Heteroscedastic Linear Discriminant Analysis Research Articles

A dynamic linear model for heteroscedastic LDA under class imbalance

Linear Discriminant Analysis (LDA) yields the optimal Bayes classifier for binary classification for normally distributed classes with equal covariance. To improve the performance of LDA, heteroscedastic LDA (HLDA) that removes the equal covariance assumption has been developed. In this paper, we show using first and second-order optimality conditions that the existing approaches either have no principled computational procedure for optimal parameter selection, or underperform in terms of the accuracy of classification and the area under the receiver operating characteristics curve (AUC) under class imbalance. Using the same optimality conditions, we then derive a dynamic Bayes optimal linear classifier for heteroscedastic LDA that is optimised via an efficient iterative procedure, which is robust against class imbalance. Experimental work is conducted on two artificial and eight real-world datasets. Our results show that the proposed algorithm compares favourably with the existing heteroscedastic LDA procedures as well as the linear support vector machine (SVM) in terms of the error rate, but is superior to all the algorithms in terms of the AUC under class imbalance. The fast training time of the proposed algorithm also encourages its use for large-data applications that show high incidence of class imbalance, such as in human activity recognition.

Improving children’s mismatched ASR using structured low-rank feature projection

The work presented in this paper explores the issues in automatic speech recognition (ASR) of children’s speech on acoustic models trained on adults’ speech. In such contexts, due to a large acoustic mismatch between training and test data, highly degraded recognition rates are noted. Even with the use of vocal tract length normalization (VTLN), the mismatched case recognition performance is still much below that for the matched case. Our earlier studies have shown that, for commonly used mel-filterbank-based cepstral features, the acoustic mismatch is exacerbated by insufficient smoothing of pitch harmonics for child speakers. To address this problem, a structured low-rank projection of the features vectors prior to learning the acoustic models as well as before decoding is proposed in this paper. To accomplish this, first a low-rank transform is learned on the training data (adults’ speech). Any dimensionality reduction technique which depends on the variance of the training data may be used for this purpose. In this work, principal component analysis and heteroscedastic linear discriminant analysis have been explored for the same. When the derived low-rank projection is applied in the mismatched testing case, it alleviates the pitch-dependent mismatch. The proposed approach provides a relative recognition performance improvement of 35% over the VTLN included baseline for the children’s mismatched ASR employing acoustic modeling based on hidden Markov models (HMM) with observation densities modeled using Gaussian mixture models (GMM). In addition to that, other acoustic modeling approaches based on subspace GMM (SGMM) and deep neural networks (DNN) have also been explored. Projecting the data to a lower-dimensional subspace is found to be effective in those frameworks as well. In the case of SGMM and DNN-based systems, the proposed approach is noted to result in relative recognition performance improvements of 33% and 21%, respectively, over their corresponding baselines.

Linear classifier design under heteroscedasticity in Linear Discriminant Analysis

Under normality and homoscedasticity assumptions, Linear Discriminant Analysis (LDA) is known to be optimal in terms of minimising the Bayes error for binary classification. In the heteroscedastic case, LDA is not guaranteed to minimise this error. Assuming heteroscedasticity, we derive a linear classifier, the Gaussian Linear Discriminant (GLD), that directly minimises the Bayes error for binary classification. In addition, we also propose a local neighbourhood search (LNS) algorithm to obtain a more robust classifier if the data is known to have a non-normal distribution. We evaluate the proposed classifiers on two artificial and ten real-world datasets that cut across a wide range of application areas including handwriting recognition, medical diagnosis and remote sensing, and then compare our algorithm against existing LDA approaches and other linear classifiers. The GLD is shown to outperform the original LDA procedure in terms of the classification accuracy under heteroscedasticity. While it compares favourably with other existing heteroscedastic LDA approaches, the GLD requires as much as 60 times lower training time on some datasets. Our comparison with the support vector machine (SVM) also shows that, the GLD, together with the LNS, requires as much as 150 times lower training time to achieve an equivalent classification accuracy on some of the datasets. Thus, our algorithms can provide a cheap and reliable option for classification in a lot of expert systems.

