"""A popular speaker recognition/diarization model (LDA and PLDA).
Authors
* Anthony Larcher 2020
* Nauman Dawalatabad 2020
Relevant Papers
- This implementation of PLDA is based on the following papers.
- PLDA model Training
* Ye Jiang et. al, "PLDA Modeling in I-Vector and Supervector Space for Speaker Verification," in Interspeech, 2012.
* Patrick Kenny et. al, "PLDA for speaker verification with utterances of arbitrary duration," in ICASSP, 2013.
- PLDA scoring (fast scoring)
* Daniel Garcia-Romero et. al, “Analysis of i-vector length normalization in speaker recognition systems,” in Interspeech, 2011.
* Weiwei-LIN et. al, "Fast Scoring for PLDA with Uncertainty Propagation," in Odyssey, 2016.
* Kong Aik Lee et. al, "Multi-session PLDA Scoring of I-vector for Partially Open-Set Speaker Detection," in Interspeech 2013.
Credits
This code is adapted from: https://git-lium.univ-lemans.fr/Larcher/sidekit
"""
import numpy
import copy
import pickle
from scipy import linalg
STAT_TYPE = numpy.float64
[docs]class StatObject_SB:
"""A utility class for PLDA class used for statistics calculations.
This is also used to pack deep embeddings and meta-information in one object.
Arguments
---------
modelset : list
List of model IDs for each session as an array of strings.
segset : list
List of session IDs as an array of strings.
start : int
Index of the first frame of the segment.
stop : int
Index of the last frame of the segment.
stat0 : tensor
An ndarray of float64. Each line contains 0-th order statistics
from the corresponding session.
stat1 : tensor
An ndarray of float64. Each line contains 1-st order statistics
from the corresponding session.
"""
def __init__(
self,
modelset=None,
segset=None,
start=None,
stop=None,
stat0=None,
stat1=None,
):
if modelset is None: # For creating empty stat server
self.modelset = numpy.empty(0, dtype="|O")
self.segset = numpy.empty(0, dtype="|O")
self.start = numpy.empty(0, dtype="|O")
self.stop = numpy.empty(0, dtype="|O")
self.stat0 = numpy.array([], dtype=STAT_TYPE)
self.stat1 = numpy.array([], dtype=STAT_TYPE)
else:
self.modelset = modelset
self.segset = segset
self.start = start
self.stop = stop
self.stat0 = stat0
self.stat1 = stat1
def __repr__(self):
ch = "-" * 30 + "\n"
ch += "modelset: " + self.modelset.__repr__() + "\n"
ch += "segset: " + self.segset.__repr__() + "\n"
ch += "seg start:" + self.start.__repr__() + "\n"
ch += "seg stop:" + self.stop.__repr__() + "\n"
ch += "stat0:" + self.stat0.__repr__() + "\n"
ch += "stat1:" + self.stat1.__repr__() + "\n"
ch += "-" * 30 + "\n"
return ch
[docs] def save_stat_object(self, filename):
with open(filename, "wb") as output:
pickle.dump(self, output, pickle.HIGHEST_PROTOCOL)
[docs] def get_model_segsets(self, mod_id):
"""Return segments of a given model.
Arguments
---------
mod_id : str
ID of the model for which segments will be returned.
"""
return self.segset[self.modelset == mod_id]
[docs] def get_model_start(self, mod_id):
"""Return start of segment of a given model.
Arguments
---------
mod_id : str
ID of the model for which start will be returned.
"""
return self.start[self.modelset == mod_id]
[docs] def get_model_stop(self, mod_id):
"""Return stop of segment of a given model.
Arguments
---------
mod_id : str
ID of the model which stop will be returned.
"""
return self.stop[self.modelset == mod_id]
[docs] def get_mean_stat1(self):
"""Return the mean of first order statistics.
"""
mu = numpy.mean(self.stat1, axis=0)
return mu
[docs] def get_total_covariance_stat1(self):
"""Compute and return the total covariance matrix of the first-order
statistics.
"""
C = self.stat1 - self.stat1.mean(axis=0)
return numpy.dot(C.transpose(), C) / self.stat1.shape[0]
[docs] def get_model_stat0(self, mod_id):
"""Return zero-order statistics of a given model
Arguments
---------
mod_id : str
ID of the model which stat0 will be returned.
