Utils that are used by modules of pyclustering. More...

Namespaces
	color
	Colors used by pyclustering library for visualization.

	graph
	Graph representation (uses format GRPR).

	metric
	Module provides various distance metrics - abstraction of the notion of distance in a metric space.

Functions
def	read_sample (filename)
	Returns data sample from simple text file. More...

def	calculate_distance_matrix (sample)
	Calculates distance matrix for data sample (sequence of points) using Euclidean distance as a metric. More...

def	read_image (filename)
	Returns image as N-dimension (depends on the input image) matrix, where one element of list describes pixel. More...

def	rgb2gray (image_rgb_array)
	Returns image as 1-dimension (gray colored) matrix, where one element of list describes pixel. More...

def	stretch_pattern (image_source)
	Returns stretched content as 1-dimension (gray colored) matrix with size of input image. More...

def	gray_pattern_borders (image)
	Returns coordinates of gray image content on the input image. More...

def	average_neighbor_distance (points, num_neigh)
	Returns average distance for establish links between specified number of nearest neighbors. More...

def	medoid (data, indexes=None, kwargs)
	Calculate medoid for input points using Euclidean distance. More...

def	euclidean_distance (a, b)
	Calculate Euclidean distance between vector a and b. More...

def	euclidean_distance_square (a, b)
	Calculate square Euclidian distance between vector a and b. More...

def	manhattan_distance (a, b)
	Calculate Manhattan distance between vector a and b. More...

def	average_inter_cluster_distance (cluster1, cluster2, data=None)
	Calculates average inter-cluster distance between two clusters. More...

def	average_intra_cluster_distance (cluster1, cluster2, data=None)
	Calculates average intra-cluster distance between two clusters. More...

def	variance_increase_distance (cluster1, cluster2, data=None)
	Calculates variance increase distance between two clusters. More...

def	calculate_ellipse_description (covariance, scale=2.0)
	Calculates description of ellipse using covariance matrix. More...

def	data_corners (data, data_filter=None)
	Finds maximum and minimum corner in each dimension of the specified data. More...

def	norm_vector (vector)
	Calculates norm of an input vector that is known as a vector length. More...

def	heaviside (value)
	Calculates Heaviside function that represents step function. More...

def	timedcall (executable_function, args)
	Executes specified method or function with measuring of execution time. More...

def	extract_number_oscillations (osc_dyn, index=0, amplitude_threshold=1.0)
	Extracts number of oscillations of specified oscillator. More...

def	allocate_sync_ensembles (dynamic, tolerance=0.1, threshold=1.0, ignore=None)
	Allocate clusters in line with ensembles of synchronous oscillators where each synchronous ensemble corresponds to only one cluster. More...

def	draw_clusters (data, clusters, noise=[], marker_descr='.', hide_axes=False, axes=None, display_result=True)
	Displays clusters for data in 2D or 3D. More...

def	draw_dynamics (t, dyn, x_title=None, y_title=None, x_lim=None, y_lim=None, x_labels=True, y_labels=True, separate=False, axes=None)
	Draw dynamics of neurons (oscillators) in the network. More...

def	set_ax_param (ax, x_title=None, y_title=None, x_lim=None, y_lim=None, x_labels=True, y_labels=True, grid=True)
	Sets parameters for matplotlib ax. More...

def	draw_dynamics_set (dynamics, xtitle=None, ytitle=None, xlim=None, ylim=None, xlabels=False, ylabels=False)
	Draw lists of dynamics of neurons (oscillators) in the network. More...

def	draw_image_color_segments (source, clusters, hide_axes=True)
	Shows image segments using colored image. More...

def	draw_image_mask_segments (source, clusters, hide_axes=True)
	Shows image segments using black masks. More...

def	linear_sum (list_vector)
	Calculates linear sum of vector that is represented by list, each element can be represented by list - multidimensional elements. More...

