Probabilistic Linear Discriminant Analysis Model Research Articles

A damage assessment methodology for structural systems using transfer learning from the audio domain

Neural network-based strategies require balanced training datasets to avoid creating unreliable classification and prediction models. While these strategies are commonly used to model the dynamics of structural and mechanical systems, the imbalanced composition of monitoring data is a fundamental challenge for damage assessment in structural systems. The monitoring data often contain abundant observations from structures in their normal operating conditions (undamaged state) and small and partial information from systems in the damaged state. Therefore, the model, trained by adopting deep learning approaches, tends to show an ill-conditioned nature, limited to specific structures in a narrow range of damage conditions.The current study presents a damage assessment strategy that overcomes the limitations of unbalanced datasets. To improve the model’s ability to distinguish between different health conditions, informative features are utilized to facilitate the differentiation of multiple classes according to the frequency content of vibration signals. The model acquires this ability by learning from a rich dataset of human voices (source domain), where low-level features that denote the vibration traits of human waveforms are extracted. Subsequently, this knowledge is transferred to the features of a target domain that has limited data for damage detection.The proposed methodology relies on creating an informative feature extractor training a Time-Delay Neural Network (TDNN) using a collection of human voice recordings. Cepstral and pitch features derived from the speech data are used as input features for the TDNN. This network is used to derive low-level features at intermediate layers of the network, called “x-vectors”. These features store non-case-dependent information about the frequency content of the signals and depict the ability to distinguish between different classes according to a change in the frequency content of the investigated system. This is not a unique attribute of the original audio source domain, and it can be employed to help differentiate categories for any vibrating system where a modification in the frequency content is representative of a transition between classes, including the structural and mechanical systems. Because of the generalization trait of the x-vector, they can be employed to construct a Probabilistic Linear Discriminant Analysis model able to classify various damage classes considering vibration measurements obtained from a different system, i.e., a structural system (target domain).Initially, the simulated acceleration response from the 12-degree of freedom structure are analyzed to affirm the effectiveness of the framework. Then, the method is further validated by using the field data of the Z24 bridge, to evaluate its reliability in real-world applications.

Generalized Domain Adaptation Framework for Parametric Back-End in Speaker Recognition

State-of-the-art speaker recognition systems comprise a speaker embedding front-end followed by a probabilistic linear discriminant analysis (PLDA) back-end. The effectiveness of these components relies on the availability of a large amount of labeled training data. In practice, it is common for domains (e.g., language, channel, demographic) in which a system is deployed to differ from that in which a system has been trained. To close the resulting gap, domain adaptation is often essential for PLDA models. Among two of its variants are Heavy-tailed PLDA (HT-PLDA) and Gaussian PLDA (G-PLDA). Though the former better fits real feature spaces than does the latter, its popularity has been severely limited by its computational complexity and, especially, by the difficulty, it presents in domain adaptation, which results from its non-Gaussian property. Various domain adaptation methods have been proposed for G-PLDA. This paper proposes a generalized framework for domain adaptation that can be applied to both of the above variants of PLDA for speaker recognition. It not only includes several existing supervised and unsupervised domain adaptation methods but also makes possible more flexible usage of available data in different domains. In particular, we introduce here two new techniques: (1) correlation-alignment in the model level, and (2) covariance regularization. To the best of our knowledge, this is the first proposed application of such techniques for domain adaptation w.r.t. HT-PLDA. The efficacy of the proposed techniques has been experimentally validated on NIST 2016, 2018, and 2019 Speaker Recognition Evaluation (SRE’16, SRE’18 and SRE’19) datasets.

