# Copyright (c) 2022 PaddlePaddle and SpeechBrain Authors. All Rights Reserved.
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"""A popular speaker recognition/diarization model (LDA and PLDA).
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 copy
import pickle
import numpy
from scipy import linalg
from paddlespeech.vector.cluster.diarization import EmbeddingMeta
def ismember(list1, list2):
c = [item in list2 for item in list1]
return c
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.
"""
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
def save_ndx_object(self, output_file_name):
with open(output_file_name, "wb") as output:
pickle.dump(self, output, pickle.HIGHEST_PROTOCOL)
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
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
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.
"""
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"
def fa_model_loop(
batch_start,
mini_batch_indices,
factor_analyser,
stat0,
stats,
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.
stats: 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(stats[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 EmbeddingMeta to match the clean_ndx
enroll.align_models(clean_ndx.modelset)
test.align_segments(clean_ndx.segset)
return clean_ndx
class PLDA:
"""
A class to train PLDA model from embeddings.
The input is in paddlespeech.vector.cluster.diarization.EmbeddingMeta 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.
"""
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
def plda(
self,
emb_meta=None,
output_file_name=None, ):
"""
Trains PLDA model with no within class covariance matrix but full residual covariance matrix.
Arguments
---------
emb_meta : paddlespeech.vector.cluster.diarization.EmbeddingMeta
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 stats)
vect_size = emb_meta.stats.shape[1]
# Initialize mean and residual covariance from the training data
self.mean = emb_meta.get_mean_stats()
self.Sigma = emb_meta.get_total_covariance_stats()
# Sum stat0 and stat1 for each speaker model
model_shifted_stat, session_per_model = emb_meta.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.stats *= self.scaling_factor
session_per_model *= self.scaling_factor
# Covariance for stats
sigma_obs = emb_meta.get_total_covariance_stats()
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
# 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_stats(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,
stats=local_stat.stats,
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.stats).dot(linalg.inv(sqr_inv_sigma))
_A = numpy.einsum("ijk,i->jk", e_hh, local_stat.stat0.squeeze())
# 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))
def scoring(
self,
enroll,
test,
ndx,
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 : paddlespeech.vector.cluster.diarization.EmbeddingMeta
A EmbeddingMeta in which stats are xvectors.
test : paddlespeech.vector.cluster.diarization.EmbeddingMeta
A EmbeddingMeta in which stats are xvectors.
ndx : paddlespeech.vector.cluster.plda.Ndx
An Ndx object defining the list of trials to perform.
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)
# 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_stats(self.mean)
test_ctr.center_stats(self.mean)
# Compute constant component of the PLDA distribution
invSigma = linalg.inv(self.Sigma)
I_spk = numpy.eye(self.F.shape[1], dtype="float")
K = self.F.T.dot(invSigma * scaling_factor).dot(self.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(self.F, self.F.T)
Sigma_tot = Sigma_ac + self.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.stats.dot(Phi),
enroll_ctr.stats.T)
seg_part = 0.5 * numpy.einsum("ij, ji->i",
test_ctr.stats.dot(Phi), test_ctr.stats.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.stats.dot(Psi).dot(test_ctr.stats.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
if __name__ == '__main__':
import random
dim, N, n_spkrs = 10, 100, 10
train_xv = numpy.random.rand(N, dim)
md = ['md' + str(random.randrange(1, n_spkrs, 1)) for i in range(N)] # spk
modelset = numpy.array(md, dtype="|O")
sg = ['sg' + str(i) for i in range(N)] # utt
segset = numpy.array(sg, dtype="|O")
stat0 = numpy.array([[1.0]] * N)
xvectors_stat = EmbeddingMeta(
modelset=modelset, segset=segset, stats=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)
# Enrollment (20 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_stat = EmbeddingMeta(modelset=en_sets, segset=en_sets, stats=en_xv)
# Test (30 utts)
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_stat = EmbeddingMeta(modelset=te_sets, segset=te_sets, stats=te_xv)
ndx = Ndx(models=en_sets, testsegs=te_sets) # trials
# PLDA Scoring
scores_plda = plda.scoring(en_stat, te_stat, ndx)
print(scores_plda.scoremat.shape) #(20, 30)