def gauss_dimensions_mean(dimensions=range(2, 100, 20),
total_points=200,
num_experiments=100,
d=None):
# data distribution
k = 2
delta = 0.7
if not d:
d = dimensions[0]
table = np.zeros((num_experiments * len(dimensions), 6))
count = 0
for D in dimensions:
for i in range(num_experiments):
### generate data
m1 = np.zeros(D)
s1 = np.eye(D)
m2 = np.concatenate((delta * np.ones(d), np.zeros(D - d)))
s2 = np.eye(D)
# flip Bernoulli coins to get number of points in each cluster
n1, n2 = np.random.multinomial(total_points, [0.5, 0.5])
# get data, construct gram Matrix
X, z = data.multivariate_normal([m1, m2], [s1, s2], [n1, n2])
rho = lambda x, y: np.linalg.norm(x - y)
G = eclust.kernel_matrix(X, rho)
##################
### cluster with different algorithms
# can change number of times we execute each experiment
# and initialization as well
table[count, 0] = D
table[count, 1] = run_clustering.energy_hartigan(k,
X,
G,
z,
init="k-means++",
run_times=5)
table[count, 2] = run_clustering.energy_lloyd(k,
X,
G,
z,
init="k-means++",
run_times=5)
table[count, 3] = run_clustering.spectral(k, X, G, z, run_times=5)
table[count, 4] = run_clustering.kmeans(k,
X,
z,
init="k-means++",
run_times=5)
table[count, 5] = run_clustering.gmm(k,
X,
z,
init="kmeans",
run_times=5)
####################
count += 1
return table
def cigars_circles(num_experiments=10, run_times=5, kind='cigars'):
table = []
for i in range(num_experiments):
this_experiment = []
if kind == 'cigars':
m1 = [0,0]
m2 = [6.5,0]
s1 = np.array([[1,0],[0,20]])
s2 = np.array([[1,0],[0,20]])
X, z = data.multivariate_normal([m1, m2], [s1, s2], [200, 200])
k = 2
init = 'k-means++'
elif kind == '2circles':
X, z = data.circles([1, 3], [0.2, 0.2], [400, 400])
k = 2
init = 'random'
elif kind == '3circles':
X, z = data.circles([1, 3, 5], [0.2, 0.2, 0.2], [400, 400, 400])
init = 'random'
k = 3
else:
raise ValueError("Don't know which example to sample.")
#sigma = 2
sigma = 1
G = eclust.kernel_matrix(X, rho_standard)
G_half = eclust.kernel_matrix(X, rho_half)
G_exp = eclust.kernel_matrix(X, lambda x,y: rho_exp(x, y, sigma))
G_rbf = eclust.kernel_matrix(X, lambda x,y: rho_rbf(x, y, sigma))
this_experiment.append(
run_clustering.energy_hartigan(k,X,G,z,init=init,
run_times=run_times))
this_experiment.append(
run_clustering.energy_hartigan(k,X,G_half,z,
init=init,run_times=run_times))
this_experiment.append(
run_clustering.energy_hartigan(k,X,G_exp,z,
init=init,run_times=run_times))
this_experiment.append(
run_clustering.energy_hartigan(k,X,G_rbf,z,
init=init,run_times=run_times))
#this_experiment.append(
# run_clustering.spectral(k,X,G_exp,z,run_times=run_times))
this_experiment.append(
run_clustering.spectral(k,X,G_rbf,z,run_times=run_times))
this_experiment.append(
run_clustering.kmeans(k,X,z,init=init,run_times=run_times))
this_experiment.append(
run_clustering.gmm(k,X,z,init="kmeans",run_times=run_times))
this_experiment.append(energy.metric.accuracy(z, energy.gmm.gmm(k,X)))
table.append(this_experiment)
table = np.array(table)
for i in range(8):
print table[:,i].mean(), scipy.stats.sem(table[:,i])
def mnist(num_experiments=10, digits=[0,1,2], num_points=100, run_times=5):
k = len(digits)
