Python API

This section includes information for using the pure Python API of bob.learn.em.

Classes

Trainers

bob.learn.em.KMeansTrainer Trains a KMeans machine.This class implements the
bob.learn.em.ML_GMMTrainer This class implements the maximum likelihood M-step of the expectation-maximisation algorithm for a GMM Machine.
bob.learn.em.MAP_GMMTrainer This class implements the maximum a posteriori M-step of the expectation-maximization algorithm for a GMM Machine.
bob.learn.em.ISVTrainer ISVTrainerReferences: [Vogt2008,McCool2013]
bob.learn.em.JFATrainer JFATrainerReferences: [Vogt2008,McCool2013]
bob.learn.em.IVectorTrainer IVectorTrainerAn IVectorTrainer to learn a Total Variability subspace $T$ (and eventually a covariance matrix $\Sigma$).
bob.learn.em.PLDATrainer This class can be used to train the F, G and
bob.learn.em.EMPCATrainer Trains a bob.learn.linear.Machine using an

Machines

bob.learn.em.KMeansMachine This class implements a k-means classifier.
bob.learn.em.Gaussian This class implements a multivariate diagonal Gaussian distribution
bob.learn.em.GMMStats A container for GMM statistics
bob.learn.em.GMMMachine This class implements a multivariate diagonal Gaussian distribution.
bob.learn.em.ISVBase A ISVBase instance can be seen as a container for U and D when performing Joint Factor Analysis (JFA).
bob.learn.em.ISVMachine A ISVMachine.
bob.learn.em.JFABase A JFABase instance can be seen as a container for U, V and D when performing Joint Factor Analysis (JFA).
bob.learn.em.JFAMachine A JFAMachine.
bob.learn.em.IVectorMachine An IVectorMachine consists of a Total Variability subspace T
bob.learn.em.PLDABase This class is a container for the F (between class variantion matrix), G (within class variantion matrix) and \Sigma matrices and the mean vector \mu of a PLDA model.
bob.learn.em.PLDAMachine This class is a container for an enrolled identity/class.

Functions

bob.learn.em.linear_scoring((models, ubm, ...) Parameters:
bob.learn.em.tnorm(...) Normalise raw scores with T-Norm
bob.learn.em.train(trainer, machine, data[, ...]) Trains a machine given a trainer and the proper data
bob.learn.em.train_jfa(trainer, jfa_base, data) Trains a bob.learn.em.JFABase given a bob.learn.em.JFATrainer and the proper data
bob.learn.em.znorm(...) Normalise raw scores with Z-Norm
bob.learn.em.ztnorm(...) Normalise raw scores with ZT-Norm.Assume that znorm and tnorm have no common subject id.
bob.learn.em.ztnorm_same_value(vect_a, vect_b) Computes the matrix of boolean D for the ZT-norm, which indicates where the client ids of the T-Norm models and Z-Norm samples match.

Detailed Information

bob.learn.em.ztnorm_same_value(vect_a, vect_b)[source]

Computes the matrix of boolean D for the ZT-norm, which indicates where the client ids of the T-Norm models and Z-Norm samples match.

vect_a An (ordered) list of client_id corresponding to the T-Norm models vect_b An (ordered) list of client_id corresponding to the Z-Norm impostor samples

bob.learn.em.get_config()[source]

Returns a string containing the configuration information.

class bob.learn.em.EMPCATrainer

Bases: object

Trains a bob.learn.linear.Machine using an Expectation-Maximization algorithm on the given dataset [Bishop1999] [Roweis1998]

Notations used are the ones from [Bishop1999]

The probabilistic model is given by: t = Wx + \mu + \epsilon

  • t is the observed data (dimension f)
  • W is a projection matrix (dimension f \times d)
  • x is the projected data (dimension d < f)
  • \mu is the mean of the data (dimension f)
  • \epsilon is the noise of the data (dimension f)
  • Gaussian with zero-mean and covariance matrix \sigma^2 Id

Constructor Documentation:

  • bob.learn.em.EMPCATrainer (other)
  • bob.learn.em.EMPCATrainer ()

Creates a EMPCATrainer

Parameters:

other : bob.learn.em.EMPCATrainer

A EMPCATrainer object to be copied.

Class Members:

compute_likelihood(linear_machine) → None

Parameters:

linear_machine : bob.learn.linear.Machine

LinearMachine Object
e_step(linear_machine, data) → None

Parameters:

linear_machine : bob.learn.linear.Machine

LinearMachine Object

data : array_like <float, 2D>

Input data
initialize(linear_machine, data[, rng]) → None

Parameters:

linear_machine : bob.learn.linear.Machine

LinearMachine Object

data : array_like <float, 2D>

Input data

rng : bob.core.random.mt19937

The Mersenne Twister mt19937 random generator used for the initialization of subspaces/arrays before the EM loop.
m_step(linear_machine, data) → None

Parameters:

linear_machine : bob.learn.linear.Machine

LinearMachine Object

data : array_like <float, 2D>

Input data
sigma2

float <– The noise sigma2 of the probabilistic model

class bob.learn.em.GMMMachine

Bases: object

This class implements a multivariate diagonal Gaussian distribution.

See Section 2.3.9 of Bishop, “Pattern recognition and machine learning”, 2006

Constructor Documentation:

  • bob.learn.em.GMMMachine (n_gaussians,n_inputs)
  • bob.learn.em.GMMMachine (other)
  • bob.learn.em.GMMMachine (hdf5)
  • bob.learn.em.GMMMachine ()

Creates a GMMMachine

Parameters:

n_gaussians : int

Number of gaussians

n_inputs : int

Dimension of the feature vector

other : bob.learn.em.GMMMachine

A GMMMachine object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

acc_statistics(input, stats) → None

Accumulate the GMM statistics for this sample(s). Inputs are checked.

Parameters:

input : array_like <float, 2D>

Input vector

stats : bob.learn.em.GMMStats

Statistics of the GMM
acc_statistics_(input, stats) → None

Accumulate the GMM statistics for this sample(s). Inputs are NOT checked.

Parameters:

input : array_like <float, 2D>

Input vector

stats : bob.learn.em.GMMStats

Statistics of the GMM
get_gaussian(i) → gaussian

Get the specified Gaussian component.

Note

An exception is thrown if i is out of range.

Parameters:

i : int

Index of the gaussian

Returns:

gaussian : bob.learn.em.Gaussian

Gaussian object
is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this GMMMachine with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.GMMMachine

A GMMMachine object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
load(hdf5) → None

Load the configuration of the GMMMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
log_likelihood(input) → output

Output the log likelihood of the sample, x, i.e. log(p(x|GMM)). Inputs are checked.

Note

The __call__ function is an alias for this. If input is 2D the average along the samples will be computed (\frac{log(p(x|GMM))}{N})

Parameters:

input : array_like <float, 1D>

Input vector

Returns:

output : float

The log likelihood
log_likelihood_(input) → output

Output the log likelihood of the sample, x, i.e. log(p(x|GMM)). Inputs are NOT checked.

