Low-rank and Sparse Soft Targets to Learn Better DNN Acoustic Models

Conventional deep neural networks (DNN) for speech acoustic modeling rely on Gaussian mixture models (GMM) and hidden Markov model (HMM) to obtain binary class labels as the targets for DNN training. Subword classes in speech recognition systems correspond to context-dependent tied states or senones. The present work addresses some limitations of GMM-HMM senone alignments for DNN training. We hypothesize that the senone probabilities obtained from a DNN trained with binary labels can provide more accurate targets to learn better acoustic models. However, DNN outputs bear inaccuracies which are exhibited as high dimensional unstructured noise, whereas the informative components are structured and low-dimensional. We exploit principle component analysis (PCA) and sparse coding to characterize the senone subspaces. Enhanced probabilities obtained from low-rank and sparse reconstructions are used as soft-targets for DNN acoustic modeling, that also enables training with untranscribed data. Experiments conducted on AMI corpus shows 4.6% relative reduction in word error rate

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation $Ax=b$, where $A$ is an $m\times n$ full-rank matrix, $b$ is a column-vector of dimension $m$, and $m$ (the number of equations) is larger than or equal to $n$ (the dimension of the unknown vector $x$). Generally, the equations are inconsistent and there is no feasible solution for $x$ unless $b$ belongs to the column-span of $A$. In the least-square approach, a candidate solution is found as the unique $x$ that minimizes the error function $\|Ax-b\|_2$. We propose a more general approach that consist in considering all the consistent subset of the equations, finding their solutions, and taking a weighted average of them to build a candidate solution. In particular, we show that by weighting the solutions with the squared determinant of their coefficient matrix, the resulting candidate solution coincides with the least square solution

Exploiting Low-dimensional Structures to Enhance DNN Based Acoustic Modeling in Speech Recognition

We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces. To that end, the training posteriors are used for dictionary learning and sparse coding. Sparse representation of the test posteriors using this dictionary enables projection to the space of training data. Relying on the fact that the intrinsic dimensions of the posterior subspaces are indeed very small and the matrix of all posteriors belonging to a class has a very low rank, we demonstrate how low-dimensional structures enable further enhancement of the posteriors and rectify the spurious errors due to mismatch conditions. The enhanced acoustic modeling method leads to improvements in continuous speech recognition task using hybrid DNN-HMM (hidden Markov model) framework in both clean and noisy conditions, where upto 15.4% relative reduction in word error rate (WER) is achieved

Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings

We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for characterizing the room acoustic from the unknown competing speech sources relying on localization of the early images of the speakers by sparse approximation of the spatial spectra of the virtual sources in a free-space model. The images are then clustered exploiting the low-rank structure of the spectro-temporal components belonging to each source. This enables us to identify the early support of the room impulse response function and its unique map to the room geometry. To further tackle the ambiguity of the reflection ratios, we propose a novel formulation of the reverberation model and estimate the absorption coefficients through a convex optimization exploiting joint sparsity model formulated upon spatio-spectral sparsity of concurrent speech representation. The acoustic parameters are then incorporated for separating individual speech signals through either structured sparse recovery or inverse filtering the acoustic channels. The experiments conducted on real data recordings demonstrate the effectiveness of the proposed approach for multi-party speech recovery and recognition.Comment: 31 page

Ad Hoc Microphone Array Calibration: Euclidean Distance Matrix Completion Algorithm and Theoretical Guarantees

This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing entries based on a novel Euclidean distance matrix completion algorithm by alternative low-rank matrix completion and projection onto the Euclidean distance space. This approach confines the recovered matrix to the EDM cone at each iteration of the matrix completion algorithm. The theoretical guarantees of the calibration performance are obtained considering the random and locally structured missing entries as well as the measurement noise on the known distances. This study elucidates the links between the calibration error and the number of microphones along with the noise level and the ratio of missing distances. Thorough experiments on real data recordings and simulated setups are conducted to demonstrate these theoretical insights. A significant improvement is achieved by the proposed Euclidean distance matrix completion algorithm over the state-of-the-art techniques for ad hoc microphone array calibration.Comment: In Press, available online, August 1, 2014. http://www.sciencedirect.com/science/article/pii/S0165168414003508, Signal Processing, 201

Convexity in source separation: Models, geometry, and algorithms

Source separation or demixing is the process of extracting multiple components entangled within a signal. Contemporary signal processing presents a host of difficult source separation problems, from interference cancellation to background subtraction, blind deconvolution, and even dictionary learning. Despite the recent progress in each of these applications, advances in high-throughput sensor technology place demixing algorithms under pressure to accommodate extremely high-dimensional signals, separate an ever larger number of sources, and cope with more sophisticated signal and mixing models. These difficulties are exacerbated by the need for real-time action in automated decision-making systems. Recent advances in convex optimization provide a simple framework for efficiently solving numerous difficult demixing problems. This article provides an overview of the emerging field, explains the theory that governs the underlying procedures, and surveys algorithms that solve them efficiently. We aim to equip practitioners with a toolkit for constructing their own demixing algorithms that work, as well as concrete intuition for why they work

Speaker Direction Finding for Practical Systems: A Comparison of Different Approaches

Speaker direction finding techniques have aroused interests due to achieving the capability of receiving high-quality dis- tant signals. Interesting concepts can be achieved through the comparison of such techniques whereby importance is in achieving high quality signals at reasonable complexity rates. With this aim in mind, this paper presents a critical compari- son between two such traditional techniques; Time-Difference of Arrival (TDOA) estimation by Generalized Cross Correla- tion (GCC) and space scanning by Steered Response Power (SRP) of a beamformer. Each is analyzed under diverse con- ditions of noise and reverberation. Simulation results and experiments based on real data have been able to show that SRP with short data segments and due to its characteristic of averaging over the spatial dimension illustrate better accuracy results than that of GCC. These results have instigated a new method in the estimation of the source direction from a set of TDOAs based on spatial curvature collision. This paper dis- cusses how this procedure reduces the computational cost more than 50 times compared to the conventional method of Root Mean Square (RMS) error minimization over the candi- date locations

Redundant Hash Addressing for Large-Scale Query by Example Spoken Query Detection

State of the art query by example spoken term detection (QbE-STD) systems rely on representation of speech in terms of sequences of class-conditional posterior probabilities estimated by deep neural network (DNN). The posteriors are often used for pattern matching or dynamic time warping (DTW). Exploiting posterior probabilities as speech representation propounds diverse advantages in a classification system. One key property of the posterior representations is that they admit a highly effective hashing strategy that enables indexing the large archive in divisions for reducing the search complexity. Moreover, posterior indexing leads to a compressed representation and enables pronunciation dewarping and partial detection with no need for DTW. We exploit these characteristics of the posterior space in the context of redundant hash addressing for query-by-example spoken term detection (QbE-STD). We evaluate the QbE-STD system on AMI corpus and demonstrate that tremendous speedup and superior accuracy is achieved compared to the state-of-the-art pattern matching and DTW solutions. The system has great potential to enable massively large scale query detection