"""
S = self.stat0[self.modelset == mod_id, :]
return S
[docs] def get_model_stat1(self, mod_id):
"""Return first-order statistics of a given model.
Arguments
---------
mod_id : str
ID of the model which stat1 will be returned.
"""
return self.stat1[self.modelset == mod_id, :]
[docs] def sum_stat_per_model(self):
"""Sum the zero- and first-order statistics per model and store them
in a new StatObject_SB.
Returns a StatObject_SB object with the statistics summed per model
and a numpy array with session_per_model.
"""
sts_per_model = StatObject_SB()
sts_per_model.modelset = numpy.unique(
self.modelset
) # nd: get uniq spkr ids
sts_per_model.segset = copy.deepcopy(sts_per_model.modelset)
sts_per_model.stat0 = numpy.zeros(
(sts_per_model.modelset.shape[0], self.stat0.shape[1]),
dtype=STAT_TYPE,
)
sts_per_model.stat1 = numpy.zeros(
(sts_per_model.modelset.shape[0], self.stat1.shape[1]),
dtype=STAT_TYPE,
)
# Keep this. may need this in future (Nauman)
# sts_per_model.start = numpy.empty(
# sts_per_model.segset.shape, "|O"
# ) # ndf: restruture this
# sts_per_model.stop = numpy.empty(sts_per_model.segset.shape, "|O")
session_per_model = numpy.zeros(numpy.unique(self.modelset).shape[0])
# For each model sum the stats
for idx, model in enumerate(sts_per_model.modelset):
sts_per_model.stat0[idx, :] = self.get_model_stat0(model).sum(
axis=0
)
sts_per_model.stat1[idx, :] = self.get_model_stat1(model).sum(
axis=0
)
session_per_model[idx] += self.get_model_stat1(model).shape[0]
return sts_per_model, session_per_model
[docs] def center_stat1(self, mu):
"""Center first order statistics.
Arguments
---------
mu : array
Array to center on.
"""
dim = self.stat1.shape[1] / self.stat0.shape[1]
index_map = numpy.repeat(numpy.arange(self.stat0.shape[1]), dim)
self.stat1 = self.stat1 - (
self.stat0[:, index_map] * mu.astype(STAT_TYPE)
)
[docs] def norm_stat1(self):
"""Divide all first-order statistics by their euclidian norm.
"""
vect_norm = numpy.clip(
numpy.linalg.norm(self.stat1, axis=1), 1e-08, numpy.inf
)
self.stat1 = (self.stat1.transpose() / vect_norm).transpose()
[docs] def rotate_stat1(self, R):
"""Rotate first-order statistics by a right-product.
Arguments
---------
R : ndarray
Matrix to use for right product on the first order statistics.
"""
self.stat1 = numpy.dot(self.stat1, R)
[docs] def whiten_stat1(self, mu, sigma, isSqrInvSigma=False):
"""Whiten first-order statistics
If sigma.ndim == 1, case of a diagonal covariance.
If sigma.ndim == 2, case of a single Gaussian with full covariance.
If sigma.ndim == 3, case of a full covariance UBM.
Arguments
---------
mu : array
Mean vector to be subtracted from the statistics.
sigma : narray
Co-variance matrix or covariance super-vector.
isSqrInvSigma : bool
True if the input Sigma matrix is the inverse of the square root of a covariance matrix.
