Added visualizing class

soft_k_means_9.py

+import numpy as np
+import matplotlib.pyplot as plt
+
+def d(u, v): # squared difference
+    diff = u - v
+    return diff.dot(diff)
+
+def cost(X, R, M):
+	cost = 0
+	for k in range(len(M)):
+		diff = X - M[k]
+		sq_distances = (diff * diff).sum(axis=1)
+		cost += (R[:,k] * sq_distances).sum()
+	return cost
+
+
+def plot_k_means(X, K, max_iter=20, beta=1.0, show_plots=True):
+	N, D = X.shape
+	M = np.zeros((K, D)) # means
+	exponents = np.empty((N, K))
+
+	for k in range(K):
+		M[k] = X[np.random.choice(N)]
+	costs = np.zeros(max_iter)
+	for i in range(max_iter):
+		for k in range(K):
+			for n in range(N):
+				exponents[n,k] = np.exp(-beta*d(M[k], X[n]))
+
+		R = exponents / exponents.sum(axis=1, keepdims=True)
+		for k in range(K):
+			M[k] = R[:,k].dot(X) / R[:,k].sum()
+		costs[i] = cost(X, R, M)
+		if i > 0:
+			if np.abs(costs[i] - costs[i-1]) < 1e-5:
+				break
+
+	if show_plots:
+		plt.plot(costs)
+		plt.title("Costs")
+		plt.show()
+
+		random_colors = np.random.random((K, 3))
+		colors = R.dot(random_colors)
+		plt.scatter(X[:,0], X[:,1], c=colors)
+		plt.show()
+
+	return M, R
+
+def main():
+	D = 2
+	s = 4
+	mu1 = np.array([0,0])
+	mu2 = np.array([s,s])
+	mu3 = np.array([0,s])
+
+	N = 900
+	X = np.zeros((N, D))
+	X[:300,:] = np.random.randn(300, D) + mu1
+	X[300:600,:] = np.random.randn(300, D) + mu2
+	X[600:,:] = np.random.randn(300, D) + mu3
+
+	plt.scatter(X[:,0], X[:,1], c='green', alpha=0.5)
+	plt.show()
+
+	K = 3
+	plot_k_means(X, K)
+
+	K = 5
+	plot_k_means(X, K, max_iter=30)
+
+	K = 5
+	plot_k_means(X, K, max_iter=30, beta=0.3)
+
+
+if __name__ == '__main__':
+	main()
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visualizing_10.py

+import numpy as np
+import matplotlib.pyplot as plt
+
+def d(u, v): # squared difference
+    diff = u - v
+    return diff.dot(diff)
+
+def cost(X, R, M):
+	cost = 0
+	for k in range(len(M)):
+		diff = X - M[k]
+		sq_distances = (diff * diff).sum(axis=1)
+		cost += (R[:,k] * sq_distances).sum()
+	return cost
+
+
+def plot_k_means(X, K, max_iter=20, beta=1.0, show_plots=True):
+	N, D = X.shape
+	M = np.zeros((K, D)) # means
+	R = np.ones((N, K)) / K
+
+	for k in range(K):
+		M[k] = X[np.random.choice(N)]
+
+
+	grid_width = 5
+	grid_height = max_iter / grid_width
+	random_colors = np.random.random((K, 3))
+	plt.figure()
+
+	costs = np.zeros(max_iter)
+	for i in range(max_iter):
+
+		colors = R.dot(random_colors)
+		plt.subplot(grid_width, grid_height, i+1)
+		plt.scatter(X[:,0], X[:,1], c=colors)
+
+
+		for k in range(K):
+			for n in range(N):
+				R[n,k] = np.exp(-beta*d(M[k], X[n])) / np.sum( np.exp(-beta*d(M[j], X[n])) for j in range(K) )
+
+		for k in range(K):
+			M[k] = R[:,k].dot(X) / R[:,k].sum()
+		costs[i] = cost(X, R, M)
+		if i > 0:
+			if np.abs(costs[i] - costs[i-1]) < 1e-5:
+				break
+	plt.show()
+	return M, R
+
+def main():
+	D = 2
+	s = 4
+	mu1 = np.array([0,0])
+	mu2 = np.array([s,s])
+	mu3 = np.array([0,s])
+
+	N = 900
+	X = np.zeros((N, D))
+	X[:300,:] = np.random.randn(300, D) + mu1
+	X[300:600,:] = np.random.randn(300, D) + mu2
+	X[600:,:] = np.random.randn(300, D) + mu3
+
+	plt.scatter(X[:,0], X[:,1], c='green', alpha=0.5)
+	plt.show()
+
+	K = 3
+	plot_k_means(X, K)
+
+	K = 5
+	plot_k_means(X, K, max_iter=30)
+
+	K = 5
+	plot_k_means(X, K, max_iter=30, beta=0.3)
+
+
+if __name__ == '__main__':
+	main()
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