f = gzip.open('experiments_data/mnist.pkl.gz', 'rb')
train_set, valid_set, test_set = cPickle.load(f)
f.close()
images_test, labels_test = train_set
images, labels = valid_set
# using training test to compute sigma
X_train, z_train = sample_digits(digits, images_test, labels_test,
num_points)
n, _ = X_train.shape
sigma = np.sqrt(sum([np.linalg.norm(X_train[i]-X_train[j])**2
for i in range(n) for j in range(n)])/(n**2))
print sigma
print
table = []
init = 'k-means++'
for i in range(num_experiments):
this_experiment = []
# now cluster on validation set
X, z = sample_digits(digits, images, labels, num_points)
G = eclust.kernel_matrix(X, rho_standard)
G_half = eclust.kernel_matrix(X, rho_half)
G_exp = eclust.kernel_matrix(X, lambda x,y: rho_exp(x, y, sigma))
G_rbf = eclust.kernel_matrix(X, lambda x,y: rho_rbf(x, y, sigma))
this_experiment.append(
run_clustering.energy_hartigan(k,X,G,z,init=init,
run_times=run_times))
this_experiment.append(
run_clustering.energy_hartigan(k,X,G_half,z,
init=init,run_times=run_times))
this_experiment.append(
run_clustering.energy_hartigan(k,X,G_exp,z,
init=init,run_times=run_times))
this_experiment.append(
run_clustering.energy_hartigan(k,X,G_rbf,z,
init=init,run_times=run_times))
this_experiment.append(
run_clustering.spectral(k,X,G_rbf,z,
run_times=run_times))
this_experiment.append(
run_clustering.kmeans(k,X,z,init="k-means++",run_times=run_times))
this_experiment.append(
run_clustering.gmm(k,X,z,init="kmeans",run_times=run_times))
# my gmm was breaking for some unknown reason
#this_experiment.append(energy.metric.accuracy(z, energy.gmm.gmm(k,X)))
table.append(this_experiment)
table = np.array(table)
for i in range(table[0,:].shape[0]):
print table[:,i].mean(), scipy.stats.sem(table[:,i])
def gauss_dimensions_cov(
dimensions=range(2, 100, 20), total_points=200, num_experiments=100,
d=10):
"""High dimensions but with nontrivial covariance."""
k = 2
if not d:
d = dimensions[0]
table = np.zeros((num_experiments * len(dimensions), 6))
count = 0
for D in dimensions:
for l in range(num_experiments):
# generate data
m1 = np.zeros(D)
m2 = np.concatenate((np.ones(d), np.zeros(D - d)))
s1 = np.eye(D)
# from uniform 1, 5
s2_1 = np.array([
1.367, 3.175, 3.247, 4.403, 1.249, 1.969, 4.035, 4.237, 2.813,
3.637
])
s2 = np.diag(np.concatenate((s2_1, np.ones(D - d))))
n1, n2 = np.random.multinomial(total_points, [0.5, 0.5])
X, z = data.multivariate_normal([m1, m2], [s1, s2], [n1, n2])
rho = lambda x, y: np.linalg.norm(x - y)
G = eclust.kernel_matrix(X, rho)
# can change the number of times we execute each experiment
# and initialization method as well
table[count, 0] = D
table[count, 1] = run_clustering.energy_hartigan(k,
X,
G,
z,
init="k-means++",
run_times=5)
table[count, 2] = run_clustering.energy_lloyd(k,
X,
G,
z,
init="k-means++",
run_times=5)
table[count, 3] = run_clustering.spectral(k, X, G, z, run_times=5)
table[count, 4] = run_clustering.kmeans(k,
X,
z,
init="k-means++",
run_times=5)
table[count, 5] = run_clustering.gmm(k,
X,
z,
init="kmeans",
run_times=5)
count += 1
return table
def gauss_dimensions_pi(num_points=range(0, 180, 10), num_experiments=10):
"""Test unbalanced clusters."""