"""
if sigma.ndim == 1:
self.center_stat1(mu)
self.stat1 = self.stat1 / numpy.sqrt(sigma.astype(STAT_TYPE))
elif sigma.ndim == 2:
# Compute the inverse square root of the co-variance matrix Sigma
sqr_inv_sigma = sigma
if not isSqrInvSigma:
# eigen_values, eigen_vectors = scipy.linalg.eigh(sigma)
eigen_values, eigen_vectors = linalg.eigh(sigma)
ind = eigen_values.real.argsort()[::-1]
eigen_values = eigen_values.real[ind]
eigen_vectors = eigen_vectors.real[:, ind]
sqr_inv_eval_sigma = 1 / numpy.sqrt(eigen_values.real)
sqr_inv_sigma = numpy.dot(
eigen_vectors, numpy.diag(sqr_inv_eval_sigma)
)
else:
pass
# Whitening of the first-order statistics
self.center_stat1(mu) # CENTERING
self.rotate_stat1(sqr_inv_sigma)
elif sigma.ndim == 3:
# we assume that sigma is a 3D ndarray of size D x n x n
# where D is the number of distributions and n is the dimension of a single distibution
n = self.stat1.shape[1] // self.stat0.shape[1]
sess_nb = self.stat0.shape[0]
self.center_stat1(mu)
self.stat1 = (
numpy.einsum(
"ikj,ikl->ilj", self.stat1.T.reshape(-1, n, sess_nb), sigma
)
.reshape(-1, sess_nb)
.T
)
else:
raise Exception("Wrong dimension of Sigma, must be 1 or 2")
[docs] def align_models(self, model_list):
"""Align models of the current StatServer to match a list of models
provided as input parameter. The size of the StatServer might be
reduced to match the input list of models.
Arguments
---------
model_list : ndarray of strings
List of models to match.
"""
indx = numpy.array(
[numpy.argwhere(self.modelset == v)[0][0] for v in model_list]
)
self.segset = self.segset[indx]
self.modelset = self.modelset[indx]
self.start = self.start[indx]
self.stop = self.stop[indx]
self.stat0 = self.stat0[indx, :]
self.stat1 = self.stat1[indx, :]
[docs] def align_segments(self, segment_list):
"""Align segments of the current StatServer to match a list of segment
provided as input parameter. The size of the StatServer might be
reduced to match the input list of segments.
Arguments
---------
segment_list: ndarray of strings
list of segments to match
"""
indx = numpy.array(
[numpy.argwhere(self.segset == v)[0][0] for v in segment_list]
)
self.segset = self.segset[indx]
self.modelset = self.modelset[indx]
self.start = self.start[indx]
self.stop = self.stop[indx]
self.stat0 = self.stat0[indx, :]
self.stat1 = self.stat1[indx, :]
[docs] def get_lda_matrix_stat1(self, rank):
"""Compute and return the Linear Discriminant Analysis matrix
on the first-order statistics. Columns of the LDA matrix are ordered
according to the corresponding eigenvalues in descending order.
Arguments
---------
rank : int
Rank of the LDA matrix to return.
"""
vect_size = self.stat1.shape[1]
unique_speaker = numpy.unique(self.modelset)
mu = self.get_mean_stat1()
class_means = numpy.zeros((unique_speaker.shape[0], vect_size))
Sw = numpy.zeros((vect_size, vect_size))
spk_idx = 0
for speaker_id in unique_speaker:
spk_sessions = self.get_model_stat1(speaker_id) - numpy.mean(
self.get_model_stat1(speaker_id), axis=0
)
Sw += (
numpy.dot(spk_sessions.transpose(), spk_sessions)
/ spk_sessions.shape[0]
)
class_means[spk_idx, :] = numpy.mean(
self.get_model_stat1(speaker_id), axis=0
)
spk_idx += 1
# Compute Between-class scatter matrix
class_means = class_means - mu
Sb = numpy.dot(class_means.transpose(), class_means)
# Compute the Eigenvectors & eigenvalues of the discrimination matrix
DiscriminationMatrix = numpy.dot(Sb, linalg.inv(Sw)).transpose()
eigen_values, eigen_vectors = linalg.eigh(DiscriminationMatrix)
eigen_values = eigen_values.real
eigen_vectors = eigen_vectors.real
# Rearrange the eigenvectors according to decreasing eigenvalues
# get indexes of the rank top eigen values
idx = eigen_values.real.argsort()[-rank:][::-1]
L = eigen_vectors[:, idx]
return L
[docs]def diff(list1, list2):
c = [item for item in list1 if item not in list2]
c.sort()
return c
[docs]def ismember(list1, list2):
c = [item in list2 for item in list1]
return c
[docs]class Ndx:
"""A class that encodes trial index information. It has a list of
model names and a list of test segment names and a matrix
indicating which combinations of model and test segment are
trials of interest.