def	square_sum (list_vector)
	Calculates square sum of vector that is represented by list, each element can be represented by list - multidimensional elements. More...

def	list_math_subtraction (a, b)
	Calculates subtraction of two lists. More...

def	list_math_substraction_number (a, b)
	Calculates subtraction between list and number. More...

def	list_math_addition (a, b)
	Addition of two lists. More...

def	list_math_addition_number (a, b)
	Addition between list and number. More...

def	list_math_division_number (a, b)
	Division between list and number. More...

def	list_math_division (a, b)
	Division of two lists. More...

def	list_math_multiplication_number (a, b)
	Multiplication between list and number. More...

def	list_math_multiplication (a, b)
	Multiplication of two lists. More...

Variables
float	pi = 3.1415926535
	The number is a mathematical constant, the ratio of a circle's circumference to its diameter. More...

Detailed Description

Utils that are used by modules of pyclustering.

Authors: Andrei Novikov (pyclu.nosp@m.ster.nosp@m.ing@y.nosp@m.ande.nosp@m.x.ru)

Date: 2014-2019

Copyright: GNU Public License

Function Documentation

◆ allocate_sync_ensembles()

def pyclustering.utils.allocate_sync_ensembles	(	dynamic,
		tolerance = `0.1`,
		threshold = `1.0`,
		ignore = `None`
	)

Allocate clusters in line with ensembles of synchronous oscillators where each synchronous ensemble corresponds to only one cluster.

Parameters

[in]	dynamic	(dynamic): Dynamic of each oscillator.
[in]	tolerance	(double): Maximum error for allocation of synchronous ensemble oscillators.
[in]	threshold	(double): Amlitude trigger when spike is taken into account.
[in]	ignore	(bool): Set of indexes that shouldn't be taken into account.

Returns: (list) Grours (lists) of indexes of synchronous oscillators, for example, [ [index_osc1, index_osc3], [index_osc2], [index_osc4, index_osc5] ].

Definition at line 650 of file __init__.py.

Referenced by pyclustering.nnet.fsync.fsync_dynamic.allocate_sync_ensembles().

◆ average_inter_cluster_distance()

def pyclustering.utils.average_inter_cluster_distance	(	cluster1,
		cluster2,
		data = `None`
	)

Calculates average inter-cluster distance between two clusters.

Clusters can be represented by list of coordinates (in this case data shouldn't be specified), or by list of indexes of points from the data (represented by list of points), in this case data should be specified.

Parameters

[in]	cluster1	(list): The first cluster where each element can represent index from the data or object itself.
[in]	cluster2	(list): The second cluster where each element can represent index from the data or object itself.
[in]	data	(list): If specified than elements of clusters will be used as indexes, otherwise elements of cluster will be considered as points.

Returns: (double) Average inter-cluster distance between two clusters.

Definition at line 351 of file __init__.py.

◆ average_intra_cluster_distance()

def pyclustering.utils.average_intra_cluster_distance	(	cluster1,
		cluster2,
		data = `None`
	)

Calculates average intra-cluster distance between two clusters.

Clusters can be represented by list of coordinates (in this case data shouldn't be specified), or by list of indexes of points from the data (represented by list of points), in this case data should be specified.

Parameters

[in]	cluster1	(list): The first cluster.
[in]	cluster2	(list): The second cluster.
[in]	data	(list): If specified than elements of clusters will be used as indexes, otherwise elements of cluster will be considered as points.

Returns: (double) Average intra-cluster distance between two clusters.

Definition at line 382 of file __init__.py.

◆ average_neighbor_distance()

def pyclustering.utils.average_neighbor_distance	(	points,
		num_neigh
	)

Returns average distance for establish links between specified number of nearest neighbors.

Parameters

[in]	points	(list): Input data, list of points where each point represented by list.
[in]	num_neigh	(uint): Number of neighbors that should be used for distance calculation.

Returns: (double) Average distance for establish links between 'num_neigh' in data set 'points'.