k = 2
D = 4
d = 2
N = 300
table = np.zeros((num_experiments * len(num_points), 6))
count = 0
for p in num_points:
for i in range(num_experiments):
# generate data
m1 = np.zeros(D)
s1 = np.eye(D)
m2 = np.concatenate((1.5 * np.ones(d), np.zeros(D - d)))
s2 = np.diag(np.concatenate((.5 * np.ones(d), np.ones(D - d))))
pi1 = (N - p) / N / 2.
pi2 = (N + p) / N / 2.
n1, n2 = np.random.multinomial(N, [pi1, pi2])
X, z = data.multivariate_normal([m1, m2], [s1, s2], [n1, n2])
rho = lambda x, y: np.linalg.norm(x - y)
G = eclust.kernel_matrix(X, rho)
table[count, 0] = p
table[count, 1] = run_clustering.energy_hartigan(k,
X,
G,
z,
init="k-means++",
run_times=5)
table[count, 2] = run_clustering.energy_lloyd(k,
X,
G,
z,
init="k-means++",
run_times=5)
table[count, 3] = run_clustering.spectral(k, X, G, z, run_times=5)
table[count, 4] = run_clustering.kmeans(k,
X,
z,
init="k-means++",
run_times=5)
table[count, 5] = run_clustering.gmm(k,
X,
z,
init="kmeans",
run_times=5)
count += 1
return table
def gauss_dimensions_mean(dimensions=range(2,100,20), total_points=200,
num_experiments=100, d=None):
# data distribution
k = 2
delta = 0.7
if not d:
d = dimensions[0]
table = np.zeros((num_experiments*len(dimensions), 6))
count = 0
for D in dimensions:
for i in range(num_experiments):
### generate data
m1 = np.zeros(D)
s1 = np.eye(D)
m2 = np.concatenate((delta*np.ones(d), np.zeros(D-d)))
s2 = np.eye(D)
# flip Bernoulli coins to get number of points in each cluster
n1, n2 = np.random.multinomial(total_points, [0.5,0.5])
# get data, construct gram Matrix
X, z = data.multivariate_normal([m1, m2], [s1, s2], [n1, n2])
rho = lambda x, y: np.linalg.norm(x-y)
G = eclust.kernel_matrix(X, rho)
##################
### cluster with different algorithms
# can change number of times we execute each experiment
# and initialization as well
table[count, 0] = D
table[count, 1] = run_clustering.energy_hartigan(k, X, G, z,
init="k-means++", run_times=5)
table[count, 2] = run_clustering.energy_lloyd(k, X, G, z,
init="k-means++", run_times=5)
table[count, 3] = run_clustering.spectral(k, X, G, z,
run_times=5)
table[count, 4] = run_clustering.kmeans(k, X, z,
init="k-means++", run_times=5)
table[count, 5] = run_clustering.gmm(k, X, z,
init="kmeans", run_times=5)
####################
count += 1
return table
def normal_or_lognormal_difference(
numpoints=range(10, 100, 10), num_experiments=100, kind='normal'):
k = 2
table = []
for n in numpoints:
for i in range(num_experiments):
this_res = [n]
# generate data
D = 20
d = 5
m1 = np.zeros(D)
s1 = 0.5 * np.eye(D)
m2 = 0.5 * np.concatenate((np.ones(d), np.zeros(D - d)))
s2 = np.eye(D)
n1, n2 = np.random.multinomial(n, [0.5, 0.5])
if kind == 'normal':
X, z = data.multivariate_normal([m1, m2], [s1, s2], [n1, n2])
else:
X, z = data.multivariate_lognormal([m1, m2], [s1, s2],
[n1, n2])
rho = lambda x, y: 2 - 2 * np.exp(-np.linalg.norm(x - y) / 2)
G = eclust.kernel_matrix(X, rho)
hart = run_clustering.energy_hartigan(k,
X,
G,
z,
init="k-means++",
run_times=5)
lloyd = run_clustering.energy_lloyd(k,
X,
G,
z,
init="k-means++",
run_times=5)
spectral = run_clustering.spectral(k, X, G, z, run_times=5)
this_res.append(hart - lloyd)
this_res.append(hart - spectral)
table.append(this_res)
table = np.array(table)
return table
def gauss_dimensions_cov(dimensions=range(2,100,20), total_points=200,
num_experiments=100, d=10):
"""High dimensions but with nontrivial covariance."""
