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density.py
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density.py
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# Created on Thu Jul 6 00:32:42 2017
# @author: tom
import numpy as np
def distance_matrix(X, C, COV):
"""
input: X numpy array nxd, matrix of n d-dimensional observations
C numpy array kxd, matrix of k d-dimensional cluster centres
COV numpy array kxdxd, matrix of covariance matrices
output: D numpy array kxn, matrix of distances between every observation
and every center
uses: np.shape(), np.tile(), np.transpose(), np.sum(), np.dot(), np.array()
objective: to find distance based on covariance between every observation
and every center
"""
n = np.shape(X)[0]
k = np.shape(C)[0]
X = np.tile(X, (k, 1, 1))
C = np.tile(C, (n, 1, 1))
C = np.transpose(C, [1, 0, 2])
C = X - C # X_knd - C_knd
D = []
for cluster in range(k):
XCp = C[cluster, :, :]
VI = COV[cluster, :, :]
D.append(np.sum(np.dot(XCp, VI) * XCp, axis=1))
return np.array(D)
def partition_matrix(D):
"""
input: D numpy array kxn, matrix of distances between every observation
and every center
output: U numpy array kxn, matrix of weights
uses: np.exp(), np.sum()
objective: to create partition matrix
"""
U = 1 / (D + np.exp(-100))
U[D < 1] = 1
return U #/ np.sum(U, axis=0, keepdims=True)
def velocity(U):
"""
input: U numpy array kxn, matrix of weights
output: ? numpy array kx1, matrix of sums of weights
uses: np.sum()
objective: to find the velocity of generating objects of every distribution
modeled as a cluster
"""
total = np.sum(U)
if total > 0:
return np.sum(U, axis=1, keepdims=True) / np.sum(U)
else:
return np.sum(U, axis=1, keepdims=True)
def density(X, C, COV):
"""
input: X numpy array nxd, matrix of n d-dimensional observations
C numpy array kxd, matrix of k d-dimensional cluster centres
COV numpy array kxdxd, matrix of covariance matrices
output: ? numpy array kx1, matrix of sums of weights
uses: distanve_matrix(), partition_matrix(), velocity()
objective: to find densities of clusters
"""
D = distance_matrix(X, C, COV)
U = partition_matrix(D)
return velocity(U)