algorithms.clustering.gmm

Module: algorithms.clustering.gmm

Inheritance diagram for nipy.algorithms.clustering.gmm:

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Gaussian Mixture Model Class: contains the basic fields and methods of GMMs The class GMM _old uses C bindings which are computationally and memory efficient.

Author : Bertrand Thirion, 2006-2009

Classes

GMM

class nipy.algorithms.clustering.gmm.GMM(k=1, dim=1, prec_type='full', means=None, precisions=None, weights=None)

Bases: object

Standard GMM.

this class contains the following members k (int): the number of components in the mixture dim (int): is the dimension of the data prec_type = ‘full’ (string) is the parameterization

of the precisions/covariance matrices: either ‘full’ or ‘diagonal’.

means: array of shape (k,dim):

all the means (mean parameters) of the components

precisions: array of shape (k,dim,dim):

the precisions (inverse covariance matrix) of the components

weights: array of shape(k): weights of the mixture

__init__(k=1, dim=1, prec_type='full', means=None, precisions=None, weights=None)

Initialize the structure, at least with the dimensions of the problem

Parameters

k (int) the number of classes of the model

dim (int) the dimension of the problem

prec_type = ‘full’ : coavriance:precision parameterization

(diagonal ‘diag’ or full ‘full’).

means = None: array of shape (self.k,self.dim)

precisions = None: array of shape (self.k,self.dim,self.dim)

or (self.k, self.dim)

weights=None: array of shape (self.k)

By default, means, precision and weights are set as

zeros()

eye()

1/k ones()

with the correct dimensions

plugin(means, precisions, weights)

Set manually the weights, means and precision of the model

Parameters

means: array of shape (self.k,self.dim)

precisions: array of shape (self.k,self.dim,self.dim)

or (self.k, self.dim)

weights: array of shape (self.k)

check()

Checking the shape of different matrices involved in the model

check_x(x)

essentially check that x.shape[1]==self.dim

x is returned with possibly reshaping

initialize(x)

Initializes self according to a certain dataset x: 1. sets the regularizing hyper-parameters 2. initializes z using a k-means algorithm, then 3. upate the parameters

Parameters

x, array of shape (n_samples,self.dim)

the data used in the estimation process

pop(like, tiny=1e-15)

compute the population, i.e. the statistics of allocation

Parameters

like: array of shape (n_samples,self.k):

the likelihood of each item being in each class

update(x, l)

Identical to self._Mstep(x,l)

likelihood(x)

return the likelihood of the model for the data x the values are weighted by the components weights

Parameters

x array of shape (n_samples,self.dim)

the data used in the estimation process

Returns

like, array of shape(n_samples,self.k)

component-wise likelihood

unweighted_likelihood_(x)

return the likelihood of each data for each component the values are not weighted by the component weights

Parameters

x: array of shape (n_samples,self.dim)

the data used in the estimation process

Returns

like, array of shape(n_samples,self.k)

unweighted component-wise likelihood

unweighted_likelihood(x)

return the likelihood of each data for each component the values are not weighted by the component weights

Parameters

x: array of shape (n_samples,self.dim)

the data used in the estimation process

Returns

like, array of shape(n_samples,self.k)

unweighted component-wise likelihood

Notes

Hopefully faster

mixture_likelihood(x)

Returns the likelihood of the mixture for x

Parameters

x: array of shape (n_samples,self.dim)

the data used in the estimation process

average_log_like(x, tiny=1e-15)

returns the averaged log-likelihood of the mode for the dataset x

Parameters

x: array of shape (n_samples,self.dim)

the data used in the estimation process

tiny = 1.e-15: a small constant to avoid numerical singularities

evidence(x)

Computation of bic approximation of evidence

Parameters

x array of shape (n_samples,dim)

the data from which bic is computed

Returns

the bic value

bic(like, tiny=1e-15)

Computation of bic approximation of evidence

Parameters

like, array of shape (n_samples, self.k)

component-wise likelihood

tiny=1.e-15, a small constant to avoid numerical singularities

Returns

the bic value, float

guess_regularizing(x, bcheck=1)

Set the regularizing priors as weakly informative according to Fraley and raftery; Journal of Classification 24:155-181 (2007)

Parameters

x array of shape (n_samples,dim)

the data used in the estimation process

map_label(x, like=None)

return the MAP labelling of x

Parameters

x array of shape (n_samples,dim)

the data under study

like=None array of shape(n_samples,self.k)

component-wise likelihood if like==None, it is recomputed

Returns

z: array of shape(n_samples): the resulting MAP labelling

of the rows of x

estimate(x, niter=100, delta=0.0001, verbose=0)

