def fuzzy_kmeans(points, k=10, num_iter=10, m=2.0, centers=None):
'''
clustering data points using fuzzy kmeans clustering method.
Args:
points(Expr or DistArray): the input data points matrix.
k(int): the number of clusters.
num_iter(int): the max iterations to run.
m(float): the parameter of fuzzy kmeans.
centers(Expr or DistArray): the initialized centers of each cluster.
'''
points = expr.force(points)
num_dim = points.shape[1]
if centers is None:
centers = expr.rand(k, num_dim)
labels = expr.zeros((points.shape[0],), dtype=np.int)
for iter in range(num_iter):
centers = expr.as_array(centers)
points_broadcast = expr.reshape(points, (points.shape[0], 1, points.shape[1]))
centers_broadcast = expr.reshape(centers, (1, centers.shape[0], centers.shape[1]))
distances = expr.sum(expr.square(points_broadcast - centers_broadcast), axis=2)
# This is used to avoid dividing zero
distances = distances + 0.00000000001
util.log_info('distances shape %s' % str(distances.shape))
distances_broadcast = expr.reshape(distances, (distances.shape[0], 1,
distances.shape[1]))
distances_broadcast2 = expr.reshape(distances, (distances.shape[0],
distances.shape[1], 1))
prob = 1.0 / expr.sum(expr.power(distances_broadcast / distances_broadcast2,
2.0 / (m - 1)), axis=2)
prob.force()
counts = expr.sum(prob, axis=0)
counts = expr.reshape(counts, (counts.shape[0], 1))
labels = expr.argmax(prob, axis=1)
centers = expr.sum(expr.reshape(points, (points.shape[0], 1, points.shape[1])) *
expr.reshape(prob, (prob.shape[0], prob.shape[1], 1)),
axis=0)
# We assume that the size of centers are relative small that can be handled
# on the master.
counts = counts.glom()
centers = centers.glom()
# If any centroids don't have any points assigned to them.
zcount_indices = (counts == 0).reshape(k)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them, which results in their
# position being the zero-vector. We reseed these centroids with new random values
# and set their counts to 1 in order to get rid of dividing by zero.
counts[zcount_indices, :] = 1
centers[zcount_indices, :] = np.random.rand(np.count_nonzero(zcount_indices),
num_dim)
centers = centers / counts
return labels
def fit(self, X, centers=None):
"""Compute k-means clustering.
Parameters
----------
X : spartan matrix, shape=(n_samples, n_features). It should be tiled by rows.
centers : numpy.ndarray. The initial centers. If None, it will be randomly generated.
"""
num_dim = X.shape[1]
num_points = X.shape[0]
labels = expr.zeros((num_points, 1), dtype=np.int)
if centers is None:
centers = expr.from_numpy(np.random.rand(self.n_clusters, num_dim))
for i in range(self.n_iter):
X_broadcast = expr.reshape(X, (X.shape[0], 1, X.shape[1]))
centers_broadcast = expr.reshape(centers, (1, centers.shape[0], centers.shape[1]))
distances = expr.sum(expr.square(X_broadcast - centers_broadcast), axis=2)
labels = expr.argmin(distances, axis=1)
center_idx = expr.arange((1, centers.shape[0]))
matches = expr.reshape(labels, (labels.shape[0], 1)) == center_idx
matches = matches.astype(np.int64)
counts = expr.sum(matches, axis=0)
centers = expr.sum(X_broadcast * expr.reshape(matches, (matches.shape[0],
matches.shape[1], 1)),
axis=0)
counts = counts.optimized().glom()
centers = centers.optimized().glom()
# If any centroids don't have any points assigined to them.
zcount_indices = (counts == 0).reshape(self.n_clusters)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them,
# which results in their position being the zero-vector. We reseed these
# centroids with new random values.
n_points = np.count_nonzero(zcount_indices)
# In order to get rid of dividing by zero.
counts[zcount_indices] = 1
centers[zcount_indices, :] = np.random.randn(n_points, num_dim)
centers = centers / counts.reshape(centers.shape[0], 1)
centers = expr.from_numpy(centers)
return centers, labels
'''
def fit(self, X, centers=None, implementation='outer'):
"""Compute k-means clustering.
Parameters
----------
X : spartan matrix, shape=(n_samples, n_features). It should be tiled by rows.
centers : numpy.ndarray. The initial centers. If None, it will be randomly generated.