Arguments
---------
modelset : list
List of unique models in a ndarray.
segset : list
List of unique test segments in a ndarray.
trialmask : 2D ndarray of bool.
Rows correspond to the models and columns to the test segments. True, if the trial is of interest.
"""
[docs] def __init__(
self, ndx_file_name="", models=numpy.array([]), testsegs=numpy.array([])
):
"""Initialize a Ndx object by loading information from a file.
Arguments
---------
ndx_file_name : str
Name of the file to load.
"""
self.modelset = numpy.empty(0, dtype="|O")
self.segset = numpy.empty(0, dtype="|O")
self.trialmask = numpy.array([], dtype="bool")
if ndx_file_name == "":
# This is needed to make sizes same
d = models.shape[0] - testsegs.shape[0]
if d != 0:
if d > 0:
last = str(testsegs[-1])
pad = numpy.array([last] * d)
testsegs = numpy.hstack((testsegs, pad))
# pad = testsegs[-d:]
# testsegs = numpy.concatenate((testsegs, pad), axis=1)
else:
d = abs(d)
last = str(models[-1])
pad = numpy.array([last] * d)
models = numpy.hstack((models, pad))
# pad = models[-d:]
# models = numpy.concatenate((models, pad), axis=1)
modelset = numpy.unique(models)
segset = numpy.unique(testsegs)
trialmask = numpy.zeros(
(modelset.shape[0], segset.shape[0]), dtype="bool"
)
for m in range(modelset.shape[0]):
segs = testsegs[numpy.array(ismember(models, modelset[m]))]
trialmask[m,] = ismember(segset, segs) # noqa E231
self.modelset = modelset
self.segset = segset
self.trialmask = trialmask
assert self.validate(), "Wrong Ndx format"
else:
ndx = Ndx.read(ndx_file_name)
self.modelset = ndx.modelset
self.segset = ndx.segset
self.trialmask = ndx.trialmask
[docs] def save_ndx_object(self, output_file_name):
with open(output_file_name, "wb") as output:
pickle.dump(self, output, pickle.HIGHEST_PROTOCOL)
[docs] def filter(self, modlist, seglist, keep):
"""Removes some of the information in an Ndx. Useful for creating a
gender specific Ndx from a pooled gender Ndx. Depending on the
value of \'keep\', the two input lists indicate the strings to
retain or the strings to discard.
Arguments
---------
modlist : array
A cell array of strings which will be compared with the modelset of 'inndx'.
seglist : array
A cell array of strings which will be compared with the segset of 'inndx'.
keep : bool
Indicating whether modlist and seglist are the models to keep or discard.
"""
if keep:
keepmods = modlist
keepsegs = seglist
else:
keepmods = diff(self.modelset, modlist)
keepsegs = diff(self.segset, seglist)
keepmodidx = numpy.array(ismember(self.modelset, keepmods))
keepsegidx = numpy.array(ismember(self.segset, keepsegs))
outndx = Ndx()
outndx.modelset = self.modelset[keepmodidx]
outndx.segset = self.segset[keepsegidx]
tmp = self.trialmask[numpy.array(keepmodidx), :]
outndx.trialmask = tmp[:, numpy.array(keepsegidx)]
assert outndx.validate, "Wrong Ndx format"
if self.modelset.shape[0] > outndx.modelset.shape[0]:
print(
"Number of models reduced from %d to %d"
% self.modelset.shape[0],
outndx.modelset.shape[0],
)
if self.segset.shape[0] > outndx.segset.shape[0]:
print(
"Number of test segments reduced from %d to %d",
self.segset.shape[0],
outndx.segset.shape[0],
)
return outndx
[docs] def validate(self):
"""Checks that an object of type Ndx obeys certain rules that
must always be true. Returns a boolean value indicating whether the object is valid
"""
ok = isinstance(self.modelset, numpy.ndarray)
ok &= isinstance(self.segset, numpy.ndarray)
ok &= isinstance(self.trialmask, numpy.ndarray)
ok &= self.modelset.ndim == 1
ok &= self.segset.ndim == 1
ok &= self.trialmask.ndim == 2
ok &= self.trialmask.shape == (
self.modelset.shape[0],
self.segset.shape[0],
)
return ok
[docs]class Scores:
"""A class for storing scores for trials. The modelset and segset
fields are lists of model and test segment names respectively.
