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hdbscan.py
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import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import sklearn.datasets as data
from scipy.cluster import hierarchy
from collections import deque
class Utils:
def __init__(self):
pass
@staticmethod
def get_data():
moons, _ = data.make_moons(n_samples=50, noise=0.1)
blobs, _ = data.make_blobs(n_samples=50, centers=[(-0.75, 2.25), (1.0, 2.0)], cluster_std=0.25)
test_data = np.vstack([moons, blobs])
return test_data
@staticmethod
def plot_data(test_data, edges, transformed_distance, color='b'):
sns.set_context('poster')
sns.set_style('white')
sns.set_color_codes()
plot_kwds = {'alpha': 0.5, 's': 80, 'linewidths': 0}
plt.scatter(test_data.T[0], test_data.T[1], color=color, **plot_kwds)
for i in range(test_data.shape[0]):
for j in range(test_data.shape[0]):
if edges[i, j]:
plt.plot([test_data[i, 0], test_data[j, 0]], [test_data[i, 1], test_data[j, 1]], 'k-',
linewidth=transformed_distance[i, j])
plt.show()
return True
@staticmethod
def get_dist(test_data):
dist_mat = np.zeros(shape=(test_data.shape[0], test_data.shape[0]))
for i in range(test_data.shape[0]):
for j in range(test_data.shape[0]):
dist_mat[i, j] = np.sqrt(np.sum([np.square(x-y) for x, y in zip(test_data[i, :], test_data[j, :])]))
return dist_mat
@staticmethod
def core_dist(dist_mat, k=5):
core_mat = np.zeros(shape=dist_mat.shape[0])
for i in range(dist_mat.shape[0]):
distance = np.sort(dist_mat[i, :])
core_mat[i] = distance[k-1]
return core_mat
@staticmethod
def transform_space(dist_mat, core_mat):
transformed_dist_mat = np.zeros(shape=(dist_mat.shape[0], dist_mat.shape[0]))
for i in range(dist_mat.shape[0]):
for j in range(dist_mat.shape[0]):
transformed_dist_mat[i, j] = np.amax([core_mat[i], core_mat[j], dist_mat[i, j]])
return transformed_dist_mat
@staticmethod
def prims_algorithm(dist_mat):
not_visited = list(range(1, dist_mat.shape[0]))
edges = np.zeros(shape=(dist_mat.shape[0], dist_mat.shape[0]))
visited = [0]
while len(not_visited):
vertex = np.argmin(dist_mat[visited, :][:, not_visited])
q, r = divmod(int(vertex), len(not_visited))
q, r = visited[q], not_visited[r]
edges[q, r] = dist_mat[q, r]
visited.append(r)
not_visited.remove(r)
return edges
@staticmethod
def cluster_hierarchy(edges, num_points):
out = np.zeros(shape=(num_points-1, 4))
e_sorted = np.argsort(edges.flatten())[-(num_points - 1):]
hierarchy_nodes = {i: [i, 1] for i in range(num_points)}
hierarchy_clusters = {i: [i] for i in range(num_points)}
hierarchy_tree = dict()
curr_hierarchy = num_points - 1
for i in range(e_sorted.shape[0]):
q, r = divmod(e_sorted[i], num_points)
s, t = hierarchy_nodes[q][1], hierarchy_nodes[r][1]
out[i, 0], out[i, 1] = hierarchy_nodes[q][0], hierarchy_nodes[r][0]
out[i, 2] = np.amax(edges[hierarchy_clusters[out[i, 0]], :][:, hierarchy_clusters[out[i, 1]]])
out[i, 3] = s + t
curr_hierarchy += 1
for j in hierarchy_clusters[out[i, 0]]:
hierarchy_nodes[j] = [curr_hierarchy, out[i, 3]]
for k in hierarchy_clusters[out[i, 1]]:
hierarchy_nodes[k] = [curr_hierarchy, out[i, 3]]
hierarchy_clusters.update({curr_hierarchy: hierarchy_clusters[out[i, 0]] + hierarchy_clusters[out[i, 1]]})
hierarchy_tree.update({curr_hierarchy: [[out[i, 0], s], [out[i, 1], t], out[i, 2]]})
return out, hierarchy_tree, hierarchy_clusters
@staticmethod
def plot_dendrogram(out):
dendrogram = hierarchy.dendrogram(out)
plt.show()
return dendrogram
@staticmethod
def condense_cluster_tree(hierarchy_tree, hierarchy_clusters, min_cluster_size, num_points):
clusters_stabilities = dict()
start = (num_points*2) - 2
clusters_stack = deque()
clusters_stack.append(start)
while len(clusters_stack):
i = clusters_stack.pop()
v = hierarchy_tree[i]
cluster_birth = 1/v[2]
points_lambda = []
while v[0][1] < min_cluster_size or v[1][1] < min_cluster_size:
next_v = None
if v[0][1] < min_cluster_size:
for _ in hierarchy_clusters[v[0][0]]:
points_lambda.append(1/v[2])
else:
next_v = v[0][0]
if v[1][1] < min_cluster_size:
for _ in hierarchy_clusters[v[1][0]]:
points_lambda.append(1/v[2])
else:
next_v = v[1][0]
v = hierarchy_tree[next_v]
cluster_death_points_fall = len(hierarchy_clusters[i]) - len(points_lambda)
cluster_death = 1/v[2]
sum_stabilities = (cluster_birth - cluster_death) * cluster_death_points_fall
sum_stabilities += -np.sum(np.array(points_lambda) - cluster_birth)
clusters_stabilities.update({i: sum_stabilities})
clusters_stack.append(v[0][0])
clusters_stack.append(v[1][0])
return clusters_stabilities
@staticmethod
def extract_clusters(hierarchy_clusters, clusters_stabilities):
for k, v in hierarchy_clusters.items()[:-1]:
pass
return True
if __name__ == '__main__':
data = Utils.get_data()
dist = Utils.get_dist(data)
core_dist = Utils.core_dist(dist)
transformed_dist = Utils.transform_space(dist, core_dist)
e = Utils.prims_algorithm(transformed_dist)
plot = Utils.plot_data(data, e, transformed_dist)
Z, tree, clusters = Utils.cluster_hierarchy(e, num_points=transformed_dist.shape[0])
# dn = Utils.plot_dendrogram(Z)
c_stabilities = Utils.condense_cluster_tree(tree, clusters, min_cluster_size=5, num_points=transformed_dist.shape[0])
clusters = Utils.extract_clusters(clusters, c_stabilities)