"""
num_dim = X.shape[1]
num_points = X.shape[0]
labels = expr.zeros((num_points, 1), dtype=np.int)
if implementation == 'map2':
if centers is None:
centers = np.random.rand(self.n_clusters, num_dim)
for i in range(self.n_iter):
labels = expr.map2(X, 0, fn=kmeans_map2_dist_mapper, fn_kw={"centers": centers},
shape=(X.shape[0], ))
counts = expr.map2(labels, 0, fn=kmeans_count_mapper,
fn_kw={'centers_count': self.n_clusters},
shape=(centers.shape[0], ))
new_centers = expr.map2((X, labels), (0, 0), fn=kmeans_center_mapper,
fn_kw={'centers_count': self.n_clusters},
shape=(centers.shape[0], centers.shape[1]))
counts = counts.optimized().glom()
centers = new_centers.optimized().glom()
# If any centroids don't have any points assigined to them.
zcount_indices = (counts == 0).reshape(self.n_clusters)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them,
# which results in their position being the zero-vector. We reseed these
# centroids with new random values.
n_points = np.count_nonzero(zcount_indices)
# In order to get rid of dividing by zero.
counts[zcount_indices] = 1
centers[zcount_indices, :] = np.random.randn(n_points, num_dim)
centers = centers / counts.reshape(centers.shape[0], 1)
return centers, labels
elif implementation == 'outer':
if centers is None:
centers = expr.rand(self.n_clusters, num_dim)
for i in range(self.n_iter):
labels = expr.outer((X, centers), (0, None), fn=kmeans_outer_dist_mapper,
shape=(X.shape[0],))
#labels = expr.argmin(distances, axis=1)
counts = expr.map2(labels, 0, fn=kmeans_count_mapper,
fn_kw={'centers_count': self.n_clusters},
shape=(centers.shape[0], ))
new_centers = expr.map2((X, labels), (0, 0), fn=kmeans_center_mapper,
fn_kw={'centers_count': self.n_clusters},
shape=(centers.shape[0], centers.shape[1]))
counts = counts.optimized().glom()
centers = new_centers.optimized().glom()
# If any centroids don't have any points assigined to them.
zcount_indices = (counts == 0).reshape(self.n_clusters)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them,
# which results in their position being the zero-vector. We reseed these
# centroids with new random values.
n_points = np.count_nonzero(zcount_indices)
# In order to get rid of dividing by zero.
counts[zcount_indices] = 1
centers[zcount_indices, :] = np.random.randn(n_points, num_dim)
centers = centers / counts.reshape(centers.shape[0], 1)
centers = expr.from_numpy(centers)
return centers, labels
elif implementation == 'broadcast':
if centers is None:
centers = expr.rand(self.n_clusters, num_dim)
for i in range(self.n_iter):
util.log_warn("k_means_ %d %d", i, time.time())
X_broadcast = expr.reshape(X, (X.shape[0], 1, X.shape[1]))
centers_broadcast = expr.reshape(centers, (1, centers.shape[0],
centers.shape[1]))
distances = expr.sum(expr.square(X_broadcast - centers_broadcast), axis=2)
labels = expr.argmin(distances, axis=1)
center_idx = expr.arange((1, centers.shape[0]))
matches = expr.reshape(labels, (labels.shape[0], 1)) == center_idx
matches = matches.astype(np.int64)
counts = expr.sum(matches, axis=0)
centers = expr.sum(X_broadcast * expr.reshape(matches, (matches.shape[0],
matches.shape[1], 1)),
axis=0)
counts = counts.optimized().glom()
centers = centers.optimized().glom()
# If any centroids don't have any points assigined to them.
zcount_indices = (counts == 0).reshape(self.n_clusters)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them,
# which results in their position being the zero-vector. We reseed these
# centroids with new random values.
n_points = np.count_nonzero(zcount_indices)
# In order to get rid of dividing by zero.
counts[zcount_indices] = 1
centers[zcount_indices, :] = np.random.randn(n_points, num_dim)
centers = centers / counts.reshape(centers.shape[0], 1)
centers = expr.from_numpy(centers)
return centers, labels
elif implementation == 'shuffle':
if centers is None:
centers = np.random.rand(self.n_clusters, num_dim)
for i in range(self.n_iter):