The element i,j of scoremat and scoremask corresponds to the
trial involving model i and test segment j.
Arguments
---------
modelset : list
List of unique models in a ndarray.
segset : list
List of unique test segments in a ndarray.
scoremask : 2D ndarray of bool
Indicates the trials of interest, i.e.,
the entry i,j in scoremat should be ignored if scoremask[i,j] is False.
scoremat : 2D ndarray
Scores matrix.
"""
[docs] def __init__(self, scores_file_name=""):
""" Initialize a Scores object by loading information from a file HDF5 format.
Arguments
---------
scores_file_name : str
Name of the file to load.
"""
self.modelset = numpy.empty(0, dtype="|O")
self.segset = numpy.empty(0, dtype="|O")
self.scoremask = numpy.array([], dtype="bool")
self.scoremat = numpy.array([])
if scores_file_name == "":
pass
else:
tmp = Scores.read(scores_file_name)
self.modelset = tmp.modelset
self.segset = tmp.segset
self.scoremask = tmp.scoremask
self.scoremat = tmp.scoremat
def __repr__(self):
ch = "modelset:\n"
ch += self.modelset + "\n"
ch += "segset:\n"
ch += self.segset + "\n"
ch += "scoremask:\n"
ch += self.scoremask.__repr__() + "\n"
ch += "scoremat:\n"
ch += self.scoremat.__repr__() + "\n"
## PLDA and LDA functionalities starts here
[docs]def fa_model_loop(
batch_start, mini_batch_indices, factor_analyser, stat0, stat1, e_h, e_hh,
):
"""A function for PLDA estimation.
Arguments
---------
batch_start : int
Index to start at in the list.
mini_batch_indices : list
Indices of the elements in the list (should start at zero).
factor_analyser : instance of PLDA class
PLDA class object.
stat0 : tensor
Matrix of zero-order statistics.
stat1: tensor
Matrix of first-order statistics.
e_h : tensor
An accumulator matrix.
e_hh: tensor
An accumulator matrix.
"""
rank = factor_analyser.F.shape[1]
if factor_analyser.Sigma.ndim == 2:
A = factor_analyser.F.T.dot(factor_analyser.F)
inv_lambda_unique = dict()
for sess in numpy.unique(stat0[:, 0]):
inv_lambda_unique[sess] = linalg.inv(
sess * A + numpy.eye(A.shape[0])
)
tmp = numpy.zeros(
(factor_analyser.F.shape[1], factor_analyser.F.shape[1]),
dtype=numpy.float64,
)
for idx in mini_batch_indices:
if factor_analyser.Sigma.ndim == 1:
inv_lambda = linalg.inv(
numpy.eye(rank)
+ (factor_analyser.F.T * stat0[idx + batch_start, :]).dot(
factor_analyser.F
)
)
else:
inv_lambda = inv_lambda_unique[stat0[idx + batch_start, 0]]
aux = factor_analyser.F.T.dot(stat1[idx + batch_start, :])
numpy.dot(aux, inv_lambda, out=e_h[idx])
e_hh[idx] = inv_lambda + numpy.outer(e_h[idx], e_h[idx], tmp)
def _check_missing_model(enroll, test, ndx):
# Remove missing models and test segments
clean_ndx = ndx.filter(enroll.modelset, test.segset, True)
# Align StatServers to match the clean_ndx
enroll.align_models(clean_ndx.modelset)
test.align_segments(clean_ndx.segset)
return clean_ndx
[docs]def fast_PLDA_scoring(
enroll,
test,
ndx,
mu,
F,
Sigma,
test_uncertainty=None,
Vtrans=None,
p_known=0.0,
scaling_factor=1.0,
check_missing=True,
):
"""Compute the PLDA scores between to sets of vectors. The list of
trials to perform is given in an Ndx object. PLDA matrices have to be
pre-computed. i-vectors/x-vectors are supposed to be whitened before.