A Discriminative Hierarchical PLDA-Based Model for Spoken Language Recognition

Spoken language recognition (SLR) refers to the automatic process used to determine the language present in a speech sample. SLR is an important task in its own right, for example, as a tool to analyze or categorize large amounts of multi-lingual data. Further, it is also an essential tool for selecting downstream applications in a work flow, for example, to chose appropriate speech recognition or machine translation models. SLR systems are usually composed of two stages, one where an embedding representing the audio sample is extracted and a second one which computes the final scores for each language. In this work, we approach the SLR task as a detection problem and implement the second stage as a probabilistic linear discriminant analysis (PLDA) model. We show that discriminative training of the PLDA parameters gives large gains with respect to the usual generative training. Further, we propose a novel hierarchical approach where two PLDA models are trained, one to generate scores for clusters of highly-related languages and a second one to generate scores conditional to each cluster. The final language detection scores are computed as a combination of these two sets of scores. The complete model is trained discriminatively to optimize a cross-entropy objective. We show that this hierarchical approach consistently outperforms the non-hierarchical one for detection of highly related languages, in many cases by large margins. We train our systems on a collection of datasets including over 100 languages, and test them both on matched and mismatched conditions, showing that the gains are robust to condition mismatch.

HiLAM-aligned kernel discriminant analysis for text-dependent speaker verification

Probabilistic Linear Discriminant Analysis (PLDA) has been a commonly used backend classifier for many text-dependent speaker verification (TDSV) systems. Lately, PLDA projections have been integrated with the traditional Dynamic Time Warping (DTW) template matching framework, resulting in the DTW Online i-vector/PLDA system. The system is shown to achieve state-of-the-art performance for TDSV task. PLDA model serves to train a subspace that compensates for channel and session variabilities. It assumes linear separability between speaker-phrase information and other components. However, this relationship is known to be non-linear. The non-linearity is more prominent in case of short speech extracts, as in the case of the online i-vectors. This results in loss of vital speaker-phrase information at PLDA modeling. To this end, this work explores Kernel Discriminant Analysis (KDA) for TDSV task. It further proposes to use Hierarchical Multi-Layer Acoustic Model (HiLAM) to complement KDA with a more effective speaker-text class definition. The proposed system is hypothesized to benefit on three counts — non-linear modeling ability of KDA, speaker idiosyncrasy information associated with HiLAM-defined speaker-text units and modeling of the exact context of the pass-phrase, as offered by HiLAM. It shows a relative Equal Error Rate (EER) reduction of up to 50.63% on Part 1 of the RSR2015 database when compared to the baseline DTW Online i-vector/PLDA system.

Investigating and improving the utility of probabilistic linear discriminant analysis for acoustic signal classification

Probabilistic linear discriminant analysis (PLDA) has achieved good performance in face recognition and speaker recognition. However, the computation of PLDA using the original formulation is inefficient when there are many training data, especially when the dimensionality of the data is high. Faced with this inefficiency issue, we propose scalable formulations for PLDA. The computation of PLDA using the scalable formulations is more efficient than using the original formulation when dealing with many training data. Using the scalable formulations, the PLDA model can significantly outperform other popular classifiers for speaker recognition, such as Support Vector Machine (SVM) and Gaussian Mixture Model (GMM). Besides of directly using PLDA as a classifier, we may also use PLDA as a feature transformation technique. This PLDA-based feature transformation technique can reduce or expand the original feature dimensionality, and at the same time keep the transformed feature vector approximately following the Gaussian distribution. Our experimental results on speaker recognition and acoustic scene classification demonstrate the effectiveness of applying PLDA for feature transformation. It is then promising to combine PLDA with other classification models for improved performance, extending the utility of PLDA to a wider range of areas.

Kronecker-decomposable robust probabilistic tensor discriminant analysis

As a generative model, probabilistic linear discriminant analysis (PLDA) has achieved good performance in supervised learning tasks. The model incorporates both within-individual and between-individual variation, and remaining unexplained data variation is assumed to follow Gaussian distribution. However, the assumption of Gaussian distribution makes the model sensitive to the presence of noise and outliers in training set. To address this issue, this paper proposes a robust probabilistic linear discriminant analysis model by assuming Laplace prior on the noise term. Instead of solving high-dimensional linear systems, we embed a Kronecker-decomposable component in the new model for tensor data, significantly reducing the size of problems. As the non-conjugacy of Laplace distribution complicates the calculation of the posteriors of latent variables, we express it to a hierarchical architecture using an Inverse Gamma distribution and then adopt variational expectation–maximization (EM) algorithm to learn model parameters. The reconstruction and classification experiments on several public databases show the superiority of the proposed model compared with the state-of-the-art LDA-based algorithms.