k = 2
if not d:
d = dimensions[0]
table = np.zeros((num_experiments*len(dimensions), 6))
count = 0
for D in dimensions:
for l in range(num_experiments):
# generate data
m1 = np.zeros(D)
m2 = np.concatenate((np.ones(d), np.zeros(D-d)))
s1 = np.eye(D)
# from uniform 1, 5
s2_1 = np.array([1.367, 3.175, 3.247, 4.403, 1.249, 1.969, 4.035, 4.237, 2.813, 3.637])
s2 = np.diag(np.concatenate((s2_1, np.ones(D-d))))
n1, n2 = np.random.multinomial(total_points, [0.5,0.5])
X, z = data.multivariate_normal([m1, m2], [s1, s2], [n1, n2])
rho = lambda x, y: np.linalg.norm(x-y)
G = eclust.kernel_matrix(X, rho)
# can change the number of times we execute each experiment
# and initialization method as well
table[count, 0] = D
table[count, 1] = run_clustering.energy_hartigan(k, X, G, z,
init="k-means++", run_times=5)
table[count, 2] = run_clustering.energy_lloyd(k, X, G, z,
init="k-means++", run_times=5)
table[count, 3] = run_clustering.spectral(k, X, G, z,
run_times=5)
table[count, 4] = run_clustering.kmeans(k, X, z,
init="k-means++", run_times=5)
table[count, 5] = run_clustering.gmm(k, X, z,
init="kmeans", run_times=5)
count += 1
return table
def gauss_dimensions_pi(num_points=range(0, 180, 10), num_experiments=10):
"""Test unbalanced clusters."""
k = 2
D = 4
d = 2
N = 300
table = np.zeros((num_experiments*len(num_points), 6))
count = 0
for p in num_points:
for i in range(num_experiments):
# generate data
m1 = np.zeros(D)
s1 = np.eye(D)
m2 = np.concatenate((1.5*np.ones(d), np.zeros(D-d)))
s2 = np.diag(np.concatenate((.5*np.ones(d), np.ones(D-d))))
pi1 = (N-p)/N/2.
pi2 = (N+p)/N/2.