Arguments
---------
enroll : speechbrain.utils.Xvector_PLDA_sp.StatObject_SB
A StatServer in which stat1 are xvectors.
test : speechbrain.utils.Xvector_PLDA_sp.StatObject_SB
A StatServer in which stat1 are xvectors.
ndx : speechbrain.utils.Xvector_PLDA_sp.Ndx
An Ndx object defining the list of trials to perform.
mu : double
The mean vector of the PLDA gaussian.
F : tensor
The between-class co-variance matrix of the PLDA.
Sigma: tensor
The residual covariance matrix.
p_known : float
Probability of having a known speaker for open-set
identification case (=1 for the verification task and =0 for the
closed-set case).
check_missing : bool
If True, check that all models and segments exist.
"""
enroll_ctr = copy.deepcopy(enroll)
test_ctr = copy.deepcopy(test)
# If models are not unique, compute the mean per model, display a warning
if not numpy.unique(enroll_ctr.modelset).shape == enroll_ctr.modelset.shape:
# logging.warning("Enrollment models are not unique, average i-vectors")
enroll_ctr = enroll_ctr.mean_stat_per_model()
# Remove missing models and test segments
if check_missing:
clean_ndx = _check_missing_model(enroll_ctr, test_ctr, ndx)
else:
clean_ndx = ndx
# Center the i-vectors around the PLDA mean
enroll_ctr.center_stat1(mu)
test_ctr.center_stat1(mu)
# If models are not unique, compute the mean per model, display a warning
if not numpy.unique(enroll_ctr.modelset).shape == enroll_ctr.modelset.shape:
# logging.warning("Enrollment models are not unique, average i-vectors")
enroll_ctr = enroll_ctr.mean_stat_per_model()
# Compute constant component of the PLDA distribution
invSigma = linalg.inv(Sigma)
I_spk = numpy.eye(F.shape[1], dtype="float")
K = F.T.dot(invSigma * scaling_factor).dot(F)
K1 = linalg.inv(K + I_spk)
K2 = linalg.inv(2 * K + I_spk)
# Compute the Gaussian distribution constant
alpha1 = numpy.linalg.slogdet(K1)[1]
alpha2 = numpy.linalg.slogdet(K2)[1]
plda_cst = alpha2 / 2.0 - alpha1
# Compute intermediate matrices
Sigma_ac = numpy.dot(F, F.T)
Sigma_tot = Sigma_ac + Sigma
Sigma_tot_inv = linalg.inv(Sigma_tot)
Tmp = linalg.inv(Sigma_tot - Sigma_ac.dot(Sigma_tot_inv).dot(Sigma_ac))
Phi = Sigma_tot_inv - Tmp
Psi = Sigma_tot_inv.dot(Sigma_ac).dot(Tmp)
# Compute the different parts of PLDA score
model_part = 0.5 * numpy.einsum(
"ij, ji->i", enroll_ctr.stat1.dot(Phi), enroll_ctr.stat1.T
)
seg_part = 0.5 * numpy.einsum(
"ij, ji->i", test_ctr.stat1.dot(Phi), test_ctr.stat1.T
)
# Compute verification scores
score = Scores() # noqa F821
score.modelset = clean_ndx.modelset
score.segset = clean_ndx.segset
score.scoremask = clean_ndx.trialmask
score.scoremat = model_part[:, numpy.newaxis] + seg_part + plda_cst
score.scoremat += enroll_ctr.stat1.dot(Psi).dot(test_ctr.stat1.T)
score.scoremat *= scaling_factor
# Case of open-set identification, we compute the log-likelihood
# by taking into account the probability of having a known impostor
# or an out-of set class
if p_known != 0:
N = score.scoremat.shape[0]
open_set_scores = numpy.empty(score.scoremat.shape)
tmp = numpy.exp(score.scoremat)
for ii in range(N):
# open-set term
open_set_scores[ii, :] = score.scoremat[ii, :] - numpy.log(
p_known * tmp[~(numpy.arange(N) == ii)].sum(axis=0) / (N - 1)
+ (1 - p_known)
)
score.scoremat = open_set_scores
return score
[docs]class LDA:
"""A class to perform Linear Discriminant Analysis.