Definition at line 201 of file __init__.py.

◆ calculate_distance_matrix()

def pyclustering.utils.calculate_distance_matrix ( sample )

Calculates distance matrix for data sample (sequence of points) using Euclidean distance as a metric.

Parameters

[in] sample (array_like): Data points that are used for distance calculation.

Returns: (list) Matrix distance between data points.

Definition at line 78 of file __init__.py.

Referenced by pyclustering.utils.metric.chi_square_distance_numpy().

◆ calculate_ellipse_description()

def pyclustering.utils.calculate_ellipse_description	(	covariance,
		scale = `2.0`
	)

Calculates description of ellipse using covariance matrix.

Parameters

[in]	covariance	(numpy.array): Covariance matrix for which ellipse area should be calculated.
[in]	scale	(float): Scale of the ellipse.

Returns: (float, float, float) Return ellipse description: angle, width, height.

Definition at line 502 of file __init__.py.

◆ data_corners()

def pyclustering.utils.data_corners	(	data,
		data_filter = `None`
	)

Finds maximum and minimum corner in each dimension of the specified data.

Parameters

[in]	data	(list): List of points that should be analysed.
[in]	data_filter	(list): List of indexes of the data that should be analysed, if it is 'None' then whole 'data' is analysed to obtain corners.

Returns: (list) Tuple of two points that corresponds to minimum and maximum corner (min_corner, max_corner).

Definition at line 526 of file __init__.py.

◆ draw_clusters()

def pyclustering.utils.draw_clusters	(	data,
		clusters,
		noise = `[]`,
		marker_descr = `'.'`,
		hide_axes = `False`,
		axes = `None`,
		display_result = `True`
	)

Displays clusters for data in 2D or 3D.

Parameters

[in]	data	(list): Points that are described by coordinates represented.
[in]	clusters	(list): Clusters that are represented by lists of indexes where each index corresponds to point in data.
[in]	noise	(list): Points that are regarded to noise.
[in]	marker_descr	(string): Marker for displaying points.
[in]	hide_axes	(bool): If True - axes is not displayed.
[in]	axes	(ax) Matplotlib axes where clusters should be drawn, if it is not specified (None) then new plot will be created.
[in]	display_result	(bool): If specified then matplotlib axes will be used for drawing and plot will not be shown.

Returns: (ax) Matplotlib axes where drawn clusters are presented.

Definition at line 746 of file __init__.py.

Referenced by pyclustering.utils.metric.chi_square_distance_numpy().

◆ draw_dynamics()

def pyclustering.utils.draw_dynamics	(	t,
		dyn,
		x_title = `None`,
		y_title = `None`,
		x_lim = `None`,
		y_lim = `None`,
		x_labels = `True`,
		y_labels = `True`,
		separate = `False`,
		axes = `None`
	)

Draw dynamics of neurons (oscillators) in the network.

It draws if matplotlib is not specified (None), othewise it should be performed manually.

Parameters

[in]	t	(list): Values of time (used by x axis).
[in]	dyn	(list): Values of output of oscillators (used by y axis).
[in]	x_title	(string): Title for Y.
[in]	y_title	(string): Title for X.
[in]	x_lim	(double): X limit.
[in]	y_lim	(double): Y limit.
[in]	x_labels	(bool): If True - shows X labels.
[in]	y_labels	(bool): If True - shows Y labels.
[in]	separate	(list): Consists of lists of oscillators where each such list consists of oscillator indexes that will be shown on separated stage.
[in]	axes	(ax): If specified then matplotlib axes will be used for drawing and plot will not be shown.

Returns: (ax) Axes of matplotlib.

Definition at line 848 of file __init__.py.

Referenced by pyclustering.utils.metric.chi_square_distance_numpy(), pyclustering.utils.draw_dynamics_set(), and pyclustering.nnet.fsync.fsync_visualizer.show_output_dynamic().