Parameters:

input : array_like <float, 1D>

Input vector

Returns:

output : float

The log likelihood
mean_supervector

array_like <float, 1D> <– The mean supervector of the GMMMachine

Concatenation of the mean vectors of each Gaussian of the GMMMachine

means

array_like <float, 2D> <– The means of the gaussians

resize(n_gaussians, n_inputs) → None

Allocates space for the statistics and resets to zero.

Parameters:

n_gaussians : int

Number of gaussians

n_inputs : int

Dimensionality of the feature vector
save(hdf5) → None

Save the configuration of the GMMMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
set_variance_thresholds(input) → None

Set the variance flooring thresholds in each dimension to the same vector for all Gaussian components if the argument is a 1D numpy arrray, and equal for all Gaussian components and dimensions if the parameter is a scalar.

Parameters:

input : float or array_like <float, 1D>

The new variance threshold, or a vector of thresholds for all Gaussian components
shape

(int,int) <– A tuple that represents the number of gaussians and dimensionality of each Gaussian (n_gaussians, dim).

variance_supervector

array_like <float, 1D> <– The variance supervector of the GMMMachine

Concatenation of the variance vectors of each Gaussian of the GMMMachine

variance_thresholds

array_like <float, 2D> <– Set the variance flooring thresholds in each dimension to the same vector for all Gaussian components if the argument is a 1D numpy arrray, and equal for all Gaussian components and dimensions if the parameter is a scalar.

variances

array_like <float, 2D> <– Variances of the gaussians

weights

array_like <float, 1D> <– The weights (also known as “mixing coefficients”)

class bob.learn.em.GMMStats

Bases: object

A container for GMM statistics

With respect to [Reynolds2000] the class computes:

Constructor Documentation:

  • bob.learn.em.GMMStats (n_gaussians,n_inputs)
  • bob.learn.em.GMMStats (other)
  • bob.learn.em.GMMStats (hdf5)
  • bob.learn.em.GMMStats ()

A container for GMM statistics.

Parameters:

n_gaussians : int

Number of gaussians

n_inputs : int

Dimension of the feature vector

other : bob.learn.em.GMMStats

A GMMStats object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

init() → None

Resets statistics to zero.

is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this GMMStats with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.GMMStats

A GMMStats object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
load(hdf5) → None

Load the configuration of the GMMStats to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
log_likelihood

float <– The accumulated log likelihood of all samples

n

array_like <float, 1D> <– For each Gaussian, the accumulated sum of responsibilities, i.e. the sum of P(gaussian_i|x)

resize(n_gaussians, n_inputs) → None

Allocates space for the statistics and resets to zero.

Parameters:

n_gaussians : int

Number of gaussians

n_inputs : int

Dimensionality of the feature vector
save(hdf5) → None

Save the configuration of the GMMStats to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
shape

(int,int) <– A tuple that represents the number of gaussians and dimensionality of each Gaussian (n_gaussians, dim).

sum_px

array_like <float, 2D> <– For each Gaussian, the accumulated sum of responsibility times the sample

sum_pxx

array_like <float, 2D> <– For each Gaussian, the accumulated sum of responsibility times the sample squared

t

int <– The number of samples

class bob.learn.em.Gaussian

Bases: object

This class implements a multivariate diagonal Gaussian distribution

Constructor Documentation:

  • bob.learn.em.Gaussian (n_inputs)
  • bob.learn.em.Gaussian (other)
  • bob.learn.em.Gaussian (hdf5)
  • bob.learn.em.Gaussian ()

Constructs a new multivariate gaussian object

Parameters:

n_inputs : int

Dimension of the feature vector

other : bob.learn.em.GMMStats

A GMMStats object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this Gaussian with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.Gaussian

A gaussian to be compared.

[r_epsilon] : float

Relative precision.

[a_epsilon] : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
load(hdf5) → None

Load the configuration of the Gassian Machine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
log_likelihood(input) → output

Output the log likelihood of the sample, x. The input size is checked.

Note

The __call__ function is an alias for this.

Parameters:

input : array_like <float, 1D>

Input vector

Returns:

output : float

The log likelihood
log_likelihood_(input) → output

Output the log likelihood given a sample. The input size is NOT checked.

Parameters:

input : array_like <float, 1D>

Input vector

Returns:

output : float

The log likelihood
mean

array_like <float, 1D> <– Mean of the Gaussian

resize(input) → None

Set the input dimensionality, reset the mean to zero and the variance to one.

Parameters:

input : int

Dimensionality of the feature vector
save(hdf5) → None

Save the configuration of the Gassian Machine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
set_variance_thresholds(input) → None

Set the variance flooring thresholds equal to the given threshold for all the dimensions.

Parameters:

input : float

Threshold
shape

(int) <– A tuple that represents the dimensionality of the Gaussian (dim,).

variance

array_like <float, 1D> <– Variance of the Gaussian

variance_thresholds

array_like <float, 1D> <– The variance flooring thresholds, i.e. the minimum allowed value of variance in each dimension.

The variance will be set to this value if an attempt is made to set it to a smaller value.

class bob.learn.em.ISVBase

Bases: object

A ISVBase instance can be seen as a container for U and D when performing Joint Factor Analysis (JFA).

References: [Vogt2008] [McCool2013]

Constructor Documentation:

  • bob.learn.em.ISVBase (ubm,ru)
  • bob.learn.em.ISVBase (other)
  • bob.learn.em.ISVBase (hdf5)
  • bob.learn.em.ISVBase ()

Creates a ISVBase

Parameters:

ubm : bob.learn.em.GMMMachine

The Universal Background Model.

ru : int

Size of U (Within client variation matrix). In the end the U matrix will have (number_of_gaussians * feature_dimension x ru)

other : bob.learn.em.ISVBase

A ISVBase object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

d

array_like <float, 1D> <– Returns the diagonal matrix diag(d) (as a 1D vector)

is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this ISVBase with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.ISVBase

A ISVBase object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
load(hdf5) → None

Load the configuration of the ISVBase to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
resize(rU) → None

Resets the dimensionality of the subspace U. U is hence uninitialized.

Parameters:

rU : int

Size of U (Within client variation matrix)
save(hdf5) → None

Save the configuration of the ISVBase to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
shape

(int,int, int) <– A tuple that represents the number of gaussians, dimensionality of each Gaussian, dimensionality of the rU (within client variability matrix) (#Gaussians, #Inputs, #rU).

supervector_length

int <– Returns the supervector length.

NGaussians x NInputs: Number of Gaussian components by the feature dimensionalityWARNING An exception is thrown if no Universal Background Model has been set yet.

u

array_like <float, 2D> <– Returns the U matrix (within client variability matrix)

ubm

bob.learn.em.GMMMachine <– Returns the UBM (Universal Background Model

class bob.learn.em.ISVMachine

Bases: object

A ISVMachine. An attached bob.learn.em.ISVBase should be provided for Joint Factor Analysis. The bob.learn.em.ISVMachine carries information about the speaker factors y and z, whereas a bob.learn.em.JFABase carries information about the matrices U and D.