Regularized Within-Class Precision Matrix Based PLDA in Text-Dependent Speaker Verification

In the field of speaker verification, probabilistic linear discriminant analysis (PLDA) is the dominant method for back-end scoring. To estimate the PLDA model, the between-class covariance and within-class precision matrices must be estimated from samples. However, the empirical covariance/precision estimated from samples has estimation errors due to the limited number of samples available. In this paper, we propose a method to improve the conventional PLDA by estimating the PLDA model using the regularized within-class precision matrix. We use graphical least absolute shrinking and selection operator (GLASSO) for the regularization. The GLASSO regularization decreases the estimation errors in the empirical precision matrix by making the precision matrix sparse, which corresponds to the reflection of the conditional independence structure. The experimental results on text-dependent speaker verification reveal that the proposed method reduce the relative equal error rate by up to 23% compared with the conventional PLDA.

Probabilistic Linear Discriminant Analysis Based on L1-Norm and Its Bayesian Variational Inference.

Probabilistic linear discriminant analysis (PLDA) is a very effective feature extraction approach and has obtained extensive and successful applications in supervised learning tasks. It employs the squared L2 -norm to measure the model errors, which assumes a Gaussian noise distribution implicitly. However, the noise in real-life applications may not follow a Gaussian distribution. Particularly, the squared L2 -norm could extremely exaggerate data outliers. To address this issue, this article proposes a robust PLDA model under the assumption of a Laplacian noise distribution, called L1-PLDA. The learning process employs the approach by expressing the Laplacian density function as a superposition of an infinite number of Gaussian distributions via introducing a new latent variable and then adopts the variational expectation-maximization (EM) algorithm to learn parameters. The most significant advantage of the new model is that the introduced latent variable can be used to detect data outliers. The experiments on several public databases show the superiority of the proposed L1-PLDA model in terms of classification and outlier detection.

A fuzzy‐clustering‐based hierarchical i‐vector/probabilistic linear discriminant analysis system for text‐dependent speaker verification

AbstractIn the i‐vector/probabilistic linear discriminant analysis (PLDA) technique, the PLDA backend classifier is modelled on i‐vectors. PLDA defines an i‐vector subspace that compensates the unwanted variability and helps to discriminate among speaker‐phrase pairs. The channel or session variability manifested in i‐vectors are known to be nonlinear in nature. PLDA training, however, assumes the variability to be linearly separable, thereby causing loss of important discriminating information. Besides, the i‐vector estimation, itself, is known to be poor in case of short utterances. This paper attempts to address these issues using a simple hierarchy‐based system. A modified fuzzy‐clustering technique is employed to divide the feature space into more characteristic feature subspaces using vocal source features. Thereafter, a separate i‐vector/PLDA model is trained for each of the subspaces. The sparser alignment owing to subspace‐specific universal background model and the relatively reduced dimensions of variability in individual subspaces help to train more effective i‐vector/PLDA models. Also, vocal source features are complementary to mel frequency cepstral coefficients, which are transformed into i‐vectors using mixture model technique. As a consequence, vocal source features and i‐vectors tend to have complementary information. Thus using vocal source features for classification in a hierarchy tree may help to differentiate some of the speaker‐phrase classes, which otherwise are not easily discriminable based on i‐vectors. The proposed technique has been validated on Part 1 of RSR2015 database, and it shows a relative equal error rate reduction of up to 37.41% with respect to the baseline i‐vector/PLDA system.

