teetool.gaussianprocess.GaussianProcess Class Reference

GaussianProcess class evaluates an ensemble of trajectories as a Gaussian process. More...

Inheritance diagram for teetool.gaussianprocess.GaussianProcess:

Public Member Functions
def	__init__ (self, cluster_data, ngaus)
	The constructor of GaussianProcess. More...
def	model_by_resampling (self)
	models the trajectory data via re-sampling, ignoring noise, missing data, trends, etc. More...
def	model_by_ml (self, type_basis, nbasis)
	models the trajectory data via maximum likelihood. More...
def	model_by_em (self, type_basis, nbasis, maximum_iterations=2001)
	models the trajectory data via expectation maximization. More...

Private Member Functions
def	_outline2vectors (self)
	obtain vectors to multiply normalised values with, allows for a transformation back to the actual values from the normalised ones. More...
def	_norm2real (self, mu_y, sig_y)
	returns the mu_y, sig_y vector to the original dimensions using the outline More...
def	_from_clusterdata2cells (self, cluster_data, basis)
def	_Ewc_Ewwc (self, yc, Hc, mu_w, sig_w_inv, BETA_EM)
def	_Ewn_Ewnwn (self, yn, Hn, mu_w, sig_w_inv, BETA_EM)
def	_E_mu (self, Ewc)
def	_E_sigma (self, mu_w, yc, Hc, Ewc, Ewwc)
def	_E_beta (self, yc, Hc, Ewc, Ewwc, ndim, Mstar)
def	_L_pYw (self, yc, Hc, Ewc, Ewwc, ndim, Mstar, BETA_EM)
def	_L_pw (self, Ewc, Ewwc, mu_w, sig_w, sig_w_inv, ndim, nbasis)
def	_getGMMCells (self, mu_y, sig_y, ngaus)
def	_getMuSigma (self, mu_y, sig_y, npoint, ngaus)

Private Attributes
	_cluster_data
	normalised cluster_data More...
	_outline
	original outline More...
	_ngaus
	number of Gaussians after modelling More...
	_ndim
	dimensionality of trajectory data More...

Detailed Description

GaussianProcess class evaluates an ensemble of trajectories as a Gaussian process.

Such a Gaussian process has a mean and covariance, and expresses itself as an ellipse (2d) or ellipsoid (3d) at a constant variance

Constructor & Destructor Documentation

__init__()

def teetool.gaussianprocess.GaussianProcess.__init__	(		self,
			cluster_data,
			ngaus
	)

The constructor of GaussianProcess.

Parameters

self	object pointer
cluster_data	trajectory data in specific format: a list of (x, Y), where x [npoints x 1] and Y [npoints x ndim]
ngaus	number of Gaussians desired

Member Function Documentation

_E_beta()

def teetool.gaussianprocess.GaussianProcess._E_beta (   self,   yc,   Hc,   Ewc,   Ewwc,   ndim,   Mstar  )

private

returns the expected noise parameter

_E_mu()

def teetool.gaussianprocess.GaussianProcess._E_mu (   self,   Ewc  )

private

returns the expected value E [ MU ]

Input:
    Ewc - list of expected values

Output:
    mu_w - average of expected values

_E_sigma()

def teetool.gaussianprocess.GaussianProcess._E_sigma (   self,   mu_w,   yc,   Hc,   Ewc,   Ewwc  )

private

return the expected variance E [ SIGMA ]
this takes into account the measured data and the model

Input:
    mu_w -
    yc -
    Hc -
    Ewc -
    Ewwc -

Output:
    sig_w -

_Ewc_Ewwc()

def teetool.gaussianprocess.GaussianProcess._Ewc_Ewwc (   self,   yc,   Hc,   mu_w,   sig_w_inv,   BETA_EM  )

private

returns the expected values Ewc and Ewwc

input:
    yc          - [points]
    Hc          - [Gram matrix]
    mu_w        - E[w]
    sig_w_inv   - 1 / E[ww]
    BETA_EM     - 1 / noise

output:
    Ewc     - [E[wn]]
    Ewnwc   - [E[wnwn]]

_Ewn_Ewnwn()

def teetool.gaussianprocess.GaussianProcess._Ewn_Ewnwn (   self,   yn,   Hn,   mu_w,   sig_w_inv,   BETA_EM  )

private

returns the expected values Ewn and Ewnwn

input:
    yn          - points
    Hn          - Gram matrix
    mu_w        - E[w]
    sig_w_inv   - 1 / E[ww]
    BETA_EM     - 1 / noise

output:
    Ewn     - E[wn]
    Ewnwn   - E[wnwn]