References: [Vogt2008] [McCool2013]

Constructor Documentation:

  • bob.learn.em.ISVMachine (isv_base)
  • bob.learn.em.ISVMachine (other)
  • bob.learn.em.ISVMachine (hdf5)

Constructor. Builds a new ISVMachine

Parameters:

isv_base : bob.learn.em.ISVBase

The ISVBase associated with this machine

other : bob.learn.em.ISVMachine

A ISVMachine object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

estimate_ux(stats, input) → None

Estimates Ux (LPT assumption) given GMM statistics.

Estimates Ux from the GMM statistics considering the LPT assumption, that is the latent session variable x is approximated using the UBM.

Parameters:

stats : bob.learn.em.GMMStats

Statistics of the GMM

input : array_like <float, 1D>

Input vector
estimate_x(stats, input) → None

Estimates the session offset x (LPT assumption) given GMM statistics.

Estimates x from the GMM statistics considering the LPT assumption, that is the latent session variable x is approximated using the UBM

Parameters:

stats : bob.learn.em.GMMStats

Statistics of the GMM

input : array_like <float, 1D>

Input vector
forward_ux(stats, ux) → None

Computes a score for the given UBM statistics and given the Ux vector

Parameters:

stats : bob.learn.em.GMMStats

Statistics as input

ux : array_like <float, 1D>

Input vector
is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this ISVMachine with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.ISVMachine

A ISVMachine object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
isv_base

bob.learn.em.ISVBase <– The ISVBase attached to this machine

load(hdf5) → None

Load the configuration of the ISVMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
save(hdf5) → None

Save the configuration of the ISVMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
shape

(int,int, int, int) <– A tuple that represents the number of gaussians, dimensionality of each Gaussian and dimensionality of the rU (within client variability matrix)) (#Gaussians, #Inputs, #rU).

supervector_length

int <– Returns the supervector length.

NGaussians x NInputs: Number of Gaussian components by the feature dimensionality@warning An exception is thrown if no Universal Background Model has been set yet.

x

array_like <float, 1D> <– Returns the X session factor. Eq (29) from [McCool2013]

The latent variable x (last one computed). This is a feature provided for convenience, but this attribute is not ‘part’ of the machine. The session latent variable x is indeed not class-specific, but depends on the sample considered. Furthermore, it is not saved into the machine or used when comparing machines.

z

array_like <float, 1D> <– Returns the z speaker factor. Eq (31) from [McCool2013]

class bob.learn.em.ISVTrainer

Bases: object

ISVTrainerReferences: [Vogt2008,McCool2013]

Constructor Documentation:

  • bob.learn.em.ISVTrainer (relevance_factor)
  • bob.learn.em.ISVTrainer (other)
  • bob.learn.em.ISVTrainer ()

Constructor. Builds a new ISVTrainer

Parameters:

other : bob.learn.em.ISVTrainer

A ISVTrainer object to be copied.

relevance_factor : float

Class Members:

acc_u_a1

array_like <float, 3D> <– Accumulator updated during the E-step

acc_u_a2

array_like <float, 2D> <– Accumulator updated during the E-step

e_step(isv_base, stats) → None

Call the e-step procedure (for the U subspace).

Parameters:

isv_base : bob.learn.em.ISVBase

ISVBase Object

stats : bob.learn.em.GMMStats

GMMStats Object
enroll(isv_machine, features, n_iter) → None

Parameters:

isv_machine : bob.learn.em.ISVMachine

ISVMachine Object

features : list(bob.learn.em.GMMStats)`

n_iter : int

Number of iterations
initialize(isv_base, stats[, rng]) → None

Initialization before the EM steps

Parameters:

isv_base : bob.learn.em.ISVBase

ISVBase Object

stats : bob.learn.em.GMMStats

GMMStats Object

rng : bob.core.random.mt19937

The Mersenne Twister mt19937 random generator used for the initialization of subspaces/arrays before the EM loop.
m_step(isv_base[, stats]) → None

Call the m-step procedure (for the U subspace).

Parameters:

isv_base : bob.learn.em.ISVBase

ISVBase Object

stats : object

Ignored.
class bob.learn.em.IVectorMachine

Bases: object

An IVectorMachine consists of a Total Variability subspace T and allows the extraction of IVectorReferences: [Dehak2010]

Constructor Documentation:

  • bob.learn.em.IVectorMachine (ubm,rt,variance_threshold)
  • bob.learn.em.IVectorMachine (other)
  • bob.learn.em.IVectorMachine (hdf5)

Constructor. Builds a new IVectorMachine

Parameters:

ubm : bob.learn.em.GMMMachine

The Universal Background Model.

rt : int

Size of the Total Variability matrix (CD x rt).

variance_threshold : float

Variance flooring threshold for the \Sigma (diagonal) matrix

other : bob.learn.em.IVectorMachine

A IVectorMachine object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this IVectorMachine with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.IVectorMachine

A IVectorMachine object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
load(hdf5) → None

Load the configuration of the IVectorMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
project(stats) → None

Projects the given GMM statistics into the i-vector subspace

Note

The __call__ function is an alias for this function

Parameters:

stats : bob.learn.em.GMMStats

Statistics as input
resize(rT) → None

Resets the dimensionality of the subspace T.

Parameters:

rT : int

Size of T (Total variability matrix)
save(hdf5) → None

Save the configuration of the IVectorMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
shape

(int,int, int) <– A tuple that represents the number of gaussians, dimensionality of each Gaussian, dimensionality of the rT (total variability matrix) (#Gaussians, #Inputs, #rT).

sigma

array_like <float, 1D> <– The residual matrix of the model sigma

supervector_length

int <– Returns the supervector length.

NGaussians x NInputs: Number of Gaussian components by the feature dimensionality@warning An exception is thrown if no Universal Background Model has been set yet.

t

array_like <float, 2D> <– Returns the Total Variability matrix, T

ubm

bob.learn.em.GMMMachine <– Returns the UBM (Universal Background Model)

variance_threshold

float <– Threshold for the variance contained in sigma

class bob.learn.em.IVectorTrainer

Bases: object

IVectorTrainerAn IVectorTrainer to learn a Total Variability subspace $T$ (and eventually a covariance matrix $\Sigma$).

References: [Dehak2010]

Constructor Documentation:

  • bob.learn.em.IVectorTrainer (update_sigma)
  • bob.learn.em.IVectorTrainer (other)
  • bob.learn.em.IVectorTrainer ()

Constructor. Builds a new IVectorTrainer

Parameters:

other : bob.learn.em.IVectorTrainer

A IVectorTrainer object to be copied.

update_sigma : bool

Class Members:

acc_fnormij_wij

array_like <float, 3D> <– Accumulator updated during the E-step

acc_nij

array_like <float, 1D> <– Accumulator updated during the E-step

acc_nij_wij2

array_like <float, 3D> <– Accumulator updated during the E-step

acc_snormij

array_like <float, 2D> <– Accumulator updated during the E-step

e_step(ivector_machine, stats) → None

Call the e-step procedure (for the U subspace).

