pyclustering.cluster.ema.ema Class Reference

Expectation-Maximization clustering algorithm for Gaussian Mixture Model (GMM). More...

Public Member Functions
def	__init__ (self, data, amount_clusters, means=None, variances=None, observer=None, tolerance=0.00001, iterations=100)
	Initializes Expectation-Maximization algorithm for cluster analysis. More...
def	process (self)
	Run clustering process of the algorithm. More...
def	get_clusters (self)
def	get_centers (self)
def	get_covariances (self)
def	get_probabilities (self)
	Returns 2-dimensional list with belong probability of each object from data to cluster correspondingly, where that first index is for cluster and the second is for point. More...

Detailed Description

Expectation-Maximization clustering algorithm for Gaussian Mixture Model (GMM).

The algorithm provides only clustering services (unsupervised learning). Here an example of data clustering process:

# Read dataset from text file
sample = read_sample(FAMOUS_SAMPLES.SAMPLE_OLD_FAITHFUL);

# Amount of cluster that should be allocated
amount = 2;

# Prepare initial means and covariances using K-Means initializer
initializer = ema_init_type.KMEANS_INITIALIZATION;
initial_means, initial_covariance = ema_initializer(sample, amount).initialize(initializer);

# Lets create observer to see clustering process
observer = ema_observer();

# Create instance of the EM algorithm
ema_instance = ema(sample, amount, initial_means, initial_covariance, observer=observer);

# Run clustering process
ema_instance.process();

# Extract clusters
clusters = ema_instance.get_clusters();
print("Obtained clusters:", clusters);

# Display allocated clusters using visualizer
covariances = ema_instance.get_covariances();
means = ema_instance.get_centers();
ema_visualizer.show_clusters(clusters, sample, covariances, means);

# Show animation process
ema_visualizer.animate_cluster_allocation(sample, observer);

Here is clustering results of the Expectation-Maximization clustering algorithm where popular sample 'OldFaithful' was used. Initial random means and covariances were used in the example. The first step is presented on the left side of the figure and final result (the last step) is on the right side:

See also

ema_visualizer

ema_observer

Definition at line 443 of file ema.py.

Constructor & Destructor Documentation

__init__()

def pyclustering.cluster.ema.ema.__init__	(		self,
			data,
			amount_clusters,
			means = None,
			variances = None,
			observer = None,
			tolerance = 0.00001,
			iterations = 100
	)

Initializes Expectation-Maximization algorithm for cluster analysis.

Parameters

[in]	data	(list): Dataset that should be analysed and where each point (object) is represented by the list of coordinates.
[in]	amount_clusters	(uint): Amount of clusters that should be allocated.
[in]	means	(list): Initial means of clusters (amount of means should be equal to amount of clusters for allocation). If this parameter is 'None' then K-Means algorithm with K-Means++ method will be used for initialization by default.
[in]	variances	(list): Initial cluster variances (or covariances in case of multi-dimensional data). Amount of covariances should be equal to amount of clusters that should be allocated. If this parameter is 'None' then K-Means algorithm with K-Means++ method will be used for initialization by default.
[in]	observer	(ema_observer): Observer for gathering information about clustering process.
[in]	tolerance	(float): Defines stop condition of the algorithm (when difference between current and previous log-likelihood estimation is less then 'tolerance' then clustering is over).
[in]	iterations	(uint): Additional stop condition parameter that defines maximum number of steps that can be performed by the algorithm during clustering process.

Definition at line 491 of file ema.py.

Member Function Documentation

get_centers()

def pyclustering.cluster.ema.ema.get_centers

(

self

)

Returns

(list) Corresponding centers (means) of clusters.

Definition at line 568 of file ema.py.

get_clusters()

def pyclustering.cluster.ema.ema.get_clusters

(

self

)

Returns

(list) Allocated clusters where each cluster is represented by list of indexes of points from dataset, for example, two cluster may have following representation [[0, 1, 4], [2, 3, 5, 6]].

Definition at line 559 of file ema.py.

Referenced by pyclustering.samples.answer_reader.get_cluster_lengths(), and pyclustering.cluster.optics.optics.process().

get_covariances()

def pyclustering.cluster.ema.ema.get_covariances

(

self

)

Returns

(list) Corresponding variances (or covariances in case of multi-dimensional data) of clusters.

Definition at line 577 of file ema.py.

get_probabilities()

def pyclustering.cluster.ema.ema.get_probabilities

(

self

)

Returns 2-dimensional list with belong probability of each object from data to cluster correspondingly, where that first index is for cluster and the second is for point.

# Get belong probablities
probabilities = ema_instance.get_probabilities();

# Show porbability of the fifth element in the first and in the second cluster
index_point = 5;
print("Probability in the first cluster:", probabilities[0][index_point]);
print("Probability in the first cluster:", probabilities[1][index_point]);

Returns

(list) 2-dimensional list with belong probability of each object from data to cluster.

Definition at line 586 of file ema.py.

process()

def pyclustering.cluster.ema.ema.process

(

self

)

Run clustering process of the algorithm.

This method should be called before call 'get_clusters()'.

Definition at line 532 of file ema.py.

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The documentation for this class was generated from the following file:

• pyclustering/cluster/ema.py