_from_clusterdata2cells()

def teetool.gaussianprocess.GaussianProcess._from_clusterdata2cells (   self,   cluster_data,   basis  )

private

converts from cluster_data (xn, Yn) list, to cells

Input:
    cluster_data -
    basis -

Output:
    yc -
    Hc -

_getGMMCells()

def teetool.gaussianprocess.GaussianProcess._getGMMCells (   self,   mu_y,   sig_y,   ngaus  )

private

return Gaussian Mixture Model (GMM) in cells

_getMuSigma()

def teetool.gaussianprocess.GaussianProcess._getMuSigma (   self,   mu_y,   sig_y,   npoint,   ngaus  )

private

returns (mu, sigma)

_L_pw()

def teetool.gaussianprocess.GaussianProcess._L_pw (   self,   Ewc,   Ewwc,   mu_w,   sig_w,   sig_w_inv,   ndim,   nbasis  )

private

returns ln( p(w) )
likelihood of parameters, before seeing the data

_L_pYw()

def teetool.gaussianprocess.GaussianProcess._L_pYw (   self,   yc,   Hc,   Ewc,   Ewwc,   ndim,   Mstar,   BETA_EM  )

private

returns ln( p (Y|w) )
likelihood of data, given the parameters

_norm2real()

def teetool.gaussianprocess.GaussianProcess._norm2real (   self,   mu_y,   sig_y  )

private

returns the mu_y, sig_y vector to the original dimensions using the outline

Parameters

self	The object pointer.
mu_y	mean vector [ngaus*ndim x 1]
sig_y	covariance matrix [ngaus*ndim x ngaus*ndim]

_outline2vectors()

def teetool.gaussianprocess.GaussianProcess._outline2vectors (   self )

private

obtain vectors to multiply normalised values with, allows for a transformation back to the actual values from the normalised ones.

Parameters

self	The object pointer.

Returns

M, vector with minimum values [ngaus*ndim x 1]

D, vector with difference values [ngaus*ndim x 1]

model_by_em()

def teetool.gaussianprocess.GaussianProcess.model_by_em	(		self,
			type_basis,
			nbasis,
			maximum_iterations = 2001
	)

models the trajectory data via expectation maximization.

It uses the basis function as specified to handle missing data, and, when noisy data is detected within a trajectory, the global trend, as learned, takes over. A suitable method in the presence of noise or an unknown shape of trajectories – the latter as different models can be compared via likelihood

Parameters

self	The object pointer.
type_basis	see Basis class for input
nbasis	see Basis class for input
maximum_iterations	maximum allowed number of evaluations till convergence

Returns

mu_y mean vector [ngaus*ndim x 1]

sig_y covariance matrix [ngaus*ndim x ngaus*ndim]

cc mean [ndim x 1] in ngaus cells

cA covariance [ndim x ndim] in ngaus cells

model_by_ml()

def teetool.gaussianprocess.GaussianProcess.model_by_ml	(		self,
			type_basis,
			nbasis
	)

models the trajectory data via maximum likelihood.

It uses the basis function as specified to handle missing data, however, noise per trajectory has no influence on the parameter estimation. A suitable method in the absence of noise and known shape of trajectories.

Parameters

self	The object pointer.
type_basis	see Basis class for input
nbasis	see Basis class for input

Returns

mu_y mean vector [ngaus*ndim x 1]

sig_y covariance matrix [ngaus*ndim x ngaus*ndim]

cc mean [ndim x 1] in ngaus cells

cA covariance [ndim x ndim] in ngaus cells

model_by_resampling()

def teetool.gaussianprocess.GaussianProcess.model_by_resampling

(

self

)

models the trajectory data via re-sampling, ignoring noise, missing data, trends, etc.

Quick method only suitable for high-quality data

Parameters

self	The object pointer.

Returns

mu_y mean vector [ngaus*ndim x 1]

sig_y covariance matrix [ngaus*ndim x ngaus*ndim]

cc mean [ndim x 1] in ngaus cells

cA covariance [ndim x ndim] in ngaus cells

Member Data Documentation

_cluster_data

teetool.gaussianprocess.GaussianProcess._cluster_data

private

normalised cluster_data

_ndim

teetool.gaussianprocess.GaussianProcess._ndim

private

dimensionality of trajectory data

_ngaus

teetool.gaussianprocess.GaussianProcess._ngaus

private

number of Gaussians after modelling

_outline

teetool.gaussianprocess.GaussianProcess._outline

private

original outline

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

• teetool/gaussianprocess.py