Parameters:

ivector_machine : bob.learn.em.ISVBase

IVectorMachine Object

stats : bob.learn.em.GMMStats

GMMStats Object
initialize(ivector_machine[, stats][, rng]) → None

Initialization before the EM steps

Parameters:

ivector_machine : bob.learn.em.IVectorMachine

IVectorMachine Object

stats : object

Ignored

rng : bob.core.random.mt19937

The Mersenne Twister mt19937 random generator used for the initialization of subspaces/arrays before the EM loop.
m_step(ivector_machine[, stats]) → None

Call the m-step procedure (for the U subspace).

Parameters:

ivector_machine : bob.learn.em.ISVBase

IVectorMachine Object

stats : object

Ignored
reset_accumulators(ivector_machine) → None

Reset the statistics accumulators to the correct size and a value of zero.

Parameters:

ivector_machine : bob.learn.em.IVectorMachine

The IVector machine containing the right dimensions
class bob.learn.em.JFABase

Bases: object

A JFABase instance can be seen as a container for U, V and D when performing Joint Factor Analysis (JFA).

References: [Vogt2008] [McCool2013]

Constructor Documentation:

  • bob.learn.em.JFABase (ubm,ru,rv)
  • bob.learn.em.JFABase (other)
  • bob.learn.em.JFABase (hdf5)
  • bob.learn.em.JFABase ()

Constructor. Builds a new JFABase

Parameters:

ubm : bob.learn.em.GMMMachine

The Universal Background Model.

ru : int

Size of U (Within client variation matrix). In the end the U matrix will have (#gaussians * #feature_dimension x ru)

rv : int

Size of V (Between client variation matrix). In the end the U matrix will have (#gaussians * #feature_dimension x rv)

other : bob.learn.em.JFABase

A JFABase object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

d

array_like <float, 1D> <– Returns the diagonal matrix diag(d) (as a 1D vector)

is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this JFABase with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.JFABase

A JFABase object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
load(hdf5) → None

Load the configuration of the JFABase to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
resize(rU, rV) → None

Resets the dimensionality of the subspace U and V. U and V are hence uninitialized

Parameters:

rU : int

Size of U (Within client variation matrix)

rV : int

Size of V (Between client variation matrix)
save(hdf5) → None

Save the configuration of the JFABase to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
shape

(int,int, int, int) <– A tuple that represents the number of gaussians, dimensionality of each Gaussian, dimensionality of the rU (within client variability matrix) and dimensionality of the rV (between client variability matrix) (#Gaussians, #Inputs, #rU, #rV).

supervector_length

int <– Returns the supervector length.

NGaussians x NInputs: Number of Gaussian components by the feature dimensionality@warning An exception is thrown if no Universal Background Model has been set yet.

u

array_like <float, 2D> <– Returns the U matrix (within client variability matrix)

ubm

bob.learn.em.GMMMachine <– Returns the UBM (Universal Background Model

v

array_like <float, 2D> <– Returns the V matrix (between client variability matrix)

class bob.learn.em.JFAMachine

Bases: object

A JFAMachine. An attached bob.learn.em.JFABase should be provided for Joint Factor Analysis. The bob.learn.em.JFAMachine carries information about the speaker factors y and z, whereas a bob.learn.em.JFABase carries information about the matrices U, V and D.

References: [Vogt2008] [McCool2013]

Constructor Documentation:

  • bob.learn.em.JFAMachine (jfa_base)
  • bob.learn.em.JFAMachine (other)
  • bob.learn.em.JFAMachine (hdf5)

Constructor. Builds a new JFAMachine

Parameters:

jfa_base : bob.learn.em.JFABase

The JFABase associated with this machine

other : bob.learn.em.JFAMachine

A JFAMachine object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

estimate_ux(stats, input) → None

Estimates Ux (LPT assumption) given GMM statistics.

Estimates Ux from the GMM statistics considering the LPT assumption, that is the latent session variable x is approximated using the UBM.

Parameters:

stats : bob.learn.em.GMMStats

Statistics of the GMM

input : array_like <float, 1D>

Input vector
estimate_x(stats, input) → None

Estimates the session offset x (LPT assumption) given GMM statistics.

Estimates x from the GMM statistics considering the LPT assumption, that is the latent session variable x is approximated using the UBM

Parameters:

stats : bob.learn.em.GMMStats

Statistics of the GMM

input : array_like <float, 1D>

Input vector
forward_ux(stats, ux) → None

Computes a score for the given UBM statistics and given the Ux vector

Parameters:

stats : bob.learn.em.GMMStats

Statistics as input

ux : array_like <float, 1D>

Input vector
is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this JFAMachine with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.JFAMachine

A JFAMachine object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
jfa_base

bob.learn.em.JFABase <– The JFABase attached to this machine

load(hdf5) → None

Load the configuration of the JFAMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
log_likelihood(stats) → None

Computes the log-likelihood of the given samples

Note

the __call__ function is an alias for this function.

Parameters:

stats : bob.learn.em.GMMStats

Statistics as input
save(hdf5) → None

Save the configuration of the JFAMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
shape

(int,int, int, int) <– A tuple that represents the number of gaussians, dimensionality of each Gaussian, dimensionality of the rU (within client variability matrix) and dimensionality of the rV (between client variability matrix) (#Gaussians, #Inputs, #rU, #rV).

supervector_length

int <– Returns the supervector length.

NGaussians x NInputs: Number of Gaussian components by the feature dimensionality@warning An exception is thrown if no Universal Background Model has been set yet.

x

array_like <float, 1D> <– Returns the X session factor. Eq (29) from [McCool2013]

The latent variable x (last one computed). This is a feature provided for convenience, but this attribute is not ‘part’ of the machine. The session latent variable x is indeed not class-specific, but depends on the sample considered. Furthermore, it is not saved into the machine or used when comparing machines.

y

array_like <float, 1D> <– Returns the y speaker factor. Eq (30) from [McCool2013]

z

array_like <float, 1D> <– Returns the z speaker factor. Eq (31) from [McCool2013]

class bob.learn.em.JFATrainer

Bases: object

JFATrainerReferences: [Vogt2008,McCool2013]

Constructor Documentation:

  • bob.learn.em.JFATrainer (other)
  • bob.learn.em.JFATrainer ()

Constructor. Builds a new JFATrainer

Parameters:

other : bob.learn.em.JFATrainer

A JFATrainer object to be copied.

Class Members:

acc_d_a1

array_like <float, 1D> <– Accumulator updated during the E-step

acc_d_a2

array_like <float, 1D> <– Accumulator updated during the E-step

acc_u_a1

array_like <float, 3D> <– Accumulator updated during the E-step

acc_u_a2

array_like <float, 2D> <– Accumulator updated during the E-step

acc_v_a1

array_like <float, 3D> <– Accumulator updated during the E-step

acc_v_a2

array_like <float, 2D> <– Accumulator updated during the E-step

e_step_d(jfa_base, stats) → None

Call the 3rd e-step procedure (for the d subspace).

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object
e_step_u(jfa_base, stats) → None

Call the 2nd e-step procedure (for the U subspace).

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object
e_step_v(jfa_base, stats) → None

Call the 1st e-step procedure (for the V subspace).

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object
enroll(jfa_machine, features, n_iter) → None

Parameters:

jfa_machine : bob.learn.em.JFAMachine

JFAMachine Object

features : [bob.learn.em.GMMStats]

n_iter : int

Number of iterations
finalize_d(jfa_base, stats) → None

Call the 3rd finalize procedure (for the d subspace).