Unsupervised adaptation of PLDA models for broadcast diarization

We present a novel model adaptation approach to deal with data variability for speaker diarization in a broadcast environment. Expensive human annotated data can be used to mitigate the domain mismatch by means of supervised model adaptation approaches. By contrast, we propose an unsupervised adaptation method which does not need for in-domain labeled data but only the recording that we are diarizing. We rely on an inner adaptation block which combines Agglomerative Hierarchical Clustering (AHC) and Mean-Shift (MS) clustering techniques with a Fully Bayesian Probabilistic Linear Discriminant Analysis (PLDA) to produce pseudo-speaker labels suitable for model adaptation. We propose multiple adaptation approaches based on this basic block, including unsupervised and semi-supervised. Our proposed solutions, analyzed with the Multi-Genre Broadcast 2015 (MGB) dataset, reported significant improvements (16% relative improvement) with respect to the baseline, also outperforming a supervised adaptation proposal with low resources (9% relative improvement). Furthermore, our proposed unsupervised adaptation is totally compatible with a supervised one. The joint use of both adaptation techniques (supervised and unsupervised) shows a 13% relative improvement with respect to only considering the supervised adaptation.

Maximum entropy PLDA for robust speaker recognition under speech coding distortion

The system combining i-vector and probabilistic linear discriminant analysis (PLDA) has been applied with great success in the speaker recognition task. The i-vector space gives a low-dimensional representation of a speech segment and training data of a PLDA model, which offers greater robustness under different conditions. In this paper, we propose a new framework based on i-vector/PLDA and Maximum Entropy (ME) to improve the performance of speaker identification system in the presence of speech coding distortion. The results are reported on TIMIT database and speech coding obtained by passing the speech test from TIMIT database through the AMR encoder/decoder. Our results show that the proposed methode achieves improved performance when compared with the i-vector/PLDA and MEGMM.

An improved mixture robust probabilistic linear discriminant analyzer for fault classification

This article introduces a novel fault classification method based on the mixture robust probabilistic linear discriminant analysis (MRPLDA). Unlike conventional probabilistic models like probabilistic principal component analysis (PPCA), probabilistic linear discriminant analysis (PLDA) introduces two sets of latent variables to represent the within-class and between-class information, resulting in an enhanced classification capability. In order to deal with outliers and non-Gaussian distributed variables commonly encountered in industrial processes, a mixture of robust PLDA model is considered by imposing the Student’s t-priors on the noise and hidden variables of the PLDA model. Based on the model, a variational Bayesian expectation–maximization algorithm is developed for parameter estimation. In order to determine the state/class of a test sample, this article proposes a new state inference method by considering the joint probability between the test and training samples. The state inference method consists of a probability approximation, an evidence inference, and a voting based decision stage. The performance of the proposed fault classification method is illustrated by a numerical example and an application study to the Tennessee Eastman (TE) process.

Scoring Heterogeneous Speaker Vectors Using Nonlinear Transformations and Tied PLDA Models

Most current state-of-the-art text-independent speaker recognition systems are based on i-vectors, and on probabilistic linear discriminant analysis (PLDA). PLDA assumes that the i-vectors of a trial are homogeneous, i.e., that they have been extracted by the same system. In other words, the enrollment and test i-vectors belong to the same class. However, it is sometimes important to score trials including “heterogeneous” i-vectors, for instance, enrollment i-vectors extracted by an old system, and test i-vectors extracted by a newer, more accurate, system. In this paper, we introduce a PLDA model that is able to score heterogeneous i-vectors independent of their extraction approach, dimensions, and any other characteristics that make a set of i-vectors of the same speaker belong to different classes. The new model, which will be referred to as nonlinear tied-PLDA (NL-Tied-PLDA), is obtained by a generalization of our recently proposed nonlinear PLDA approach, which jointly estimates the PLDA parameters and the parameters of a nonlinear transformation of the i-vectors. The generalization consists of estimating a class-dependent nonlinear transformation of the i-vectors, with the constraint that the transformed i-vectors of the same speaker share the same speaker factor. The resulting model is flexible and accurate, as assessed by the results of a set of experiments performed on the extended core NIST SRE 2012 evaluation. In particular, NL-Tied-PLDA provides better results on heterogeneous trials with respect to the corresponding homogeneous trials scored by the old system, and, in some configurations, it also reaches the accuracy of the new system. Similar results were obtained on the female-extended core NIST SRE 2010 telephone condition.

