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soft_means_culstering.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon May 2 18:12:41 2022
@author: karimkhalil
"""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import random
class Cluster():
def __init__(self, N, K, D):
self.N = N
self.K = K
self.D = D
self.means = np.random.randn(self.K,self.D) + np.random.randint(0,5, size=(self.K,self.D))
def euc (self, x,y):
x = np.array(x)
y = np.array(y)
return sum((x-y)**2)
def cost(self, X, R, M):
"""
X: data matrix hoding the data
R: Responsibility matrix holding the weights of the K clusters in the columns
M: cluster centers matrix holding. centers converges to the mean in all iterations
"""
cost = 0
for k in range(len(M)):
# method 1
# for n in range(len(X)):
# cost += R[n,k]*d(M[k], X[n])
# method 2
diff = X - M[k]
sq_distances = (diff * diff).sum(axis=1)
cost += (R[:,k] * sq_distances).sum()
return cost
def create_sample(self):
# ranges = np.zeros((int(self.N / self.K), self.D))
X = np.random.randn(self.N, self.D)
size_k = self.N / self.K
l= []
###### prepare ranges list
beg = 0
end = size_k
for k in range(self.K):
beg = int(k * size_k)
# print(f'from: {beg}')
for d in range(self.D):
end = int(beg + size_k)
l.append((beg, end))
# print(f'to: {end}')
## create array with means
X = np.random.randn(self.N , self.D)
## scale arrays with the means array
for i,j in enumerate(l):
X[j[0]:j[1]] = X[j[0]:j[1]] + self.means[i]
return X
def clusters_hard(self, max_iter = 20):
cluster_centers = np.zeros((self.K,self.D))
X = self.create_sample()
X = np.column_stack([X, np.zeros((self.N,3))]) # extend sample array by columns for distance , identities & number of iterations
# random selection of cluster centers
for k in range(self.K):
z = np.random.choice(self.N)
cluster_centers[k] = X[z,:2]
cluster_centers_original = cluster_centers.copy()
cluster_id = X[:,2]
euc_dist = X[:,3]
saved_cluster_id = []
x_alliter = []
for it in range(max_iter):
old_cluster_id = cluster_id.copy()
saved_cluster_id.append(old_cluster_id)
X[:, 4] = it
for n in range(self.N): # for every observation
l = []
for k in range(self.K): # for every observation calculate the euc distance of the 3 points k
dist = self.euc(X[n,:2], cluster_centers[k])
l.append(dist)
lowest = min(l)
id = l.index(lowest)
X[n,2] = id
cluster_id[n] = id
X[n,3] = dist
euc_dist[n] = dist
## 2: recalculate means & update cluster centers
for k in range(self.K):
cluster_centers[k,:] = X[X[:,2] == k, :2].mean(axis=0) ## new cluster center
x_alliter.append(X.copy())
## check for convergence
if np.all(old_cluster_id == cluster_id):
print(f'converged on step: {it}')
break
XX = np.concatenate(x_alliter)
df = pd.DataFrame(XX , columns = ['x' , 'y' , 'cluster' , 'euc' , 'iteration'])
df_cost = df.groupby('iteration')['euc'].sum().reset_index()
return X, cluster_centers , df , df_cost , x_alliter
def clusters_soft(self, max_iter=20, beta = 3.0):
R = np.zeros((self.N, self.K)) ## responsibility matrix holding the weights
cluster_centers = np.zeros((self.K,self.D))
X = self.create_sample()
X = np.column_stack([X, np.zeros((self.N,3))]) # extend sample array by columns for distance , identities & number of iterations
#random selection of cluster centers
for k in range(self.K):
z = np.random.choice(self.N)
cluster_centers[k] = X[z,:2]
cluster_centers_original = cluster_centers.copy()
cluster_id = X[:,2]
euc_dist = X[:,3]
saved_cluster_id = []
x_alliter = []
costs = []
for it in range(max_iter):
old_cluster_id = cluster_id.copy()
saved_cluster_id.append(old_cluster_id)
X[:, 4] = it
for n in range(self.N): # for every observation
l = []
for k in range(self.K): # for every observation calculate the euc distance of the 3 points k
dist = self.euc(X[n,:2], cluster_centers[k])
exp = np.exp(-0.3 * dist)
l.append(exp)
l2 = [i/ sum(l) for i in l]
R[n] = l2
cluster_centers = R.T@X[:,:2]/R.sum(axis=0, keepdims=True).T
c = self.cost(X[:,:2], R, cluster_centers)
costs.append(c)
# print(c)
if it > 0:
if np.abs(costs[-1] - costs[-2]) < 1e-5:
break
random_colors = np.random.random((self.K, 3))
colors = R.dot(random_colors)
# x_alliter.append(X.copy())
## check for convergence
# if np.all(old_cluster_id == cluster_id):
# print(f'converged on step: {it}')
# break
# XX = np.concatenate(x_alliter)
# df = pd.DataFrame(XX , columns = ['x' , 'y' , 'cluster' , 'euc' , 'iteration'])
# df_cost = df.groupby('iteration')['euc'].sum().reset_index()
return X, R , cluster_centers , colors
cluster = Cluster(400, 4 , 2)
cluster.clusters_soft(100)
# data , cluster_centers , df, df_cost , all_iter = cluster.clusters_hard()
data , R, cluster_centers , colors = cluster.clusters_soft(100)
# data , cluster_centers , df, df_cost , all_iter = cluster.clusters_hard(1)
# print(exp)
# print(exp/sum(exp))
# print(sum(exp/sum(exp)))
# plt.scatter(data[:,0] , data[:,1] , s=40 , marker="o")
# plt.show()
plt.scatter(data[:,0] , data[:,1] , s=40, c=colors, marker="o")
plt.scatter(cluster_centers[:,0] , cluster_centers[:,1] , s=200, c='black' , marker="*")