It returns the low dimensional representation as per LDA.
Arguments
---------
reduced_dim : int
The dimension of the output representation.
"""
def __init__(self,):
self.transform_mat = None
[docs] def do_lda(self, stat_server=None, reduced_dim=2, transform_mat=None):
"""Performs LDA and projects the vectors onto lower dimension space.
Arguments
---------
stat_server : object of speechbrain.processing.PLDA_LDA.StatObject_SB.
Contains vectors and meta-information to perform LDA.
reduced_dim : int
Dimension of the reduced space.
"""
# Get transformation matrix and project
if transform_mat is None:
self.transform_mat = stat_server.get_lda_matrix_stat1(reduced_dim)
else:
self.transform_mat = transform_mat
# Projection
new_train_obj = copy.deepcopy(stat_server)
new_train_obj.rotate_stat1(self.transform_mat)
return new_train_obj
[docs]class PLDA:
"""A class to train PLDA model from embeddings.
The input is in speechbrain.utils.StatObject_SB format.
Trains a simplified PLDA model no within-class covariance matrix but full residual covariance matrix.
Arguments
---------
mean : tensor
Mean of the vectors.
F : tensor
Eigenvoice matrix.
Sigma : tensor
Residual matrix.
Example
-------
>>> from speechbrain.processing.PLDA_LDA import *
>>> import random, numpy
>>> dim, N = 10, 100
>>> n_spkrs = 10
>>> train_xv = numpy.random.rand(N, dim)
>>> md = ['md'+str(random.randrange(1,n_spkrs,1)) for i in range(N)]
>>> modelset = numpy.array(md, dtype="|O")
>>> sg = ['sg'+str(i) for i in range(N)]
>>> segset = numpy.array(sg, dtype="|O")
>>> s = numpy.array([None] * N)
>>> stat0 = numpy.array([[1.0]]* N)
>>> xvectors_stat = StatObject_SB(modelset=modelset, segset=segset, start=s, stop=s, stat0=stat0, stat1=train_xv)
>>> # Training PLDA model: M ~ (mean, F, Sigma)
>>> plda = PLDA(rank_f=5)
>>> plda.plda(xvectors_stat)
>>> print (plda.mean.shape)
(10,)
>>> print (plda.F.shape)
(10, 5)
>>> print (plda.Sigma.shape)
(10, 10)
>>> # Enrolment (20 utts), Test (30 utts)
>>> en_N = 20
>>> en_xv = numpy.random.rand(en_N, dim)
>>> en_sgs = ['en'+str(i) for i in range(en_N)]
>>> en_sets = numpy.array(en_sgs, dtype="|O")
>>> en_s = numpy.array([None] * en_N)
>>> en_stat0 = numpy.array([[1.0]]* en_N)
>>> en_stat = StatObject_SB(modelset=en_sets, segset=en_sets, start=en_s, stop=en_s, stat0=en_stat0, stat1=en_xv)
>>> te_N = 30
>>> te_xv = numpy.random.rand(te_N, dim)
>>> te_sgs = ['te'+str(i) for i in range(te_N)]
>>> te_sets = numpy.array(te_sgs, dtype="|O")
>>> te_s = numpy.array([None] * te_N)
>>> te_stat0 = numpy.array([[1.0]]* te_N)
>>> te_stat = StatObject_SB(modelset=te_sets, segset=te_sets, start=te_s, stop=te_s, stat0=te_stat0, stat1=te_xv)
>>> ndx = Ndx(models=en_sets, testsegs=te_sets)
>>> # PLDA Scoring
>>> scores_plda = fast_PLDA_scoring(en_stat, te_stat, ndx, plda.mean, plda.F, plda.Sigma)
>>> print (scores_plda.scoremat.shape)
(20, 30)
"""
def __init__(
self,
mean=None,
F=None,
Sigma=None,
rank_f=100,
nb_iter=10,
scaling_factor=1.0,
):
self.mean = None
self.F = None
self.Sigma = None
self.rank_f = rank_f
self.nb_iter = nb_iter
self.scaling_factor = scaling_factor
if mean is not None:
self.mean = mean
if F is not None:
self.F = F
if Sigma is not None:
self.Sigma = Sigma
[docs] def plda(
self,
stat_server=None,
output_file_name=None,
whiten=False,
w_stat_server=None,
):
"""Trains PLDA model with no within class covariance matrix but full residual covariance matrix.