# Reset them to zero.
new_centers = expr.ndarray((self.n_clusters, num_dim),
reduce_fn=lambda a, b: a + b)
new_counts = expr.ndarray((self.n_clusters, 1), dtype=np.int,
reduce_fn=lambda a, b: a + b)
_ = expr.shuffle(X,
_find_cluster_mapper,
kw={'d_pts': X,
'old_centers': centers,
'new_centers': new_centers,
'new_counts': new_counts,
'labels': labels},
shape_hint=(1,),
cost_hint={hash(labels): {'00': 0,
'01': np.prod(labels.shape)}})
_.force()
new_counts = new_counts.glom()
new_centers = new_centers.glom()
# If any centroids don't have any points assigined to them.
zcount_indices = (new_counts == 0).reshape(self.n_clusters)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them,
# which results in their position being the zero-vector. We reseed these
# centroids with new random values.
n_points = np.count_nonzero(zcount_indices)
# In order to get rid of dividing by zero.
new_counts[zcount_indices] = 1
new_centers[zcount_indices, :] = np.random.randn(n_points, num_dim)
new_centers = new_centers / new_counts
centers = new_centers
return centers, labels
def fit(self, X, centers=None, implementation='map2'):
"""Compute k-means clustering.
Parameters
----------
X : spartan matrix, shape=(n_samples, n_features). It should be tiled by rows.
centers : numpy.ndarray. The initial centers. If None, it will be randomly generated.
"""
num_dim = X.shape[1]
num_points = X.shape[0]
labels = expr.zeros((num_points, 1), dtype=np.int)
if implementation == 'map2':
if centers is None:
centers = np.random.rand(self.n_clusters, num_dim)
for i in range(self.n_iter):
labels = expr.map2(X,
0,
fn=kmeans_map2_dist_mapper,
fn_kw={"centers": centers},
shape=(X.shape[0], ))
counts = expr.map2(labels,
0,
fn=kmeans_count_mapper,
fn_kw={'centers_count': self.n_clusters},
shape=(centers.shape[0], ))
new_centers = expr.map2(
(X, labels), (0, 0),
fn=kmeans_center_mapper,
fn_kw={'centers_count': self.n_clusters},
shape=(centers.shape[0], centers.shape[1]))
counts = counts.optimized().glom()
centers = new_centers.optimized().glom()
# If any centroids don't have any points assigined to them.
zcount_indices = (counts == 0).reshape(self.n_clusters)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them,
# which results in their position being the zero-vector. We reseed these
# centroids with new random values.
n_points = np.count_nonzero(zcount_indices)
# In order to get rid of dividing by zero.
counts[zcount_indices] = 1
centers[zcount_indices, :] = np.random.randn(
n_points, num_dim)
centers = centers / counts.reshape(centers.shape[0], 1)
return centers, labels
elif implementation == 'outer':
if centers is None:
centers = expr.rand(self.n_clusters, num_dim)
for i in range(self.n_iter):
labels = expr.outer((X, centers), (0, None),
fn=kmeans_outer_dist_mapper,
shape=(X.shape[0], ))
#labels = expr.argmin(distances, axis=1)
counts = expr.map2(labels,
0,
fn=kmeans_count_mapper,
fn_kw={'centers_count': self.n_clusters},
shape=(centers.shape[0], ))
new_centers = expr.map2(
(X, labels), (0, 0),
fn=kmeans_center_mapper,
fn_kw={'centers_count': self.n_clusters},
shape=(centers.shape[0], centers.shape[1]))
counts = counts.optimized().glom()
centers = new_centers.optimized().glom()
# If any centroids don't have any points assigined to them.
zcount_indices = (counts == 0).reshape(self.n_clusters)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them,
# which results in their position being the zero-vector. We reseed these
# centroids with new random values.
n_points = np.count_nonzero(zcount_indices)
# In order to get rid of dividing by zero.
counts[zcount_indices] = 1
centers[zcount_indices, :] = np.random.randn(
n_points, num_dim)
centers = centers / counts.reshape(centers.shape[0], 1)
centers = expr.from_numpy(centers)
return centers, labels
elif implementation == 'broadcast':
if centers is None:
centers = expr.rand(self.n_clusters, num_dim)
for i in range(self.n_iter):
util.log_warn("k_means_ %d %d", i, time.time())
X_broadcast = expr.reshape(X, (X.shape[0], 1, X.shape[1]))
centers_broadcast = expr.reshape(
centers, (1, centers.shape[0], centers.shape[1]))
distances = expr.sum(expr.square(X_broadcast -
centers_broadcast),
axis=2)
labels = expr.argmin(distances, axis=1)
center_idx = expr.arange((1, centers.shape[0]))
matches = expr.reshape(labels,
(labels.shape[0], 1)) == center_idx
matches = matches.astype(np.int64)
counts = expr.sum(matches, axis=0)
centers = expr.sum(
X_broadcast *
expr.reshape(matches,
(matches.shape[0], matches.shape[1], 1)),
axis=0)
counts = counts.optimized().glom()
centers = centers.optimized().glom()