n1, n2 = np.random.multinomial(N, [pi1,pi2])
X, z = data.multivariate_normal([m1, m2], [s1, s2], [n1, n2])
rho = lambda x, y: np.linalg.norm(x-y)
G = eclust.kernel_matrix(X, rho)
table[count, 0] = p
table[count, 1] = run_clustering.energy_hartigan(k, X, G, z,
init="k-means++", run_times=5)
table[count, 2] = run_clustering.energy_lloyd(k, X, G, z,
init="k-means++", run_times=5)
table[count, 3] = run_clustering.spectral(k, X, G, z,
run_times=5)
table[count, 4] = run_clustering.kmeans(k, X, z,
init="k-means++", run_times=5)
table[count, 5] = run_clustering.gmm(k, X, z,
init="kmeans", run_times=5)
count += 1
return table
def normal_or_lognormal_difference(numpoints=range(10,100,10),
num_experiments=100,
kind='normal'):
k = 2
table = []
for n in numpoints:
for i in range(num_experiments):
this_res = [n]
# generate data
D = 20
d = 5
m1 = np.zeros(D)
s1 = 0.5*np.eye(D)
m2 = 0.5*np.concatenate((np.ones(d), np.zeros(D-d)))
s2 = np.eye(D)
n1, n2 = np.random.multinomial(n, [0.5,0.5])
if kind == 'normal':
X, z = data.multivariate_normal([m1, m2], [s1, s2], [n1,n2])
else:
X, z = data.multivariate_lognormal([m1, m2], [s1, s2], [n1,n2])
rho = lambda x, y: 2-2*np.exp(-np.linalg.norm(x-y)/2)
G = eclust.kernel_matrix(X, rho)
hart = run_clustering.energy_hartigan(k, X, G, z,
init="k-means++", run_times=5)
lloyd = run_clustering.energy_lloyd(k, X, G, z,
init="k-means++", run_times=5)
spectral = run_clustering.spectral(k, X, G, z,
run_times=5)
this_res.append(hart-lloyd)
this_res.append(hart-spectral)
table.append(this_res)
table = np.array(table)
return table
# delete missing entries
delete_missing = np.where(data == '?')[0]
data = np.delete(data, delete_missing, axis=0)
data = np.array(data, dtype=float)
true_labels = np.delete(true_labels, delete_missing, axis=0)
# normalize data
data = (data - data.mean(axis=0)) / data.std(axis=0)
G = energy.eclust.kernel_matrix(data, rho)
#G = energy.eclust.kernel_matrix(data, rho_gauss)
#G = energy.eclust.kernel_matrix(data, rho_exp)
kmeans_labels = cluster.kmeans(6, data, run_times=10, init="k-means++")
gmm_labels = cluster.gmm(6, data, run_times=10, init="kmeans")
spectral_labels = cluster.spectral(6, data, G, run_times=10)
energy_spectral_labels = cluster.energy_spectral(6, data, G, run_times=10)
lloyd_labels = cluster.energy_lloyd(6, data, G, run_times=10, init="spectral")
hart_labels = cluster.energy_hartigan(6,
data,
G,
run_times=10,
init="spectral")
t = PrettyTable([
'Algorithm', 'Accuracy', 'A-Rand', 'Mutual Info', 'V-Measure',
'Fowlkes-Mallows'
])
algos = [
'kmeans', 'GMM', 'spectral', 'energy_spectral', 'energy_lloyd',
# delete missing entries
delete_missing = np.where(data=='?')[0]
data = np.delete(data, delete_missing, axis=0)
data = np.array(data, dtype=float)
true_labels = np.delete(true_labels, delete_missing, axis=0)
# normalize data
data = (data - data.mean(axis=0))/data.std(axis=0)
G = energy.eclust.kernel_matrix(data, rho)
#G = energy.eclust.kernel_matrix(data, rho_gauss)
#G = energy.eclust.kernel_matrix(data, rho_exp)
kmeans_labels = cluster.kmeans(6, data, run_times=10, init="k-means++")
gmm_labels = cluster.gmm(6, data, run_times=10, init="kmeans")
spectral_labels = cluster.spectral(6, data, G, run_times=10)
energy_spectral_labels = cluster.energy_spectral(6, data, G, run_times=10)
lloyd_labels = cluster.energy_lloyd(6, data, G, run_times=10, init="spectral")
hart_labels = cluster.energy_hartigan(6,data,G,run_times=10,init="spectral")
t = PrettyTable(['Algorithm', 'Accuracy', 'A-Rand', 'Mutual Info', 'V-Measure',
'Fowlkes-Mallows'])
algos = ['kmeans', 'GMM', 'spectral', 'energy_spectral', 'energy_lloyd',
'energy_hartigan']
pred_labels = [kmeans_labels, gmm_labels, spectral_labels,
energy_spectral_labels, lloyd_labels, hart_labels]
for algo, pred_label in zip(algos, pred_labels):
t.add_row([algo,
energy.metric.accuracy(true_labels, pred_label),