def assign_data(dataset, clusters):
'''
Calculates the cluster assignments given a dataset and cluster centers
Args:
dataset: Set of points
clusters: Centers of clusters
Returns:
min_dist: List of point classes in the same order they appear in the dataset
'''
dists = square_distance(clusters, dataset) # ||x - mu||
min_dist = tf.argmin(dists, 1) # argmin ||x - mu||
return min_dist
def assign_data(dataset, clusters):
'''
Calculates the cluster assignments given a dataset and cluster centers
Args:
dataset: Set of points
clusters: Centers of clusters
Returns:
min_dist: List of point classes in the same order they appear in the dataset
'''
dists = square_distance(clusters, dataset) # ||x - mu||
min_dist = tf.argmin(dists, 1) # argmin ||x - mu||
return min_dist
def loss_function(mu, data):
'''
Definition of the loss function for K-Means Clustering
L(mu) = sum_n( min_k( x_n - mu_k ) )
Args:
mu: Data cluster centers
data: Data set
Returns:
cost: Definition of the loss
'''
dists = square_distance(mu, data) # ||x - mu||
min_dist = tf.reduce_min(dists, 1) # min ||x - mu||
cost = tf.reduce_mean(min_dist) # sum(min ||x - mu||)
return cost
def loss_function(mu, data):
'''
Definition of the loss function for K-Means Clustering
L(mu) = sum_n( min_k( x_n - mu_k ) )
Args:
mu: Data cluster centers
data: Data set
Returns:
cost: Definition of the loss
'''
dists = square_distance(mu, data) # ||x - mu||
min_dist = tf.reduce_min(dists, 1) # min ||x - mu||
cost = tf.reduce_mean(min_dist) # sum(min ||x - mu||)
return cost
def log_density(x, mu, sigma):
'''
Calculates log P(x | mu, sigma), i.e. the log probability density
function for the mixture of gaussians
Args:
x: Data points
mu: Cluster centers
sigma: Cluster variance
Returns:
Log probability density function of the data
'''
den = tf.sqrt(2 * pi * sigma) # sqrt(2pi*sigma^2)
D = tf.to_float(tf.rank(x))
logp = -D * tf.log(den) # 1/(sqrt(2pi) * sigma)
dists = square_distance(x, mu) # (x - mu)^2
logp -= dists / (2 * sigma) # 1/den - (x - mu)^2 / (2*sigma^2)
return logp
def log_density(x, mu, sigma):
'''
Calculates log P(x | mu, sigma), i.e. the log probability density
function for the mixture of gaussians
Args:
x: Data points
mu: Cluster centers
sigma: Cluster variance
Returns:
Log probability density function of the data
'''
den = tf.sqrt(2 * pi * sigma) # sqrt(2pi*sigma^2)
D = tf.to_float(tf.rank(x))
logp = -D*tf.log(den) # 1/(sqrt(2pi) * sigma)
dists = square_distance(x, mu) # (x - mu)^2
logp -= dists / (2*sigma) # 1/den - (x - mu)^2 / (2*sigma^2)
return logp