Joint Estimation of PLDA and Nonlinear Transformations of Speaker Vectors

The Gaussian probabilistic linear discriminant anal-ysis (PLDA) model assumes Gaussian distributed priors for the latent variables that represent the speaker and channel factors. Assuming that each training i-vector belongs to a different speaker, as is usually done in i-vector extraction, i-vectors generated by a PLDA model can be considered independent and identically distributed with Gaussian distribution. Thus, we have recently proposed to transform the development i-vectors so that their distribution becomes more Gaussian-like. This is obtained by means of a sequence of affine and nonlinear transformations whose parameters are trained by maximum likelihood (ML) estimation on the development set. The evaluation i-vectors are then subject to the same transformation. Although the i-vector “gaussianization” has shown to be effective, since the i-vectors extracted from segments of the same speaker are not independent, the original assumption is not satisfactory. In this work, we show that the model can be improved by properly exploiting the information about the speaker labels, which was ignored in the previous model. In particular, a more effective PLDA model can be obtained by jointly estimating the PLDA parameters and the parameters of the nonlinear transformation of the i-vectors. In other words, while the goal of the previous approach was to “gaussianize” the training i-vectors distribution, the objective of this work is to embed the estimation of the nonlinear i-vector transformation in the PLDA model estimation. We will thus refer to this model as the nonlinear PLDA model. We show that this new approach provides significant gain with respect to PLDA, and a small, yet consistent, improvement with respect to our former i-vector “gaussianization” approach, without further additional costs.

Analysis of speech quality measures for the task of estimating the reliability of speaker verification decisions

Despite the great advances made in the speaker recognition field, like joint factor analysis (JFA) and i-vectors, there are still situations where the quality of the speech signals involved in a speaker verification (SV) trial are not good enough to take reliable decisions. This fact motivated us to investigate speech quality measures that are related to the SV performance. We analyzed measures like signal-to-noise ratio (SNR), modulation index, number of speech frames, jitter, shimmer, or likelihood of the data given the universal background model (UBM), JFA and probabilistic linear discriminant analysis models. Besides, we introduce a novel and promising measure based on the vector Taylor series (VTS) paradigm, used to adapt a clean GMM to noisy speech. We used Bayesian networks to combine these measures and produce a probabilistic reliability measure. We applied it to detect trials badly classified. We trained our Bayesian network on NIST SRE08 distorted with noise and reverberation and evaluated on a distorted version of SRE10. We found that, for noise, the best measures were SNR and modulation index; and for reverberation, the UBM likelihood. VTS based measures performed well for both types of distortions.

Fast Scoring of Full Posterior PLDA Models

A low-dimensional representation of a speech segment, the so-called i-vector, in combination with probabilistic linear discriminant analysis (PLDA) models, is the current state-of-the-art in speaker recognition. An i-vector is a compact representation of a Gaussian Mixture Model (GMM) supervector, which captures most of the GMM supervectors variability. It is usually obtained by a MAP estimate of the mean of a posterior distribution. A new PLDA model has been recently presented that, unlike the standard one, exploits the intrinsic i-vector uncertainty. This approach, referred to in this paper as Full Posterior Distribution PLDA (FP-PLDA), is particularly effective for speaker detection of short and variable duration speech segments. It is, however, computationally far more expensive than standard PLDA, making it unattractive for real applications. This paper presents three simplifications of FP-PLDA based on approximate diagonalizations of matrices involved in FP-PLDA scoring. Using in sequence these approximations allows obtaining computational costs comparable to PLDA models, with only a small performance degradation with respect to the more accurate, but less efficient, FP-PLDA models. In particular, up to 10% better performance than PLDA is obtained, with similar computational complexity, on short speech segments of variable duration, randomly extracted from the interviews and telephone conversations included in the NIST SRE 2010 extended dataset. The benefits of the proposed diagonalization approaches have also been confirmed on a short utterance text-independent verification task, where approximately 43% and 34% improvement of the EER and minimum DCF08, respectively, has been obtained with respect to PLDA.