◆ draw_dynamics_set()

def pyclustering.utils.draw_dynamics_set	(	dynamics,
		xtitle = `None`,
		ytitle = `None`,
		xlim = `None`,
		ylim = `None`,
		xlabels = `False`,
		ylabels = `False`
	)

Draw lists of dynamics of neurons (oscillators) in the network.

Parameters

[in]	dynamics	(list): List of network outputs that are represented by values of output of oscillators (used by y axis).
[in]	xtitle	(string): Title for Y.
[in]	ytitle	(string): Title for X.
[in]	xlim	(double): X limit.
[in]	ylim	(double): Y limit.
[in]	xlabels	(bool): If True - shows X labels.
[in]	ylabels	(bool): If True - shows Y labels.

Definition at line 976 of file __init__.py.

Referenced by pyclustering.nnet.fsync.fsync_visualizer.show_output_dynamics().

◆ draw_image_color_segments()

def pyclustering.utils.draw_image_color_segments	(	source,
		clusters,
		hide_axes = `True`
	)

Shows image segments using colored image.

Each color on result image represents allocated segment. The first image is initial and other is result of segmentation.

Parameters

[in]	source	(string): Path to image.
[in]	clusters	(list): List of clusters (allocated segments of image) where each cluster consists of indexes of pixel from source image.
[in]	hide_axes	(bool): If True then axes will not be displayed.

Definition at line 1021 of file __init__.py.

◆ draw_image_mask_segments()

def pyclustering.utils.draw_image_mask_segments	(	source,
		clusters,
		hide_axes = `True`
	)

Shows image segments using black masks.

Each black mask of allocated segment is presented on separate plot. The first image is initial and others are black masks of segments.

Parameters

[in]	source	(string): Path to image.
[in]	clusters	(list): List of clusters (allocated segments of image) where each cluster consists of indexes of pixel from source image.
[in]	hide_axes	(bool): If True then axes will not be displayed.

Definition at line 1073 of file __init__.py.

Referenced by pyclustering.utils.metric.chi_square_distance_numpy().

◆ euclidean_distance()

def pyclustering.utils.euclidean_distance	(	a,
		b
	)

Calculate Euclidean distance between vector a and b.

The Euclidean between vectors (points) a and b is calculated by following formula:

$dist(a, b) = \sqrt{ \sum_{i=0}^{N}(b_{i} - a_{i})^{2}) };$

Where N is a length of each vector.

Parameters

[in]	a	(list): The first vector.
[in]	b	(list): The second vector.

Returns: (double) Euclidian distance between two vectors.

Note: This function for calculation is faster then standard function in ~100 times!

Definition at line 283 of file __init__.py.

Referenced by pyclustering.utils.average_neighbor_distance(), and pyclustering.utils.calculate_distance_matrix().

◆ euclidean_distance_square()

def pyclustering.utils.euclidean_distance_square	(	a,
		b
	)

Calculate square Euclidian distance between vector a and b.

Parameters

[in]	a	(list): The first vector.
[in]	b	(list): The second vector.

Returns: (double) Square Euclidian distance between two vectors.

Definition at line 307 of file __init__.py.

Referenced by pyclustering.utils.average_inter_cluster_distance(), pyclustering.utils.average_intra_cluster_distance(), pyclustering.utils.euclidean_distance(), and pyclustering.utils.variance_increase_distance().

◆ extract_number_oscillations()

def pyclustering.utils.extract_number_oscillations	(	osc_dyn,
		index = `0`,
		amplitude_threshold = `1.0`
	)

Extracts number of oscillations of specified oscillator.

Parameters

[in]	osc_dyn	(list): Dynamic of oscillators.
[in]	index	(uint): Index of oscillator in dynamic.
[in]	amplitude_threshold	(double): Amplitude threshold when oscillation is taken into account, for example, when oscillator amplitude is greater than threshold then oscillation is incremented.

Returns: (uint) Number of oscillations of specified oscillator.

Definition at line 611 of file __init__.py.