Subspace filtering approach based on orthogonal projection for better analysis of stressed speech under clean and noisy environments

This study explores a novel subspace projection-based approach for analysis of stressed speech. Studies have shown that stress influences the speech production system and it results in a large acoustic variation between the neutral and the stressed speech. This degrades the discrimination capability of an automatic speech recognition system trained on neutral speech when tested on stressed speech. An effort is made to reduce the acoustic mismatch by explicitly normalizing the stress-specific attributes. The stress-specific divergences are normalized by exploiting the subspace filtering technique. To accomplish this, an orthogonal projection based linear relationship between the speech and the stress information has been explored to filter an effective speech subspace, which consists of speech information. Speech subspace is constructed using K-means clustering followed by singular value decomposition method using neutral speech data. The speech and the stress information are separated by projecting the stressed speech orthogonally onto an effective speech subspace. Experimental results indicate that, the bases of an effective subspace comprises the first few eigenvectors corresponding to the highest eigenvalues. To further improve the system performance, both the neutral and the stressed speech are projected onto the lower dimensional subspace. The projections derived using the neutral speech employs heteroscedastic linear discriminant analysis in maximum likelihood linear transformations-based semi-tied adaptation framework. Consistent improvements are noted for the proposed technique in all the discussed cases.

A preliminary study on improving the recognition of esophageal speech using a hybrid system based on statistical voice conversion.

In this paper, we propose a hybrid system based on a modified statistical GMM voice conversion algorithm for improving the recognition of esophageal speech. This hybrid system aims to compensate for the distorted information present in the esophageal acoustic features by using a voice conversion method. The esophageal speech is converted into a “target” laryngeal speech using an iterative statistical estimation of a transformation function. We did not apply a speech synthesizer for reconstructing the converted speech signal, given that the converted Mel cepstral vectors are used directly as input of our speech recognition system. Furthermore the feature vectors are linearly transformed by the HLDA (heteroscedastic linear discriminant analysis) method to reduce their size in a smaller space having good discriminative properties. The experimental results demonstrate that our proposed system provides an improvement of the phone recognition accuracy with an absolute increase of 3.40 % when compared with the phone recognition accuracy obtained with neither HLDA nor voice conversion.

Comparison of Linear Discriminant Analysis Approaches in Automatic Speech Recognition

Speech recognition systems are commonly modelled by hidden Markov models with Gaussian mixture models as observation density functions. These models have a significant number of parameters, which usually leads to the problem of data sparsity, especially for under-resourced languages such as Serbian. One of the ways to overcome the problem of data sparsity is the reduction of the number of features. Linear discriminant analysis (LDA) and heteroscedastic LDA (HLDA) are two common ways to reduce the dimensionality in an automatic speech recognition task. The paper compares the properties of speech recognition systems for Serbian in which both techniques are applied with variable types of input features as well as the number of output features of (H)LDA. The best results are obtained in the case of HLDA with input vectors consisting of concatenations of feature vectors across 7 successive frames, where each feature vector contains 12 mel frequency cepstral coefficients (MFCCs) and normalized energy, and the number of output features is 32 or 35.DOI: http://dx.doi.org/10.5755/j01.eee.19.7.5167

Evaluation of weighted Fisher criteria for large category dimensionality reduction in application to Chinese handwriting recognition

To improve the class separability of Fisher linear discriminant analysis (FDA) for large category problems, we investigate the weighted Fisher criterion (WFC) by integrating weighting functions for dimensionality reduction. The objective of WFC is to maximize the sum of weighted distances of all class pairs. By setting larger weights for the most confusable classes, WFC can improve the class separation while the solution remains an eigen-decomposition problem. We evaluate five weighting functions in three different weighting spaces in a typical large category problem of handwritten Chinese character recognition. The weighting functions include four based on existing methods, namely, FDA, approximate pairwise accuracy criterion (aPAC), power function (POW), confused distance maximization (CDM), and a new one based on K-nearest neighbors (KNN). All the weighting functions can be calculated in the original feature space, low-dimensional space, or fractional space. Our experiments on a 3,755-class Chinese handwriting database demonstrate that WFC can improve the classification accuracy significantly compared to FDA. Among the weighting functions, the KNN method in the original space is the most competitive model which achieves significantly higher classification accuracy and has a low computational complexity. To further improve the performance, we propose a nonparametric extension of the KNN method from the class level to the sample level. The sample level KNN (SKNN) method is shown to outperform significantly other methods in Chinese handwriting recognition such as the locally linear discriminant analysis (LLDA), neighbor class linear discriminant analysis (NCLDA), and heteroscedastic linear discriminant analysis (HLDA).