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object
finalize_u(jfa_base, stats) → None

Call the 2nd finalize procedure (for the U subspace).

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object
finalize_v(jfa_base, stats) → None

Call the 1st finalize procedure (for the V subspace).

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object
initialize(jfa_base, stats[, rng]) → None

Initialization before the EM steps

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object

rng : bob.core.random.mt19937

The Mersenne Twister mt19937 random generator used for the initialization of subspaces/arrays before the EM loop.
m_step_d(jfa_base, stats) → None

Call the 3rd m-step procedure (for the d subspace).

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object
m_step_u(jfa_base, stats) → None

Call the 2nd m-step procedure (for the U subspace).

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object
m_step_v(jfa_base, stats) → None

Call the 1st m-step procedure (for the V subspace).

Parameters:

jfa_base : bob.learn.em.JFABase

JFABase Object

stats : bob.learn.em.GMMStats

GMMStats Object
class bob.learn.em.KMeansMachine

Bases: object

This class implements a k-means classifier. See Section 9.1 of Bishop, “Pattern recognition and machine learning”, 2006

Constructor Documentation:

  • bob.learn.em.KMeansMachine (n_means,n_inputs)
  • bob.learn.em.KMeansMachine (other)
  • bob.learn.em.KMeansMachine (hdf5)
  • bob.learn.em.KMeansMachine ()

Creates a KMeansMachine

Parameters:

n_means : int

Number of means

n_inputs : int

Dimension of the feature vector

other : bob.learn.em.KMeansMachine

A KMeansMachine object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

get_closest_mean(input) → output

Calculate the index of the mean that is closest (in terms of square Euclidean distance) to the data sample, x.

Parameters:

input : array_like <float, 1D>

The data sample (feature vector)

Returns:

output : (int, int)

Tuple containing the closest mean and the minimum distance from the input
get_distance_from_mean(input, i) → output

Return the power of two of the square Euclidean distance of the sample, x, to the i’th mean.

Note

An exception is thrown if i is out of range.

Parameters:

input : array_like <float, 1D>

The data sample (feature vector)

i : int

The index of the mean

Returns:

output : float

Square Euclidean distance of the sample, x, to the i’th mean
get_mean(i) → mean

Get the i’th mean.

Note

An exception is thrown if i is out of range.

Parameters:

i : int

Index of the mean

Returns:

mean : array_like <float, 1D>

Mean array
get_min_distance(input) → output

Output the minimum (Square Euclidean) distance between the input and the closest mean

Parameters:

input : array_like <float, 1D>

The data sample (feature vector)

Returns:

output : float

The minimum distance
get_variances_and_weights_for_each_cluster(input) → output

For each mean, find the subset of the samples that is closest to that mean, and calculate 1) the variance of that subset (the cluster variance) 2) the proportion of the samples represented by that subset (the cluster weight)

Parameters:

input : array_like <float, 2D>

The data sample (feature vector)

Returns:

output : (array_like <float, 2D>, array_like <float, 1D>)

A tuple with the variances and the weights respectively
is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this KMeansMachine with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.KMeansMachine

A KMeansMachine object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
load(hdf5) → None

Load the configuration of the KMeansMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
means

array_like <float, 2D> <– The means

resize(n_means, n_inputs) → None

Allocates space for the statistics and resets to zero.

Parameters:

n_means : int

Number of means

n_inputs : int

Dimensionality of the feature vector
save(hdf5) → None

Save the configuration of the KMeansMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
set_mean(i, mean) → None

Set the i’th mean.

Note

An exception is thrown if i is out of range.

Parameters:

i : int

Index of the mean

mean : array_like <float, 1D>

Mean array
shape

(int,int) <– A tuple that represents the number of means and dimensionality of the feature vector``(n_means, dim)``.

class bob.learn.em.KMeansTrainer

Bases: object

Trains a KMeans machine.This class implements the expectation-maximization algorithm for a k-means machine.See Section 9.1 of Bishop, “Pattern recognition and machine learning”, 2006It uses a random initialization of the means followed by the expectation-maximization algorithm

Constructor Documentation:

  • bob.learn.em.KMeansTrainer (initialization_method)
  • bob.learn.em.KMeansTrainer (other)
  • bob.learn.em.KMeansTrainer ()

Creates a KMeansTrainer

Parameters:

initialization_method : str

The initialization method of the means. Possible values are: ‘RANDOM’, ‘RANDOM_NO_DUPLICATE’, ‘KMEANS_PLUS_PLUS’

other : bob.learn.em.KMeansTrainer

A KMeansTrainer object to be copied.

Class Members:

average_min_distance

str <– Average min (square Euclidean) distance. Useful to parallelize the E-step.

compute_likelihood(kmeans_machine) → None

This functions returns the average min (Square Euclidean) distance (average distance to the closest mean)

Parameters:

kmeans_machine : bob.learn.em.KMeansMachine

KMeansMachine Object
e_step(kmeans_machine, data) → None

Compute the E-step, which is basically the distances

Accumulate across the dataset: -zeroeth and first order statistics -average (Square Euclidean) distance from the closest mean

Parameters:

kmeans_machine : bob.learn.em.KMeansMachine

KMeansMachine Object

data : array_like <float, 2D>

Input data
first_order_statistics

array_like <float, 2D> <– Returns the internal statistics. Useful to parallelize the E-step

initialization_method

str <– Initialization method.

Possible values:

RANDOM: Random initialization

RANDOM_NO_DUPLICATE: Random initialization without repetition

KMEANS_PLUS_PLUS: Apply the kmeans++ initialization http://en.wikipedia.org/wiki/K-means%2B%2B

initialize(kmeans_machine, data[, rng]) → None

Initialise the means randomly

Data is split into as many chunks as there are means, then each mean is set to a random example within each chunk.

Parameters:

kmeans_machine : bob.learn.em.KMeansMachine

KMeansMachine Object

data : array_like <float, 2D>

Input data

rng : bob.core.random.mt19937

The Mersenne Twister mt19937 random generator used for the initialization of subspaces/arrays before the EM loop.
m_step(kmeans_machine[, data]) → None

Updates the mean based on the statistics from the E-step

Parameters:

kmeans_machine : bob.learn.em.KMeansMachine

KMeansMachine Object

data : object

Ignored.
reset_accumulators(kmeans_machine) → None

Reset the statistics accumulators to the correct size and a value of zero.

Parameters:

kmeans_machine : bob.learn.em.KMeansMachine

KMeansMachine Object
zeroeth_order_statistics

array_like <float, 1D> <– Returns the internal statistics. Useful to parallelize the E-step

class bob.learn.em.MAP_GMMTrainer

Bases: object

This class implements the maximum a posteriori M-step of the expectation-maximization algorithm for a GMM Machine. The prior parameters are encoded in the form of a GMM (e.g. a universal background model). The EM algorithm thus performs GMM adaptation.