Referenced by pyclustering.nnet.fsync.fsync_dynamic.extract_number_oscillations().

◆ gray_pattern_borders()

def pyclustering.utils.gray_pattern_borders ( image )

Returns coordinates of gray image content on the input image.

Parameters

[in] image (Image): PIL Image instance that is processed.

Returns: (tuple) Returns coordinates of gray image content as (width_start, height_start, width_end, height_end).

Definition at line 159 of file __init__.py.

Referenced by pyclustering.utils.stretch_pattern().

◆ heaviside()

def pyclustering.utils.heaviside ( value )

Calculates Heaviside function that represents step function.

If input value is greater than 0 then returns 1, otherwise returns 0.

Parameters

[in] value (double): Argument of Heaviside function.

Returns: (double) Value of Heaviside function.

Definition at line 577 of file __init__.py.

◆ linear_sum()

def pyclustering.utils.linear_sum ( list_vector )

Calculates linear sum of vector that is represented by list, each element can be represented by list - multidimensional elements.

Parameters

[in] list_vector (list): Input vector.

Returns: (list|double) Linear sum of vector that can be represented by list in case of multidimensional elements.

Definition at line 1153 of file __init__.py.

◆ list_math_addition()

def pyclustering.utils.list_math_addition	(	a,
		b
	)

Addition of two lists.

Each element from list 'a' is added to element from list 'b' accordingly.

Parameters

[in]	a	(list): List of elements that supports mathematic addition..
[in]	b	(list): List of elements that supports mathematic addition..

Returns: (list) Results of addtion of two lists.

Definition at line 1230 of file __init__.py.

Referenced by pyclustering.utils.variance_increase_distance().

◆ list_math_addition_number()

def pyclustering.utils.list_math_addition_number	(	a,
		b
	)

Addition between list and number.

Each element from list 'a' is added to number 'b'.

Parameters

[in]	a	(list): List of elements that supports mathematic addition.
[in]	b	(double): Value that supports mathematic addition.

Returns: (list) Result of addtion of two lists.

Definition at line 1244 of file __init__.py.

◆ list_math_division()

def pyclustering.utils.list_math_division	(	a,
		b
	)

Division of two lists.

Each element from list 'a' is divided by element from list 'b' accordingly.

Parameters

[in]	a	(list): List of elements that supports mathematic division.
[in]	b	(list): List of elements that supports mathematic division.

Returns: (list) Result of division of two lists.

Definition at line 1272 of file __init__.py.

◆ list_math_division_number()

def pyclustering.utils.list_math_division_number	(	a,
		b
	)

Division between list and number.

Each element from list 'a' is divided by number 'b'.

Parameters

[in]	a	(list): List of elements that supports mathematic division.
[in]	b	(double): Value that supports mathematic division.

Returns: (list) Result of division between list and number.

Definition at line 1258 of file __init__.py.

Referenced by pyclustering.utils.variance_increase_distance().

◆ list_math_multiplication()

def pyclustering.utils.list_math_multiplication	(	a,
		b
	)

Multiplication of two lists.

Each element from list 'a' is multiplied by element from list 'b' accordingly.

Parameters

[in]	a	(list): List of elements that supports mathematic multiplication.
[in]	b	(list): List of elements that supports mathematic multiplication.

Returns: (list) Result of multiplication of elements in two lists.

Definition at line 1300 of file __init__.py.

Referenced by pyclustering.utils.square_sum().

◆ list_math_multiplication_number()

def pyclustering.utils.list_math_multiplication_number	(	a,
		b
	)

Multiplication between list and number.

Each element from list 'a' is multiplied by number 'b'.

Parameters

[in]	a	(list): List of elements that supports mathematic division.
[in]	b	(double): Number that supports mathematic division.

Returns: (list) Result of division between list and number.

Definition at line 1286 of file __init__.py.