Improved acoustic models for spontaneous speech recognition

This paper describes advances for acoustic models in Chinese spontaneous Conversational Telephone Speech (CTS) recognition task. A number of approaches were investigated in the acoustic modeling, including Heteroscedastic Linear Discriminant Analysis (HLDA), Vocal Tract Length Normalization (VTLN), Gaussianization, Minimum Phone Error (MPE), Feature space MPE (fMPE), and etc. Considering pronunciation variations in continuous speech, tones in recognition vocabulary were modified due to the Sandhi rule. The acoustic models were trained on over 200 hours of audio data from standard LDC corpora. The improved acoustic models reduce the relative Character Error Rate (CER) by about 25% over the baseline acoustic models on standard LDC test set and China 863 program evaluation data set. Acknowledgment: This work is partially supported by the National Natural Science Foundation of China (No's. 10925419, 90920302, 10874203, 60875014, 61072124, 11074275, 11161140319).

Combining formant frequency based on variable order LPC coding with acoustic features for TIMIT phone recognition

Combination of multiple acoustic features has great potential to improve Automatic Speech Recognition (ASR) accuracy. Our contribution in this research was to investigate one novel method when using voiced formants' features in combination with standard MFCC features in order to enhance TIMIT phone recognition. These voiced features provide accurate formants frequencies using a Variable Order LPC Coding (VO-LPC) algorithm that was combined with continuity constraints. The overall estimating formants were concatenated with MFCC features when a voiced frame could be detected. For feature-level combination, Heteroscedastic Linear Discriminant Analysis (HLDA) based approach had been used successfully to find an optimal linear combination of successive vectors of a single feature stream. A series of experiments on phone recognition speaker-independent continuous-speech had been carried out using a subset of the large read-speech TIMIT phone corpus. Hidden Markov Model Toolkit (HTK) was also used throughout all carried experiments. Using such feature level combination, optimized mixture splitting and a bigram language model, a detailed analysis on this combination performance was discussed for Context-Independent (CI) and Context-Dependent (CD) Hidden Markov Models (HMM). Experimental results from our proposed procedure showed that phone error rate was successfully decreased by about 3%. At phonetic level group, an increase of 8% and of 10% was observed respectively for vowel and liquid group. These results proved clear phone enhancement regarding existing state of the art.

Optimized discriminative transformations for speech features based on minimum classification error

Feature extraction is an important component of pattern classification and speech recognition. Extracted features should discriminate classes from each other while being robust to environmental conditions such as noise. For this purpose, several feature transformations are proposed which can be divided into two main categories: data-dependent transformation and classifier-dependent transformation. The drawback of data-dependent transformation is that its optimization criteria are different from the measure of classification error which can potentially degrade the classifier’s performance. In this paper, we propose a framework to optimize data-dependent feature transformations such as PCA (Principal Component Analysis), LDA (Linear Discriminant Analysis) and HLDA (Heteroscedastic LDA) using minimum classification error (MCE) as the main objective. The classifier itself is based on Hidden Markov Model (HMM). In our proposed HMM minimum classification error technique, the transformation matrices are modified to minimize the classification error for the mapped features, and the dimension of the feature vector is not changed. To evaluate the proposed methods, we conducted several experiments on the TIMIT phone recognition and the Aurora2 isolated word recognition tasks. The experimental results show that the proposed methods improve performance of PCA, LDA and HLDA transformation for mapping Mel-frequency cepstral coefficients (MFCC).

Time–Frequency Cepstral Features and Heteroscedastic Linear Discriminant Analysis for Language Recognition

The shifted delta cepstrum (SDC) is a widely used feature extraction for language recognition (LRE). With a high context width due to incorporation of multiple frames, SDC outperforms traditional delta and acceleration feature vectors. However, it also introduces correlation into the concatenated feature vector, which increases redundancy and may degrade the performance of backend classifiers. In this paper, we first propose a time-frequency cepstral (TFC) feature vector, which is obtained by performing a temporal discrete cosine transform (DCT) on the cepstrum matrix and selecting the transformed elements in a zigzag scan order. Beyond this, we increase discriminability through a heteroscedastic linear discriminant analysis (HLDA) on the full cepstrum matrix. By utilizing block diagonal matrix constraints, the large HLDA problem is then reduced to several smaller HLDA problems, creating a block diagonal HLDA (BDHLDA) algorithm which has much lower computational complexity. The BDHLDA method is finally extended to the GMM domain, using the simpler TFC features during re-estimation to provide significantly improved computation speed. Experiments on NIST 2003 and 2007 LRE evaluation corpora show that TFC is more effective than SDC, and that the GMM-based BDHLDA results in lower equal error rate (EER) and minimum average cost (Cavg) than either TFC or SDC approaches.

