_mesuring_method (function): function taking 2 Matrices A (N1:D) and B (N2:D) and returning distance
movement_threshold_delta (float): threshold value, if centroids move less we assume that algorithm covered
Returns: boolean True if centroids coverd False if not
"""
distances_between_old_and_new_centroids = distance_mesuring_method(previous_centroids, new_centroids)
centroids_covered = np.max(distances_between_old_and_new_centroids.diagonal()) <= movement_threshold_delta
return centroids_covered
def perform_k_means_algorithm(X, k, distance_mesuring_method, movement_threshold_delta=0):
"""
Function performs k-means algorithm on a given dataset, finds and returns k centroids
Args:
X (numpy.ndarray) : dataset points array, size N:D
distance_mesuring_method (function): function taking 2 Matrices A (N1:D) and B (N2:D) and returning distance
between all points from matrix A and all points from matrix B, size N1:N2.
k (int): number of centroids
movement_threshold_delta (float): threshold value, if centroids move less we assume that algorithm covered
Returns:
(numpy.ndarray): array of k centroids, size K:D
"""
new_centroids = get_initial_centroids(X=X, k=k)
centroids_covered = False
while not centroids_covered:
previous_centroids = new_centroids
clusters = get_clusters(X, previous_centroids, distance_mesuring_method)
new_centroids = np.array([np.mean(clusters[key], axis=0, dtype=X.dtype) for key in sorted(clusters.keys())])
centroids_covered = has_centroids_covered(previous_centroids, new_centroids, distance_mesuring_method, movement_threshold_delta)
return new_centroids
def get_reduced_colors_image(image, number_of_colors):
"""
Function returns given image with reduced number of colors
Args:
image (numpy.ndarray): original opencv image, function finds its reduced colors form
number_of_colors (integer): number of colors in reduced image
Returns:
(numpy.ndarray): image with reduced number of colors
"""
h, w, d = image.shape
X = np.reshape(image, (h * w, d))
X = np.array(X, dtype=np.int32)
centroids = perform_k_means_algorithm(X, k=number_of_colors, distance_mesuring_method=get_euclidean_distance, movement_threshold_delta=4)
distance_matrix = get_euclidean_distance(X, centroids)
closest_cluster_ids = np.argmin(distance_matrix, axis=1)
X_reconstructed = centroids[closest_cluster_ids]
X_reconstructed = np.array(X_reconstructed, dtype=np.uint8)
reduced_image = np.reshape(X_reconstructed, (h, w, d))
return reduced_image
if __name__ == '__main__':
k_values = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 32, 64, 128, 256]
reconstrutions = []
img = cv2.imread("image.jpg")
for k in k_values:
reduced_colors_image = get_reduced_colors_image(img, k)
cv2.imwrite(f"images/k{k}.jpg", reduced_colors_image)