◆ list_math_substraction_number()

def pyclustering.utils.list_math_substraction_number	(	a,
		b
	)

Calculates subtraction between list and number.

Each element from list 'a' is subtracted by number 'b'.

Parameters

[in]	a	(list): List of elements that supports mathematical subtraction.
[in]	b	(list): Value that supports mathematical subtraction.

Returns: (list) Results of subtraction between list and number.

Definition at line 1216 of file __init__.py.

◆ list_math_subtraction()

def pyclustering.utils.list_math_subtraction	(	a,
		b
	)

Calculates subtraction of two lists.

Each element from list 'a' is subtracted by element from list 'b' accordingly.

Parameters

[in]	a	(list): List of elements that supports mathematical subtraction.
[in]	b	(list): List of elements that supports mathematical subtraction.

Returns: (list) Results of subtraction of two lists.

Definition at line 1202 of file __init__.py.

◆ manhattan_distance()

def pyclustering.utils.manhattan_distance	(	a,
		b
	)

Calculate Manhattan distance between vector a and b.

Parameters

[in]	a	(list): The first cluster.
[in]	b	(list): The second cluster.

Returns: (double) Manhattan distance between two vectors.

Definition at line 328 of file __init__.py.

◆ medoid()

def pyclustering.utils.medoid	(	data,
		indexes = `None`,
		kwargs
	)

Calculate medoid for input points using Euclidean distance.

Parameters

[in]	data	(list): Set of points for that median should be calculated.
[in]	indexes	(list): Indexes of input set of points that will be taken into account during median calculation.
[in]	**kwargs	Arbitrary keyword arguments (available arguments: 'metric', 'data_type').

Keyword Args:

metric (distance_metric): Metric that is used for distance calculation between two points.
data_type (string): Data type of input sample 'data' (available values: 'points', 'distance_matrix').

Returns: (uint) index of point in input set that corresponds to median.

Definition at line 233 of file __init__.py.

◆ norm_vector()

def pyclustering.utils.norm_vector ( vector )

Calculates norm of an input vector that is known as a vector length.

Parameters

[in] vector (list): The input vector whose length is calculated.

Returns: (double) vector norm known as vector length.

Definition at line 558 of file __init__.py.

◆ read_image()

def pyclustering.utils.read_image ( filename )

Returns image as N-dimension (depends on the input image) matrix, where one element of list describes pixel.

Parameters

[in] filename (string): Path to image.

Returns: (list) Pixels where each pixel described by list of RGB-values.

Definition at line 92 of file __init__.py.

Referenced by pyclustering.utils.metric.chi_square_distance_numpy().

◆ read_sample()

def pyclustering.utils.read_sample ( filename )

Returns data sample from simple text file.

This function should be used for text file with following format:

point_1_coord_1 point_1_coord_2 ... point_1_coord_n
point_2_coord_1 point_2_coord_2 ... point_2_coord_n
... ...

Parameters

[in] filename (string): Path to file with data.

Returns: (list) Points where each point represented by list of coordinates.

Definition at line 54 of file __init__.py.

Referenced by pyclustering.utils.metric.chi_square_distance_numpy().

◆ rgb2gray()

def pyclustering.utils.rgb2gray ( image_rgb_array )

Returns image as 1-dimension (gray colored) matrix, where one element of list describes pixel.

Luma coding is used for transformation and that is calculated directly from gamma-compressed primary intensities as a weighted sum:

$Y = 0.2989R + 0.587G + 0.114B$

Parameters

[in] image_rgb_array (list): Image represented by RGB list.

Returns: (list) Image as gray colored matrix, where one element of list describes pixel.

colored_image = read_image(file_name);

gray_image = rgb2gray(colored_image);

See also: read_image()

Definition at line 107 of file __init__.py.

Referenced by pyclustering.utils.metric.chi_square_distance_numpy(), and pyclustering.utils.stretch_pattern().