Constructor Documentation:

  • bob.learn.em.MAP_GMMTrainer (prior_gmm, relevance_factor, [update_means], [update_variances], [update_weights], [mean_var_update_responsibilities_threshold])
  • bob.learn.em.MAP_GMMTrainer (prior_gmm, alpha, [update_means], [update_variances], [update_weights], [mean_var_update_responsibilities_threshold])
  • bob.learn.em.MAP_GMMTrainer (other)

Creates a MAP_GMMTrainer

Additionally to the copy constructor, there are two different ways to call this constructor, one using the relevance_factor and one using the alpha, both which have the same signature. Hence, the only way to differentiate the two functions is by using keyword arguments.

Parameters:

prior_gmm : bob.learn.em.GMMMachine

The prior GMM to be adapted (Universal Background Model UBM).

relevance_factor : float

If set the Reynolds Adaptation procedure will be applied. See Eq (14) from [Reynolds2000]

alpha : float

Set directly the alpha parameter (Eq (14) from [Reynolds2000]), ignoring zeroth order statistics as a weighting factor.

update_means : bool

[Default: True] Update means on each iteration

update_variances : bool

[Default: True] Update variances on each iteration

update_weights : bool

[Default: True] Update weights on each iteration

mean_var_update_responsibilities_threshold : float

[Default: min_float] Threshold over the responsibilities of the Gaussians Equations 9.24, 9.25 of Bishop, Pattern recognition and machine learning, 2006 require a division by the responsibilities, which might be equal to zero because of numerical issue. This threshold is used to avoid such divisions.

other : bob.learn.em.MAP_GMMTrainer

A MAP_GMMTrainer object to be copied.

Class Members:

alpha

float <– Set directly the alpha parameter (Eq (14) from [Reynolds2000]), ignoring zeroth order statistics as a weighting factor.

compute_likelihood(gmm_machine) → None

This functions returns the average min (Square Euclidean) distance (average distance to the closest mean)

Parameters:

gmm_machine : bob.learn.em.GMMMachine

GMMMachine Object
e_step(gmm_machine, data) → None

Calculates and saves statistics across the dataset and saves these as gmm_statistics.

Calculates the average log likelihood of the observations given the GMM,and returns this in average_log_likelihood.The statistics, gmm_statistics, will be used in the m_step() that follows.

Parameters:

gmm_machine : bob.learn.em.GMMMachine

GMMMachine Object

data : array_like <float, 2D>

Input data
gmm_statistics

GMMStats <– The GMM statistics that were used internally in the E- and M-steps

Setting and getting the internal GMM statistics might be useful to parallelize the GMM training.

initialize(gmm_machine[, data]) → None

Initialization before the EM steps

Parameters:

gmm_machine : bob.learn.em.GMMMachine

GMMMachine Object

data : object

Ignored.
m_step(gmm_machine[, data]) → None

Performs a maximum a posteriori (MAP) update of the GMM parameters using the accumulated statistics in gmm_statistics and the parameters of the prior model

Parameters:

gmm_machine : bob.learn.em.GMMMachine

GMMMachine Object

data : object

Ignored.
relevance_factor

float <– If set the reynolds_adaptation parameters, will apply the Reynolds Adaptation Factor. See Eq (14) from [Reynolds2000]

class bob.learn.em.ML_GMMTrainer

Bases: object

This class implements the maximum likelihood M-step of the expectation-maximisation algorithm for a GMM Machine.

Constructor Documentation:

  • bob.learn.em.ML_GMMTrainer (update_means, [update_variances], [update_weights], [mean_var_update_responsibilities_threshold])
  • bob.learn.em.ML_GMMTrainer (other)

Creates a ML_GMMTrainer

Parameters:

update_means : bool

Update means on each iteration

update_variances : bool

Update variances on each iteration

update_weights : bool

Update weights on each iteration

mean_var_update_responsibilities_threshold : float

Threshold over the responsibilities of the Gaussians Equations 9.24, 9.25 of Bishop, Pattern recognition and machine learning, 2006 require a division by the responsibilities, which might be equal to zero because of numerical issue. This threshold is used to avoid such divisions.

other : bob.learn.em.ML_GMMTrainer

A ML_GMMTrainer object to be copied.

Class Members:

compute_likelihood(gmm_machine) → None

This functions returns the average min (Square Euclidean) distance (average distance to the closest mean)

Parameters:

gmm_machine : bob.learn.em.GMMMachine

GMMMachine Object
e_step(gmm_machine, data) → None

Calculates and saves statistics across the dataset,and saves these as m_ss.

Calculates the average log likelihood of the observations given the GMM,and returns this in average_log_likelihood.The statistics, gmm_statistics, will be used in the m_step() that follows.

Parameters:

gmm_machine : bob.learn.em.GMMMachine

GMMMachine Object

data : array_like <float, 2D>

Input data
gmm_statistics

GMMStats <– The GMM statistics that were used internally in the E- and M-steps

Setting and getting the internal GMM statistics might be useful to parallelize the GMM training.

initialize(gmm_machine[, data]) → None

Initialization before the EM steps

Parameters:

gmm_machine : bob.learn.em.GMMMachine

GMMMachine Object

data : object

Ignored.
m_step(gmm_machine[, data]) → None

Performs a maximum likelihood (ML) update of the GMM parameters using the accumulated statistics in gmm_statistics

See Section 9.2.2 of Bishop, “Pattern recognition and machine learning”, 2006

Parameters:

gmm_machine : bob.learn.em.GMMMachine

GMMMachine Object

data : object

Ignored.
class bob.learn.em.PLDABase

Bases: object

This class is a container for the F (between class variantion matrix), G (within class variantion matrix) and \Sigma matrices and the mean vector \mu of a PLDA model. This alsoprecomputes useful matrices to make the model scalable.References: [ElShafey2014,PrinceElder2007,LiFu2012]

Constructor Documentation:

  • bob.learn.em.PLDABase (dim_d,dim_f,dim_g,variance_threshold)
  • bob.learn.em.PLDABase (other)
  • bob.learn.em.PLDABase (hdf5)

Constructor, builds a new PLDABase. F, G and \Sigma are initialized to the ‘eye’ matrix (matrix with 1’s on the diagonal and 0 outside), and \mu is initialized to 0.