Multimodal Physical Activity Recognition by Fusing Temporal and Cepstral Information

A physical activity (PA) recognition algorithm for a wearable wireless sensor network using both ambulatory electrocardiogram (ECG) and accelerometer signals is proposed. First, in the time domain, the cardiac activity mean and the motion artifact noise of the ECG signal are modeled by a Hermite polynomial expansion and principal component analysis, respectively. A set of time domain accelerometer features is also extracted. A support vector machine (SVM) is employed for supervised classification using these time domain features. Second, motivated by their potential for handling convolutional noise, cepstral features extracted from ECG and accelerometer signals based on a frame level analysis are modeled using Gaussian mixture models (GMMs). Third, to reduce the dimension of the tri-axial accelerometer cepstral features which are concatenated and fused at the feature level, heteroscedastic linear discriminant analysis is performed. Finally, to improve the overall recognition performance, fusion of the multimodal (ECG and accelerometer) and multidomain (time domain SVM and cepstral domain GMM) subsystems at the score level is performed. The classification accuracy ranges from 79.3% to 97.3% for various testing scenarios and outperforms the state-of-the-art single accelerometer based PA recognition system by over 24% relative error reduction on our nine-category PA database.

A novel Bayesian logistic discriminant model: An application to face recognition

The linear discriminant analysis (LDA) is a linear classifier which has proven to be powerful and competitive compared to the main state-of-the-art classifiers. However, the LDA algorithm assumes the sample vectors of each class are generated from underlying multivariate normal distributions of common covariance matrix with different means (i.e., homoscedastic data). This assumption has restricted the use of LDA considerably. Over the years, authors have defined several extensions to the basic formulation of LDA. One such method is the heteroscedastic LDA (HLDA) which is proposed to address the heteroscedasticity problem. Another method is the nonparametric DA (NDA) where the normality assumption is relaxed. In this paper, we propose a novel Bayesian logistic discriminant (BLD) model which can address both normality and heteroscedasticity problems. The normality assumption is relaxed by approximating the underlying distribution of each class with a mixture of Gaussians. Hence, the proposed BLD provides more flexibility and better classification performances than the LDA, HLDA and NDA. A subclass and multinomial versions of the BLD are proposed. The posterior distribution of the BLD model is elegantly approximated by a tractable Gaussian form using variational transformation and Jensen's inequality, allowing a straightforward computation of the weights. An extensive comparison of the BLD to the LDA, support vector machine (SVM), HLDA, NDA and subclass discriminant analysis (SDA), performed on artificial and real data sets, has shown the advantages and superiority of our proposed method. In particular, the experiments on face recognition have clearly shown a significant improvement of the proposed BLD over the LDA.

Effective Acoustic Modeling for Pronunciation Quality Scoring of Strongly Accented Mandarin Speech

In this paper we present our investigation into improving the performance of our computer-assisted language learning (CALL) system through exploiting the acoustic model and features within the speech recognition framework. First, to alleviate channel distortion, speaker-dependent cepstrum mean normalization (CMN) is adopted and the average correlation coefficient (average CC) between machine and expert scores is improved from 78.00% to 84.14%. Second, heteroscedastic linear discriminant analysis (HLDA) is adopted to enhance the discriminability of the acoustic model, which successfully increases the average CC from 84.14% to 84.62%. Additionally, HLDA causes the scoring accuracy to be more stable at various pronunciation proficiency levels, and thus leads to an increase in the speaker correct-rank rate from 85.59% to 90.99%. Finally, we use maximum a posteriori (MAP) estimation to tune the acoustic model to fit strongly accented test speech. As a result, the average CC is improved from 84.62% to 86.57%. These three novel techniques improve the accuracy of evaluating pronunciation quality.

Linear Discriminant Analysis Using a Generalized Mean of Class Covariances and Its Application to Speech Recognition

To precisely model the time dependency of features is one of the important issues for speech recognition. Segmental unit input HMM with a dimensionality reduction method has been widely used to address this issue. Linear discriminant analysis (LDA) and heteroscedastic extensions, e.g., heteroscedastic linear discriminant analysis (HLDA) or heteroscedastic discriminant analysis (HDA), are popular approaches to reduce dimensionality. However, it is difficult to find one particular criterion suitable for any kind of data set in carrying out dimensionality reduction while preserving discriminative information. In this paper, we propose a new framework which we call power linear discriminant analysis (PLDA). PLDA can be used to describe various criteria including LDA, HLDA, and HDA with one control parameter. In addition, we provide an efficient selection method using a control parameter without training HMMs nor testing recognition performance on a development data set. Experimental results show that the PLDA is more effective than conventional methods for various data sets.