Arguments
---------
stat_server : speechbrain.processing.PLDA_LDA.StatObject_SB
Contains vectors and meta-information to perform PLDA
rank_f : int
Rank of the between-class covariance matrix.
nb_iter : int
Number of iterations to run.
scaling_factor : float
Scaling factor to downscale statistics (value between 0 and 1).
output_file_name : str
Name of the output file where to store PLDA model.
"""
# Dimension of the vector (x-vectors stored in stat1)
vect_size = stat_server.stat1.shape[1] # noqa F841
# Whitening (Optional)
if whiten is True:
w_mean = w_stat_server.get_mean_stat1()
w_Sigma = w_stat_server.get_total_covariance_stat1()
stat_server.whiten_stat1(w_mean, w_Sigma)
# Initialize mean and residual covariance from the training data
self.mean = stat_server.get_mean_stat1()
self.Sigma = stat_server.get_total_covariance_stat1()
# Sum stat0 and stat1 for each speaker model
model_shifted_stat, session_per_model = stat_server.sum_stat_per_model()
# Number of speakers (classes) in training set
class_nb = model_shifted_stat.modelset.shape[0]
# Multiply statistics by scaling_factor
model_shifted_stat.stat0 *= self.scaling_factor
model_shifted_stat.stat1 *= self.scaling_factor
session_per_model *= self.scaling_factor
# Covariance for stat1
sigma_obs = stat_server.get_total_covariance_stat1()
evals, evecs = linalg.eigh(sigma_obs)
# Initial F (eigen voice matrix) from rank
idx = numpy.argsort(evals)[::-1]
evecs = evecs.real[:, idx[: self.rank_f]]
self.F = evecs[:, : self.rank_f]
# Estimate PLDA model by iterating the EM algorithm
for it in range(self.nb_iter):
# E-step
# print(
# f"E-step: Estimate between class covariance, it {it+1} / {nb_iter}"
# )
# Copy stats as they will be whitened with a different Sigma for each iteration
local_stat = copy.deepcopy(model_shifted_stat)
# Whiten statistics (with the new mean and Sigma)
local_stat.whiten_stat1(self.mean, self.Sigma)
# Whiten the EigenVoice matrix
eigen_values, eigen_vectors = linalg.eigh(self.Sigma)
ind = eigen_values.real.argsort()[::-1]
eigen_values = eigen_values.real[ind]
eigen_vectors = eigen_vectors.real[:, ind]
sqr_inv_eval_sigma = 1 / numpy.sqrt(eigen_values.real)
sqr_inv_sigma = numpy.dot(
eigen_vectors, numpy.diag(sqr_inv_eval_sigma)
)
self.F = sqr_inv_sigma.T.dot(self.F)
# Replicate self.stat0
index_map = numpy.zeros(vect_size, dtype=int)
_stat0 = local_stat.stat0[:, index_map]
e_h = numpy.zeros((class_nb, self.rank_f))
e_hh = numpy.zeros((class_nb, self.rank_f, self.rank_f))
# loop on model id's
fa_model_loop(
batch_start=0,
mini_batch_indices=numpy.arange(class_nb),
factor_analyser=self,
stat0=_stat0,
stat1=local_stat.stat1,
e_h=e_h,
e_hh=e_hh,
)
# Accumulate for minimum divergence step
_R = numpy.sum(e_hh, axis=0) / session_per_model.shape[0]
_C = e_h.T.dot(local_stat.stat1).dot(linalg.inv(sqr_inv_sigma))
_A = numpy.einsum("ijk,i->jk", e_hh, local_stat.stat0.squeeze())
# M-step
# print("M-step")
self.F = linalg.solve(_A, _C).T
# Update the residual covariance
self.Sigma = sigma_obs - self.F.dot(_C) / session_per_model.sum()
# Minimum Divergence step
self.F = self.F.dot(linalg.cholesky(_R))