def test003_cluster(self):
N = 250
mu = np.array([[-2, 0], [2, 2], [1.1, -0.95]])
Sigma = np.array([[[1., -0.1], [-0.1, 1.3]], [[0.6, 0.2], [0.2, 1.8]],
[[2.2, -0.3], [-0.3, 0.7]]])
X1 = np.random.multivariate_normal(mu[0], Sigma[0], size=N // 3)
X2 = np.random.multivariate_normal(mu[1], Sigma[1], size=N // 3)
X3 = np.random.multivariate_normal(mu[2], Sigma[2], size=N // 3)
X = np.vstack((X1, X2, X3))
gmm = GaussianMixtureModel(3, do_logging=True)
gmm.fit(X, callback=plot_progress_2D, num_restarts=5)
x_min, x_max = np.min(X[:, 0]), np.max(X[:, 0])
y_min, y_max = np.min(X[:, 1]), np.max(X[:, 1])
x = np.linspace(1.1 * x_min, 1.1 * x_max, 200)
y = np.linspace(1.1 * y_min, 1.1 * y_max, 200)
xx, yy = np.meshgrid(x, y)
xxyy = np.array([xx.ravel(), yy.ravel()]).T
p = gmm.density(xxyy).reshape(xx.shape)
plt.scatter(X1[:, 0], X1[:, 1], color='r', marker='x')
plt.scatter(X2[:, 0], X2[:, 1], color='m', marker='o')
plt.scatter(X3[:, 0], X3[:, 1], color='g', marker='v')
plt.contourf(x, y, p, alpha=0.5)
plt.colorbar()
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.title('GMM Density Estimates')
plt.show()
return
def test005_cluster_complex(self):
N = 600
K = 5
m = 2
np.random.seed(2718)
mu = 3 * np.random.normal(size=(K, 2))
Sigma = np.stack([np.eye(2)] * K)
for _ in range(m):
L = np.random.multivariate_normal(np.zeros(2), np.eye(2), size=K)
Sigma += np.einsum('kp,kq->kpq', L, L)
Sigma *= 0.5
X = np.random.multivariate_normal(mu[0], Sigma[0], size=N // 2)
for k in range(1, K):
Xk = np.random.multivariate_normal(mu[k], Sigma[k], size=N // 2)
X = np.vstack((X, Xk))
gmm = GaussianMixtureModel(K + 3)
gmm.fit(X, num_restarts=25)
fig = gmm.plot_scatter_density(X)
fig.show()
fig.savefig('example2.png')
plt.show()
return
def test002_basic(self):
N, p = 150, 5
X = np.random.normal(size=(N, p))
K = 2
gmm = GaussianMixtureModel(K, do_logging=True)
gmm.fit(X)
return
def test001_basic(self):
N, p = 150, 2
X = 2 * np.random.normal(size=(N, p))
K = 1 # Number of clusters
gmm = GaussianMixtureModel(num_clusters=K, do_logging=True)
gmm.fit(X)
return
def test007_pruning(self):
N = 200
mu = np.array([[-4, 0], [4, 4]])
Sigma = np.array([[[1., -0.1], [-0.1, 1.3]], [[0.6, 0.2], [0.2, 1.8]]])
X1 = np.random.multivariate_normal(mu[0], Sigma[0], size=N // 2)
X2 = np.random.multivariate_normal(mu[1], Sigma[1], size=N // 2)
X = np.vstack((X1, X2))
gmm = GaussianMixtureModel(200, do_logging=True, prune_clusters=True)
gmm.fit(X, callback=plot_progress_2D, num_restarts=5)
return
def test004_cluster_simple(self):
N = 200
mu = np.array([[-2, 0], [2, 2]])
Sigma = np.array([[[1., -0.1], [-0.1, 1.3]], [[0.6, 0.2], [0.2, 1.8]]])
X1 = np.random.multivariate_normal(mu[0], Sigma[0], size=N // 2)
X2 = np.random.multivariate_normal(mu[1], Sigma[1], size=N // 2)
X = np.vstack((X1, X2))
gmm = GaussianMixtureModel(2)
gmm.fit(X, num_restarts=10)
fig = gmm.plot_scatter_density(X)
fig.savefig('example1.png')
plt.show()
return
def test006_high_dim(self):
N = 600
K = 5
m = 2
p = 10
mu = 3 * np.random.normal(size=(K, p))
Sigma = np.stack([np.eye(p)] * K)
for _ in range(m):
L = np.random.multivariate_normal(np.zeros(p), np.eye(p), size=K)
Sigma += np.einsum('kp,kq->kpq', L, L)
Sigma *= 0.5
X = np.random.multivariate_normal(mu[0], Sigma[0], size=N // 2)
for k in range(1, K):
Xk = np.random.multivariate_normal(mu[k], Sigma[k], size=N // 2)
X = np.vstack((X, Xk))
gmm = GaussianMixtureModel(K + 3)
gmm.fit(X, num_restarts=25)
return