Estimation of the model given a dataset x

Parameters

x array of shape (n_samples,dim)

the data from which the model is estimated

niter=100: maximal number of iterations in the estimation process

delta = 1.e-4: increment of data likelihood at which

convergence is declared

verbose=0: verbosity mode

Returns

bic : an asymptotic approximation of model evidence

initialize_and_estimate(x, z=None, niter=100, delta=0.0001, ninit=1, verbose=0)

Estimation of self given x

Parameters

x array of shape (n_samples,dim)

the data from which the model is estimated

z = None: array of shape (n_samples)

a prior labelling of the data to initialize the computation

niter=100: maximal number of iterations in the estimation process

delta = 1.e-4: increment of data likelihood at which

convergence is declared

ninit=1: number of initialization performed

to reach a good solution

verbose=0: verbosity mode

Returns

the best model is returned

train(x, z=None, niter=100, delta=0.0001, ninit=1, verbose=0)

Idem initialize_and_estimate

test(x, tiny=1e-15)

Returns the log-likelihood of the mixture for x

Parameters

x array of shape (n_samples,self.dim)

the data used in the estimation process

Returns

ll: array of shape(n_samples)

the log-likelihood of the rows of x

show_components(x, gd, density=None, mpaxes=None)

Function to plot a GMM – Currently, works only in 1D

Parameters

x: array of shape(n_samples, dim)

the data under study

gd: GridDescriptor instance

density: array os shape(prod(gd.n_bins))

density of the model one the discrete grid implied by gd by default, this is recomputed

mpaxes: axes handle to make the figure, optional,

if None, a new figure is created

show(x, gd, density=None, axes=None)

Function to plot a GMM, still in progress Currently, works only in 1D and 2D

Parameters

x: array of shape(n_samples, dim)

the data under study

gd: GridDescriptor instance

density: array os shape(prod(gd.n_bins))

density of the model one the discrete grid implied by gd by default, this is recomputed

GridDescriptor

class nipy.algorithms.clustering.gmm.GridDescriptor(dim=1, lim=None, n_bins=None)

Bases: object

A tiny class to handle cartesian grids

__init__(dim=1, lim=None, n_bins=None)

Parameters

dim: int, optional,

the dimension of the grid

lim: list of len(2*self.dim),

the limits of the grid as (xmin, xmax, ymin, ymax, …)

n_bins: list of len(self.dim),

the number of bins in each direction

set(lim, n_bins=10)

set the limits of the grid and the number of bins

Parameters

lim: list of len(2*self.dim),

the limits of the grid as (xmin, xmax, ymin, ymax, …)

n_bins: list of len(self.dim), optional

the number of bins in each direction

make_grid()

Compute the grid points

Returns

grid: array of shape (nb_nodes, self.dim)

where nb_nodes is the prod of self.n_bins

Functions

nipy.algorithms.clustering.gmm.best_fitting_GMM(x, krange, prec_type='full', niter=100, delta=0.0001, ninit=1, verbose=0)

Given a certain dataset x, find the best-fitting GMM with a number k of classes in a certain range defined by krange

Parameters

x: array of shape (n_samples,dim)

the data from which the model is estimated

krange: list of floats,

the range of values to test for k

prec_type: string (to be chosen within ‘full’,’diag’), optional,

the covariance parameterization

niter: int, optional,

maximal number of iterations in the estimation process

delta: float, optional,

increment of data likelihood at which convergence is declared

ninit: int

number of initialization performed

verbose=0: verbosity mode

Returns

mg : the best-fitting GMM instance

nipy.algorithms.clustering.gmm.plot2D(x, my_gmm, z=None, with_dots=True, log_scale=False, mpaxes=None, verbose=0)

Given a set of points in a plane and a GMM, plot them

Parameters

x: array of shape (npoints, dim=2),

sample points

my_gmm: GMM instance,

whose density has to be ploted

z: array of shape (npoints), optional

that gives a labelling of the points in x by default, it is not taken into account

with_dots, bool, optional

whether to plot the dots or not

log_scale: bool, optional

whether to plot the likelihood in log scale or not

mpaxes=None, int, optional

if not None, axes handle for plotting

verbose: verbosity mode, optional

Returns

gd, GridDescriptor instance,

that represents the grid used in the function

ax, handle to the figure axes

Notes

my_gmm is assumed to have have a ‘nixture_likelihood’ method that takes an array of points of shape (np, dim) and returns an array of shape (np,my_gmm.k) that represents the likelihood component-wise