Parameters:

dim_d : int

Dimensionality of the feature vector.

dim_f : int

Size of F (between class variantion matrix).

dim_g : int

Size of G (within class variantion matrix).

variance_threshold : float

The smallest possible value of the variance (Ignored if set to 0.)

other : bob.learn.em.PLDABase

A PLDABase object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

clear_maps() → None

Clears the maps (\gamma_a and loglike_constterm_a).

compute_gamma(a, res) → None

Tells if the \gamma_a matrix for a given a (number of samples) exists. \gamma_a=(Id + a F^T \beta F)^{-1}

Parameters:

a : int

Index

res : array_like <float, 2D>

Input data
compute_log_like_const_term(a, res) → None

Computes the log likelihood constant term for a given a (number of samples), given the provided \gamma_a matrix. l_{a} = \frac{a}{2} ( -D log(2\pi) -log|\Sigma| +log|\alpha|
+log|\gamma_a|)

Parameters:

a : int

Index

res : array_like <float, 2D>

Input data
compute_log_likelihood_point_estimate(xij, hi, wij) → output

Gets the log-likelihood of an observation, given the current model and the latent variables (point estimate).This will basically compute p(x_{ij} | h_{i}, w_{ij}, \Theta), given by \mathcal{N}(x_{ij}|[\mu + F h_{i} + G w_{ij} +
\epsilon_{ij}, \Sigma]), which is in logarithm, \frac{D}{2}
log(2\pi) -\frac{1}{2} log(det(\Sigma)) -\frac{1}{2}
{(x_{ij}-(\mu+F h_{i}+G w_{ij}))^{T}\Sigma^{-1}(x_{ij}-(\mu+F
h_{i}+G w_{ij}))}

Parameters:

xij : array_like <float, 1D>

hi : array_like <float, 1D>

wij : array_like <float, 1D>

Returns:

output : float

f

array_like <float, 2D> <– Returns the F matrix (between class variantion matrix)

g

array_like <float, 2D> <– Returns the G matrix (between class variantion matrix)

get_add_gamma(a) → output

Gets the gamma_a matrix for a given f_a (number of samples). \gamma_a=(Id + a F^T \beta F)^{-1}
=\mathcal{F}_{a}.Tries to find it from the base machine and then from this machine.

Parameters:

a : int

Index

Returns:

output : array_like <float, 2D>

get_add_log_like_const_term(a) → output

Gets the log likelihood constant term for a given a (number of samples). l_{a} = \frac{a}{2} ( -D log(2\pi) -log|\Sigma|
+log|\alpha| +log|\gamma_a|)

Parameters:

a : int

Index

Returns:

output : float

get_gamma(a) → output

Gets the \gamma_a matrix for a given a (number of samples). \gamma_{a}=(Id + a F^T \beta F)^{-1} =
\mathcal{F}_{a}

Parameters:

a : int

Index

Returns:

output : array_like <float, 2D>

Get the \gamma matrix
get_log_like_const_term(a) → output

Gets the log likelihood constant term for a given a (number of samples). l_{a}=\frac{a}{2} ( -D log(2\pi) -log|\Sigma|
+log|\alpha| +log|\gamma_a|)

Parameters:

a : int

Index

Returns:

output : float

has_gamma(a) → output

Tells if the \gamma_a matrix for a given a (number of samples) exists. \gamma_a=(Id + aF^T \beta F)^{-1}

Parameters:

a : int

Index

Returns:

output : bool

has_log_like_const_term(a) → output

Tells if the log likelihood constant term for a given a (number of samples) exists in this machine (does not check the base machine). l_{a}=\frac{a}{2} ( -D log(2\pi) -log|\Sigma|
+log|\alpha| +log|\gamma_a|)

Parameters:

a : int

Index

Returns:

output : bool

is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this PLDABase with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.PLDABase

A PLDABase object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
load(hdf5) → None

Load the configuration of the PLDABase to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
mu

array_like <float, 1D> <– Gets the \mu mean vector of the PLDA model

resize(dim_d, dim_f, dim_g) → None

Resizes the dimensionality of the PLDA model. Paramaters \mu, F, G and \Sigma are reinitialized.

Parameters:

dim_d : int

Dimensionality of the feature vector.

dim_f : int

Size of F (between class variantion matrix).

dim_g : int

Size of G (within class variantion matrix).
save(hdf5) → None

Save the configuration of the PLDABase to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
shape

(int,int, int) <– A tuple that represents the dimensionality of the feature vector dim_d, the F matrix and the G matrix.

sigma

array_like <float, 1D> <– Gets the \sigma (diagonal) covariance matrix of the PLDA model

variance_threshold

float <–

class bob.learn.em.PLDAMachine

Bases: object

This class is a container for an enrolled identity/class. It contains information extracted from the enrollment samples. It should be used in combination with a PLDABase instance.

References: [ElShafey2014], [PrinceElder2007], [LiFu2012]

Constructor Documentation:

  • bob.learn.em.PLDAMachine (plda_base)
  • bob.learn.em.PLDAMachine (other)
  • bob.learn.em.PLDAMachine (hdf5,plda_base)

Constructor, builds a new PLDAMachine.

Parameters:

plda_base : bob.learn.em.PLDABase

other : bob.learn.em.PLDAMachine

A PLDAMachine object to be copied.

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading

Class Members:

clear_maps() → None

Clears the maps (\gamma_a and loglike_constterm_a).

compute_log_likelihood(sample, with_enrolled_samples) → output

Compute the log-likelihood of the given sample and (optionally) the enrolled samples

Parameters:

sample : array_like <float, 1D>,array_like <float, 2D>

Sample

with_enrolled_samples : bool

Returns:

output : float

The log-likelihood
get_add_gamma(a) → output

Gets the gamma_a matrix for a given f_a (number of samples). \gamma_a=(Id + a F^T \beta F)^{-1}
=\mathcal{F}_{a}.Tries to find it from the base machine and then from this machine.

Parameters:

a : int

Index

Returns:

output : array_like <float, 2D>

get_add_log_like_const_term(a) → output

Gets the log likelihood constant term for a given a (number of samples). l_{a} = \frac{a}{2} ( -D log(2\pi) -log|\Sigma|
+log|\alpha| +log|gamma_a|)

Parameters:

a : int

Index

Returns:

output : float

get_gamma(a) → output

Gets the \gamma_a matrix for a given a (number of samples). \gamma_{a}=(Id + a F^T \beta F)^{-1}=
\mathcal{F}_{a}

Parameters:

a : int

Index

Returns:

output : array_like <float, 2D>

Get the \gamma matrix
get_log_like_const_term(a) → output

Gets the log likelihood constant term for a given a (number of samples). l_{a}=\frac{a}{2}( -D log(2\pi) -log|\Sigma|
+log|\alpha| + log|\gamma_a|)

Parameters:

a : int

Index

Returns:

output : float

has_gamma(a) → output

Tells if the \gamma_a matrix for a given a (number of samples) exists. \gamma_a=(Id + a F^T \beta F)^{-1}

Parameters:

a : int

Index

Returns:

output : bool

has_log_like_const_term(a) → output

Tells if the log likelihood constant term for a given a (number of samples) exists in this machine (does not check the base machine). l_{a}=\frac{a}{2} ( -D log(2\pi) -log|\Sigma|
+log|\alpha| +log|\gamma_a|)

Parameters:

a : int

Index

Returns:

output : bool

is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this PLDAMachine with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.PLDAMachine

A PLDAMachine object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
load(hdf5) → None

Load the configuration of the PLDAMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for reading
log_likelihood

float <– Get the current log likelihood

log_likelihood_ratio(samples) → output

Computes a log likelihood ratio from a 1D or 2D blitz::Array

Parameters:

samples : array_like <float, 1D>,array_like <float, 2D>

Sample

Returns:

output : float

The log-likelihood ratio
n_samples

int <– Number of enrolled samples

plda_base

bob.learn.em.PLDABase <– The PLDABase attached to this machine

save(hdf5) → None

Save the configuration of the PLDAMachine to a given HDF5 file

Parameters:

hdf5 : bob.io.base.HDF5File

An HDF5 file open for writing
shape

(int,int, int) <– A tuple that represents the dimensionality of the feature vector dim_d, the F matrix and the G matrix.

w_sum_xit_beta_xi

float <– Gets the A = -0.5 \sum_{i} x_{i}^T \beta x_{i} value

weighted_sum

array_like <float, 1D> <– Get/Set \sum_{i} F^T \beta x_{i} value

class bob.learn.em.PLDATrainer

Bases: object

This class can be used to train the F, G and \Sigma matrices and the mean vector \mu of a PLDA model.References: [ElShafey2014],[PrinceElder2007]_,[LiFu2012]_

Constructor Documentation:

  • bob.learn.em.PLDATrainer (use_sum_second_order)
  • bob.learn.em.PLDATrainer (other)
  • bob.learn.em.PLDATrainer ()
Default constructor.
Initializes a new PLDA trainer. The training stage will place the resulting components in the PLDABase.