Combining Spectral Representations for Large-Vocabulary Continuous Speech Recognition

In this paper, we investigate the combination of complementary acoustic feature streams in large-vocabulary continuous speech recognition (LVCSR). We have explored the use of acoustic features obtained using a pitch-synchronous analysis, Straight, in combination with conventional features such as Mel frequency cepstral coefficients. Pitch-synchronous acoustic features are of particular interest when used with vocal tract length normalization (VTLN) which is known to be affected by the fundamental frequency. We have combined these spectral representations directly at the acoustic feature level using heteroscedastic linear discriminant analysis (HLDA) and at the system level using ROVER. We evaluated this approach on three LVCSR tasks: dictated newspaper text (WSJCAM0), conversational telephone speech (CTS), and multiparty meeting transcription. The CTS and meeting transcription experiments were both evaluated using standard NIST test sets and evaluation protocols. Our results indicate that combining conventional and pitch-synchronous acoustic feature sets using HLDA results in a consistent, significant decrease in word error rate across all three tasks. Combining at the system level using ROVER resulted in a further significant decrease in word error rate.

An Equalized Heteroscedastic Linear Discriminant Analysis Algorithm

Heteroscedastic linear discriminant analysis (HLDA) is a widely used feature extraction algorithm. This method, however, suffers from unbalanced training data in some cases. In this letter, we equalize the objective function and statistics of HLDA and present an equalized HLDA algorithm, which balances the training data according to the class prior probability. Simulations as well as experimental results for the task of language identification are used to demonstrate the effectiveness of the proposed method.

Analysis of Feature Extraction and Channel Compensation in a GMM Speaker Recognition System

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, several feature extraction and channel compensation techniques found in state-of-the-art speaker verification systems are analyzed and discussed. For the NIST SRE 2006 submission, cepstral mean subtraction, feature warping, RelAtive SpecTrAl (RASTA) filtering, heteroscedastic linear discriminant analysis (HLDA), feature mapping, and eigenchannel adaptation were incrementally added to minimize the system's error rate. This paper deals with eigenchannel adaptation in more detail and includes its theoretical background and implementation issues. The key part of the paper is, however, the post-evaluation analysis, undermining a common myth that “the more boxes in the scheme, the better the system.” All results are presented on NIST Speaker Recognition Evaluation (SRE) 2005 and 2006 data. </para>

Tree-Based Covariance Modeling of Hidden Markov Models

In this paper, we present a tree-based, full covariance hidden Markov modeling technique for automatic speech recognition applications. A multilayered tree is built first to organize all covariance matrices into a hierarchical structure. Kullback-Leibler divergence is used in the tree-building to measure inter-Gaussian distortion and successive splitting is used to construct the multilayer covariance tree. To cope with the data sparseness problem in estimating a full covariance matrix, we interpolate the diagonal covariance matrix of a leaf-node at the bottom of the tree with the full covariance of its parent and ancestors along the path up to the root node. The interpolation coefficients are estimated in the maximum likelihood sense via the EM algorithm. The interpolation is performed in three different parametric forms: 1) inverse covariance matrix, 2) covariance matrix, and 3) off-diagonal terms of the full covariance matrix. The proposed algorithm is tested in three different databases: 1) the DARPA resource management (RM), 2) the switchboard, and 3) a Chinese dictation. In all three databases, we show that the proposed tree-based full covariance modeling consistently performs better than the baseline diagonal covariance modeling. The algorithm outperforms other covariance modeling techniques, including: 1) the semi-tied covariance modeling (STC), 2) heteroscedastic linear discriminant analysis (HLDA), 3) mixtures of inverse covariance (MIC), and 4) direct full covariance modeling

Subclass discriminant analysis

Over the years, many Discriminant Analysis (DA) algorithms have been proposed for the study of high-dimensional data in a large variety of problems. Each of these algorithms is tuned to a specific type of data distribution (that which best models the problem at hand). Unfortunately, in most problems the form of each class pdf is a priori unknown, and the selection of the DA algorithm that best fits our data is done over trial-and-error. Ideally, one would like to have a single formulation which can be used for most distribution types. This can be achieved by approximating the underlying distribution of each class with a mixture of Gaussians. In this approach, the major problem to be addressed is that of determining the optimal number of Gaussians per class, i.e., the number of subclasses. In this paper, two criteria able to find the most convenient division of each class into a set of subclasses are derived. Extensive experimental results are shown using five databases. Comparisons are given against Linear Discriminant Analysis (LDA), Direct LDA (DLDA), Heteroscedastic LDA (HLDA), Nonparametric DA (NDA), and Kernel-Based LDA (K-LDA). We show that our method is always the best or comparable to the best.