# If any centroids don't have any points assigined to them.
zcount_indices = (counts == 0).reshape(self.n_clusters)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them,
# which results in their position being the zero-vector. We reseed these
# centroids with new random values.
n_points = np.count_nonzero(zcount_indices)
# In order to get rid of dividing by zero.
counts[zcount_indices] = 1
centers[zcount_indices, :] = np.random.randn(
n_points, num_dim)
centers = centers / counts.reshape(centers.shape[0], 1)
centers = expr.from_numpy(centers)
return centers, labels
elif implementation == 'shuffle':
if centers is None:
centers = np.random.rand(self.n_clusters, num_dim)
for i in range(self.n_iter):
# Reset them to zero.
new_centers = expr.ndarray((self.n_clusters, num_dim),
reduce_fn=lambda a, b: a + b)
new_counts = expr.ndarray((self.n_clusters, 1),
dtype=np.int,
reduce_fn=lambda a, b: a + b)
_ = expr.shuffle(X,
_find_cluster_mapper,
kw={
'd_pts': X,
'old_centers': centers,
'new_centers': new_centers,
'new_counts': new_counts,
'labels': labels
},
shape_hint=(1, ),
cost_hint={
hash(labels): {
'00': 0,
'01': np.prod(labels.shape)
}
})
_.force()
new_counts = new_counts.glom()
new_centers = new_centers.glom()
# If any centroids don't have any points assigined to them.
zcount_indices = (new_counts == 0).reshape(self.n_clusters)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them,
# which results in their position being the zero-vector. We reseed these
# centroids with new random values.
n_points = np.count_nonzero(zcount_indices)
# In order to get rid of dividing by zero.
new_counts[zcount_indices] = 1
new_centers[zcount_indices, :] = np.random.randn(
n_points, num_dim)
new_centers = new_centers / new_counts
centers = new_centers
return centers, labels
def fuzzy_kmeans(points, k=10, num_iter=10, m=2.0, centers=None):
'''
clustering data points using fuzzy kmeans clustering method.
Args:
points(Expr or DistArray): the input data points matrix.
k(int): the number of clusters.
num_iter(int): the max iterations to run.
m(float): the parameter of fuzzy kmeans.
centers(Expr or DistArray): the initialized centers of each cluster.
'''
points = expr.force(points)
num_dim = points.shape[1]
if centers is None:
centers = expr.rand(k, num_dim)
labels = expr.zeros((points.shape[0], ), dtype=np.int)
for iter in range(num_iter):
centers = expr.as_array(centers)
points_broadcast = expr.reshape(points,
(points.shape[0], 1, points.shape[1]))
centers_broadcast = expr.reshape(
centers, (1, centers.shape[0], centers.shape[1]))
distances = expr.sum(expr.square(points_broadcast - centers_broadcast),
axis=2)
# This is used to avoid dividing zero
distances = distances + 0.00000000001
util.log_info('distances shape %s' % str(distances.shape))
distances_broadcast = expr.reshape(
distances, (distances.shape[0], 1, distances.shape[1]))
distances_broadcast2 = expr.reshape(
distances, (distances.shape[0], distances.shape[1], 1))
prob = 1.0 / expr.sum(expr.power(
distances_broadcast / distances_broadcast2, 2.0 / (m - 1)),
axis=2)
prob.force()
counts = expr.sum(prob, axis=0)
counts = expr.reshape(counts, (counts.shape[0], 1))
labels = expr.argmax(prob, axis=1)
centers = expr.sum(
expr.reshape(points, (points.shape[0], 1, points.shape[1])) *
expr.reshape(prob, (prob.shape[0], prob.shape[1], 1)),
axis=0)
# We assume that the size of centers are relative small that can be handled
# on the master.
counts = counts.glom()
centers = centers.glom()
# If any centroids don't have any points assigned to them.
zcount_indices = (counts == 0).reshape(k)
if np.any(zcount_indices):
# One or more centroids may not have any points assigned to them, which results in their
# position being the zero-vector. We reseed these centroids with new random values
# and set their counts to 1 in order to get rid of dividing by zero.
counts[zcount_indices, :] = 1
centers[zcount_indices, :] = np.random.rand(
np.count_nonzero(zcount_indices), num_dim)
centers = centers / counts
return labels
