"""

generates data with multiple clusters.

Checked.

"""

mu = 3

range_from_value = .1

if n_clusters == 1:

Z = np.random.multivariate_normal(mean=np.zeros([k, ]), cov=np.eye(k), size=n).transpose()

cluster_ids = np.ones([n])

else:

Z = np.zeros([k, n])

cluster_ids = np.array([random.choice(range(n_clusters)) for i in range(n)])

for id in list(set(cluster_ids)):

idxs = cluster_ids == id

cluster_mu = (np.random.random([k]) - .5) * 5

Z[:, idxs] = np.random.multivariate_normal(mean=cluster_mu, cov=.05 * np.eye(k), size=idxs.sum()).transpose()

A = np.random.random([d, k]) - .5

mu = np.array([(np.random.uniform() * range_from_value * 2 (1 - range_from_value)) * mu for i in range(d)])

sigmas = np.array([(np.random.uniform() * range_from_value * 2 (1 - range_from_value)) * sigma for i in range(d)])

noise = np.zeros([d, n])

for j in range(d):

noise[j, :] = mu[j] np.random.normal(loc=0, scale=sigmas[j], size=n)

X = (np.dot(A, Z) noise).transpose()

Y = deepcopy(X)

Y[Y < 0] = 0

rand_matrix = np.random.random(Y.shape)

cutoff = np.exp(-decay_coef * (Y ** 2))

zero_mask = rand_matrix < cutoff

Y[zero_mask] = 0

print('Fraction of zeros: %2.3f; decay coef: %2.3f' % ((Y == 0).mean(), decay_coef))

import matplotlib.pyplot as plt

random.seed(35)

np.random.seed(32)

n = 200

d = 20

k = 2

sigma = .3

n_clusters = 3

decay_coef = .1

X, Y, Z, ids = generateSimulatedDimensionalityReductionData(n_clusters, n, d, k, sigma, decay_coef)

Zhat, params = block_ZIFA.fitModel(Y, k)

colors = ['red', 'blue', 'green']

cluster_ids = sorted(list(set(ids)))

model = FactorAnalysis(n_components=k)

factor_analysis_Zhat = model.fit_transform(Y)

plt.figure(figsize=[15, 5])

plt.subplot(131)

for id in cluster_ids:

plt.scatter(Z[ids == id, 0], Z[ids == id, 1], color=colors[id - 1], s=4)

plt.title('True Latent Positions\nFraction of Zeros %2.3f' % (Y == 0).mean())

plt.xlim([-4, 4])

plt.ylim([-4, 4])

plt.subplot(132)

for id in cluster_ids:

plt.scatter(Zhat[ids == id, 0], Zhat[ids == id, 1], color=colors[id - 1], s=4)

plt.xlim([-4, 4])

plt.ylim([-4, 4])

plt.title('ZIFA Estimated Latent Positions')

# title(titles[method])

plt.subplot(133)

for id in cluster_ids:

plt.scatter(factor_analysis_Zhat[ids == id, 0], factor_analysis_Zhat[ids == id, 1], color = colors[id - 1], s = 4)

plt.xlim([-4, 4])

plt.ylim([-4, 4])

plt.title('Factor Analysis Estimated Latent Positions')