def point_and_circle_clustering():
"""
TO BE COMPLETED.
Used in question 2.8
"""
# Generate data and compute number of clusters
X, Y = point_and_circle(600)
num_classes = len(np.unique(Y))
"""
Choose parameters
"""
k = 50
var = 1.0 # exponential_euclidean's sigma^2
chosen_eig_indices = [0, 1] # indices of the ordered eigenvalues to pick
# build laplacian
W = build_similarity_graph(X, var=var, k=k)
L_unn = build_laplacian(W, 'unn')
L_norm = build_laplacian(W, 'rw')
Y_unn = spectral_clustering(L_unn,
chosen_eig_indices,
num_classes=num_classes)
Y_norm = spectral_clustering(L_norm,
chosen_eig_indices,
num_classes=num_classes)
plot_clustering_result(X, Y, L_unn, Y_unn, Y_norm, 1)
def point_and_circle_clustering():
"""
TO BE COMPLETED.
Used in question 2.8
"""
# Generate data and compute number of clusters
X, Y = point_and_circle(600, sigma=.2)
num_classes = len(np.unique(Y))
"""
Choose parameters
"""
k = 0
eps = 0.4
var = 1 # exponential_euclidean's sigma^2
# build laplacian
W = build_similarity_graph(X, var=var, eps=eps, k=k)
L_unn = build_laplacian(W, 'unn')
L_norm = build_laplacian(W, 'rw')
Y_unn = spectral_clustering_adaptive(L_unn, num_classes=num_classes)
Y_norm = spectral_clustering_adaptive(L_norm, num_classes=num_classes)
plot_clustering_result(X, Y, L_unn, Y_unn, Y_norm, 1)
def point_and_circle_clustering(eig_max=15):
"""
TO BE COMPLETED.
Used in question 2.8
"""
# Generate data and compute number of clusters
X, Y = point_and_circle(600)
num_classes = len(np.unique(Y))
"""
Choose parameters
"""
k = 0
var = 1.0 # exponential_euclidean's sigma^2
#chosen_eig_indices = [1, 2, 3] # indices of the ordered eigenvalues to pick
if k == 0: # compute epsilon
dists = sd.cdist(
X, X, 'euclidean'
) # dists[i, j] = euclidean distance between x_i and x_j
min_tree = min_span_tree(dists)
l = []
n1, m1 = min_tree.shape
for i in range(n1):
for j in range(m1):
if min_tree[i][j] == True:
l.append(dists[i][j])
#distance_threshold = sorted(l)[-1]
distance_threshold = sorted(l)[-1]
eps = np.exp(-(distance_threshold)**2.0 / (2 * var))
W = build_similarity_graph(X, var=var, eps=eps, k=k)
# build laplacian
else:
W = build_similarity_graph(X, var=var, k=k)
L_unn = build_laplacian(W, 'unn')
L_norm = build_laplacian(W, 'sym')
#eigenvalues,U = np.linalg.eig(L_unn)
#indexes = np.argsort(eigenvalues)
#eigenvalues = eigenvalues[indexes]
#U = U[:,indexes]
#chosen_eig_indices = choose_eigenvalues(eigenvalues, eig_max = eig_max)
chosen_eig_indices = [0, 1]
Y_unn = spectral_clustering(L_unn,
chosen_eig_indices,
num_classes=num_classes)
Y_norm = spectral_clustering(L_norm,
chosen_eig_indices,
num_classes=num_classes)
plot_clustering_result(X, Y, L_unn, Y_unn, Y_norm, 1)
distance_threshold = np.max(dists[min_tree])
eps = np.exp(-distance_threshold**2 / (2 * var))
"""
use the build_similarity_graph function to build the graph W
W: (n x n) dimensional matrix representing
the adjacency matrix of the graph
use plot_graph_matrix to plot the graph
"""
W = build_similarity_graph(X, var=var, eps=eps, k=0)
plot_graph_matrix(X, Y, W)
if __name__ == '__main__':
n = 300
blobs_data, blobs_clusters = blobs(n)
moons_data, moons_clusters = two_moons(n)
point_circle_data, point_circle_clusters = point_and_circle(n)
worst_blobs_data, worst_blobs_clusters = worst_case_blob(n, 1.0)
var = 1
X, Y = moons_data, moons_clusters
n_samples = X.shape[0]
dists = pairwise_distances(X).reshape((n_samples, n_samples))
min_tree = min_span_tree(dists)
eps = np.exp(-np.max(dists[min_tree])**2 / (2 * var))
W_eps = build_similarity_graph(X, var=var, eps=0.6)
W_knn = build_similarity_graph(X, k=15)
plot_graph_matrix(X, Y, W_eps)
plot_graph_matrix(X, Y, W_knn)