Parameters:

other : bob.learn.em.PLDATrainer

A PLDATrainer object to be copied.

use_sum_second_order : bool

Class Members:

e_step(plda_base, data) → None

Expectation step before the EM steps

Parameters:

plda_base : bob.learn.em.PLDABase

PLDAMachine Object

data : list

enroll(plda_machine, data) → None

Main procedure for enrolling a PLDAMachine

Parameters:

plda_machine : bob.learn.em.PLDAMachine

PLDAMachine Object

data : list

finalize(plda_base, data) → None

finalize before the EM steps

Parameters:

plda_base : bob.learn.em.PLDABase

PLDAMachine Object

data : list

init_f_method

str <– The method used for the initialization of $F$.

Possible values are: (‘RANDOM_F’, ‘BETWEEN_SCATTER’)

init_g_method

str <– The method used for the initialization of $G$.

Possible values are: (‘RANDOM_G’, ‘WITHIN_SCATTER’)

init_sigma_method

str <– The method used for the initialization of $\Sigma$.

Possible values are: (‘RANDOM_SIGMA’, ‘VARIANCE_G’, ‘CONSTANT’, ‘VARIANCE_DATA’)

initialize(plda_base, data[, rng]) → None

Initialization before the EM steps

Parameters:

plda_base : bob.learn.em.PLDABase

PLDAMachine Object

data : list

rng : bob.core.random.mt19937

The Mersenne Twister mt19937 random generator used for the initialization of subspaces/arrays before the EM loop.
is_similar_to(other[, r_epsilon][, a_epsilon]) → output

Compares this PLDATrainer with the other one to be approximately the same.

The optional values r_epsilon and a_epsilon refer to the relative and absolute precision for the weights, biases and any other values internal to this machine.

Parameters:

other : bob.learn.em.PLDAMachine

A PLDAMachine object to be compared.

r_epsilon : float

Relative precision.

a_epsilon : float

Absolute precision.

Returns:

output : bool

True if it is similar, otherwise false.
m_step(plda_base, data) → None

Maximization step

Parameters:

plda_base : bob.learn.em.PLDABase

PLDAMachine Object

data : list

use_sum_second_order

bool <– Tells whether the second order statistics are stored during the training procedure, or only their sum.

z_first_order

array_like <float, 2D> <–

z_second_order

array_like <float, 3D> <–

z_second_order_sum

array_like <float, 2D> <–

bob.learn.em.linear_scoring(models, ubm, test_stats, test_channelOffset, frame_length_normalisation) → output

Parameters:

models : [bob.learn.em.GMMMachine]

ubm : bob.learn.em.GMMMachine

test_stats : [bob.learn.em.GMMStats]

test_channelOffset : [array_like<float,1>]

frame_length_normalisation : bool

Returns:

output : array_like<float,1>

Score
bob.learn.em.tnorm(rawscores_probes_vs_models, rawscores_probes_vs_tmodels) → output

Normalise raw scores with T-Norm

Parameters:

rawscores_probes_vs_models : array_like <float, 2D>

Raw set of scores

rawscores_probes_vs_tmodels : array_like <float, 2D>

T-Scores (raw scores of the T probes against the models)

Returns:

output : array_like <float, 2D>

The scores T Normalized
bob.learn.em.train(trainer, machine, data, max_iterations=50, convergence_threshold=None, initialize=True, rng=None)[source]

Trains a machine given a trainer and the proper data

Parameters:
trainer
: one of KMeansTrainer, MAP_GMMTrainer, ML_GMMTrainer, ISVTrainer, IVectorTrainer, PLDATrainer, EMPCATrainer
A trainer mechanism
machine
: one of KMeansMachine, GMMMachine, ISVBase, IVectorMachine, PLDAMachine, bob.learn.linear.Machine
A container machine
data
: array_like <float, 2D>
The data to be trained
max_iterations
: int
The maximum number of iterations to train a machine
convergence_threshold
: float
The convergence threshold to train a machine. If None, the training procedure will stop with the iterations criteria
initialize
: bool
If True, runs the initialization procedure
rng
: bob.core.random.mt19937
The Mersenne Twister mt19937 random generator used for the initialization of subspaces/arrays before the EM loop
bob.learn.em.train_jfa(trainer, jfa_base, data, max_iterations=10, initialize=True, rng=None)[source]

Trains a bob.learn.em.JFABase given a bob.learn.em.JFATrainer and the proper data

Parameters:
trainer
: bob.learn.em.JFATrainer
A JFA trainer mechanism
jfa_base
: bob.learn.em.JFABase
A container machine
data
: [[bob.learn.em.GMMStats]]
The data to be trained
max_iterations
: int
The maximum number of iterations to train a machine
initialize
: bool
If True, runs the initialization procedure
rng
: bob.core.random.mt19937
The Mersenne Twister mt19937 random generator used for the initialization of subspaces/arrays before the EM loops
bob.learn.em.znorm(rawscores_probes_vs_models, rawscores_zprobes_vs_models) → output

Normalise raw scores with Z-Norm

Parameters:

rawscores_probes_vs_models : array_like <float, 2D>

Raw set of scores

rawscores_zprobes_vs_models : array_like <float, 2D>

Z-Scores (raw scores of the Z probes against the models)

Returns:

output : array_like <float, 2D>

The scores Z Normalized
bob.learn.em.ztnorm(rawscores_probes_vs_models, rawscores_zprobes_vs_models, rawscores_probes_vs_tmodels, rawscores_zprobes_vs_tmodels, mask_zprobes_vs_tmodels_istruetrial) → output

Normalise raw scores with ZT-Norm.Assume that znorm and tnorm have no common subject id.

Parameters:

rawscores_probes_vs_models : array_like <float, 2D>

Raw set of scores

rawscores_zprobes_vs_models : array_like <float, 2D>

Z-Scores (raw scores of the Z probes against the models)

rawscores_probes_vs_tmodels : array_like <float, 2D>

T-Scores (raw scores of the T probes against the models)

rawscores_zprobes_vs_tmodels : array_like <float, 2D>

ZT-Scores (raw scores of the Z probes against the T-models)

mask_zprobes_vs_tmodels_istruetrial : array_like <float, 2D>

Returns:

output : array_like <float, 2D>

The scores ZT Normalized