Noise robust speaker verification via the fusion of SNR-independent and SNR-dependent PLDA

While i-vectors with probabilistic linear discriminant analysis (PLDA) can achieve state-of-the-art performance in speaker verification, the mismatch caused by acoustic noise remains a key factor affecting system performance. In this paper, a fusion system that combines a multi-condition signal-to-noise ratio (SNR)-independent PLDA model and a mixture of SNR-dependent PLDA models is proposed to make speaker verification systems more noise robust. First, the whole range of SNR that a verification system is expected to operate is divided into several narrow ranges. Then, a set of SNR-dependent PLDA models, one for each narrow SNR range, are trained. During verification, the SNR of the test utterance is used to determine which of the SNR-dependent PLDA models is used for scoring. To further enhance performance, the SNR-dependent and SNR-independent models are fused using linear and logistic regression fusion. The performance of the fusion system and the SNR-dependent system is evaluated on the NIST 2012 speaker recognition evaluation for both noisy and clean conditions. Results show that a mixture of SNR-dependent PLDA models perform better in both clean and noisy conditions. It was also found that the fusion system is more robust than the conventional i-vector/PLDA systems under noisy conditions.

Autonomous selection of i-vectors for PLDA modelling in speaker verification

Recently, systems combining i-vector and probabilistic linear discriminant analysis (PLDA) have become one of the state-of-the-art methods in text-independent speaker verification. The training data of a PLDA model is often collected from a large, diverse population. However, including irrelevant or noisy training data may deteriorate the verification performance. In this paper, we first show that data selection using k-NN improves the speaker verification performance. We then present a robust way of selecting k based on the local distance-based outlier factor (LDOF). We call this method flexible k-NN (fk-NN). We conduct experiments on male and female trials of several telephone conditions of the NIST 2006, 2008, 2010 and 2012 Speaker Recognition Evaluations (SRE). By using fk-NN, we discard a substantial amount of irrelevant or noisy training data without depending on tuning k, and achieve significant performance improvements on the NIST SRE sets.

PLDA in the i-supervector space for text-independent speaker verification

Abstract In this paper, we advocate the use of the uncompressed form of i-vector and depend on subspace modeling using probabilistic linear discriminant analysis (PLDA) in handling the speaker and session (or channel) variability. An i-vector is a low-dimensional vector containing both speaker and channel information acquired from a speech segment. When PLDA is used on an i-vector, dimension reduction is performed twice: first in the i-vector extraction process and second in the PLDA model. Keeping the full dimensionality of the i-vector in the i-supervector space for PLDA modeling and scoring would avoid unnecessary loss of information. We refer to the uncompressed i-vector as the i-supervector. The drawback in using the i-supervector with PLDA is the inversion of large matrices in the estimation of the full posterior distribution, which we show can be solved rather efficiently by portioning large matrices into smaller blocks. We also introduce the Gaussianized rank-norm, as an alternative to whitening, for feature normalization prior to PLDA modeling. We found that the i-supervector performs better during normalization. A better performance is obtained by combining the i-supervector and i-vector at the score level. Furthermore, we also analyze the computational complexity of the i-supervector system, compared with that of the i-vector, at four different stages of loading matrix estimation, posterior extraction, PLDA modeling, and PLDA scoring.

From single to multiple enrollment i-vectors: Practical PLDA scoring variants for speaker verification

The availability of multiple utterances (and hence, i-vectors) for speaker enrollment brings up several alternatives for their utilization with probabilistic linear discriminant analysis (PLDA). This paper provides an overview of their effective utilization, from a practical viewpoint. We derive expressions for the evaluation of the likelihood ratio for the multi-enrollment case, with details on the computation of the required matrix inversions and determinants. The performance of five different scoring methods, and the effect of i-vector length normalization is compared experimentally. We conclude that length normalization is a useful technique for all but one of the scoring methods considered, and averaging i-vectors is the most effective out of the methods compared. We also study the application of multicondition training on the PLDA model. Our experiments indicate that multicondition training is more effective in estimating PLDA hyperparameters than it is for likelihood computation. Finally, we look at the effect of the configuration of the enrollment data on PLDA scoring, studying the properties of conditional dependence and number-of-enrollment-utterances per target speaker. Our experiments indicate that these properties affect the performance of the PLDA model. These results further support the conclusion that i-vector averaging is a simple and effective way to process multiple enrollment utterances.