◆ set_ax_param()

def pyclustering.utils.set_ax_param	(	ax,
		x_title = `None`,
		y_title = `None`,
		x_lim = `None`,
		y_lim = `None`,
		x_labels = `True`,
		y_labels = `True`,
		grid = `True`
	)

Sets parameters for matplotlib ax.

Parameters

[in]	ax	(Axes): Axes for which parameters should applied.
[in]	x_title	(string): Title for Y.
[in]	y_title	(string): Title for X.
[in]	x_lim	(double): X limit.
[in]	y_lim	(double): Y limit.
[in]	x_labels	(bool): If True - shows X labels.
[in]	y_labels	(bool): If True - shows Y labels.
[in]	grid	(bool): If True - shows grid.

Definition at line 932 of file __init__.py.

Referenced by pyclustering.utils.draw_dynamics().

◆ square_sum()

def pyclustering.utils.square_sum ( list_vector )

Calculates square sum of vector that is represented by list, each element can be represented by list - multidimensional elements.

Parameters

[in] list_vector (list): Input vector.

Returns: (double) Square sum of vector.

Definition at line 1180 of file __init__.py.

◆ stretch_pattern()

def pyclustering.utils.stretch_pattern ( image_source )

Returns stretched content as 1-dimension (gray colored) matrix with size of input image.

Parameters

[in] image_source (Image): PIL Image instance.

Returns: (list, Image) Stretched image as gray colored matrix and source image.

Definition at line 134 of file __init__.py.

◆ timedcall()

def pyclustering.utils.timedcall	(	executable_function,
		args
	)

Executes specified method or function with measuring of execution time.

Parameters

[in]	executable_function	(pointer): Pointer to function or method.
[in]	args	(*): Arguments of called function or method.

Returns: (tuple) Execution time and result of execution of function or method (execution_time, result_execution).

Definition at line 593 of file __init__.py.

◆ variance_increase_distance()

def pyclustering.utils.variance_increase_distance	(	cluster1,
		cluster2,
		data = `None`
	)

Calculates variance increase distance between two clusters.

Clusters can be represented by list of coordinates (in this case data shouldn't be specified), or by list of indexes of points from the data (represented by list of points), in this case data should be specified.

Parameters

[in]	cluster1	(list): The first cluster.
[in]	cluster2	(list): The second cluster.
[in]	data	(list): If specified than elements of clusters will be used as indexes, otherwise elements of cluster will be considered as points.

Returns: (double) Average variance increase distance between two clusters.

Definition at line 433 of file __init__.py.

Variable Documentation

◆ pi

float pyclustering.utils.pi = 3.1415926535

The number $pi$ is a mathematical constant, the ratio of a circle's circumference to its diameter.

Definition at line 51 of file __init__.py.

Namespaces

Functions

Variables

Detailed Description

Function Documentation

◆ allocate_sync_ensembles()

◆ average_inter_cluster_distance()

◆ average_intra_cluster_distance()

◆ average_neighbor_distance()

◆ calculate_distance_matrix()

◆ calculate_ellipse_description()

◆ data_corners()

◆ draw_clusters()

◆ draw_dynamics()

◆ draw_dynamics_set()

◆ draw_image_color_segments()

◆ draw_image_mask_segments()

◆ euclidean_distance()

◆ euclidean_distance_square()

◆ extract_number_oscillations()

◆ gray_pattern_borders()

◆ heaviside()

◆ linear_sum()

◆ list_math_addition()

◆ list_math_addition_number()

◆ list_math_division()

◆ list_math_division_number()

◆ list_math_multiplication()

◆ list_math_multiplication_number()

◆ list_math_substraction_number()

◆ list_math_subtraction()

◆ manhattan_distance()

◆ medoid()

◆ norm_vector()

◆ read_image()

◆ read_sample()

◆ rgb2gray()

◆ set_ax_param()

◆ square_sum()

◆ stretch_pattern()

◆ timedcall()

◆ variance_increase_distance()

Variable Documentation

◆ pi