Saul, Lawrence K
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Publication Exploratory analysis and visualization of speech and music by locally linear embedding(2004-05-17) Jain, Viren; Saul, Lawrence KMany problems in voice recognition and audio processing involve feature extraction from raw waveforms. The goal of feature extraction is to reduce the dimensionality of the audio signal while preserving the informative signatures that, for example, distinguish different phonemes in speech or identify particular instruments in music. If the acoustic variability of a data set is described by a small number of continuous features, then we can imagine the data as lying on a low dimensional manifold in the high dimensional space of all possible waveforms. Locally linear embedding (LLE) is an unsupervised learning algorithm for feature extraction in this setting. In this paper, we present results from the exploratory analysis and visualization of speech and music by LLE.Publication Real-Time Pitch Determination of One or More Voices by Nonnegative Matrix Factorization(2004-12-13) Sha, Fei; Saul, Lawrence KAn auditory "scene", composed of overlapping acoustic sources, can be viewed as a complex object whose constituent parts are the individual sources. Pitch is known to be an important cue for auditory scene analysis. In this paper, with the goal of building agents that operate in human environments, we describe a real-time system to identify the presence of one or more voices and compute their pitch. The signal processing in the front end is based on instantaneous frequency estimation, a method for tracking the partials of voiced speech, while the pattern-matching in the back end is based on nonnegative matrix factorization, an unsupervised algorithm for learning the parts of complex objects. While supporting a framework to analyze complicated auditory scenes, our system maintains real-time operability and state-of-the-art performance in clean speech.Publication Multiplicative Updates for Classification by Mixture Models(2001-12-03) Saul, Lawrence K; Lee, Daniel DWe investigate a learning algorithm for the classification of nonnegative data by mixture models. Multiplicative update rules are derived that directly optimize the performance of these models as classifiers. The update rules have a simple closed form and an intuitive appeal. Our algorithm retains the main virtues of the Expectation-Maximization (EM) algorithm—its guarantee of monotonic improvement, and its absence of tuning parameters—with the added advantage of optimizing a discriminative objective function. The algorithm reduces as a special case to the method of generalized iterative scaling for log-linear models. The learning rate of the algorithm is controlled by the sparseness of the training data. We use the method of nonnegative matrix factorization (NMF) to discover sparse distributed representations of the data. This form of feature selection greatly accelerates learning and makes the algorithm practical on large problems. Experiments show that discriminatively trained mixture models lead to much better classification than comparably sized models trained by EM.Publication Statistical signal processing with nonnegativity constraints(2003-09-01) Saul, Lawrence K; Sha, Fei; Lee, Daniel DNonnegativity constraints arise frequently in statistical learning and pattern recognition. Multiplicative updates provide natural solutions to optimizations involving these constraints. One well known set of multiplicative updates is given by the Expectation-Maximization algorithm for hidden Markov models, as used in automatic speech recognition. Recently, we have derived similar algorithms for nonnegative deconvolution and nonnegative quadratic programming. These algorithms have applications to low-level problems in voice processing, such as fundamental frequency estimation, as well as high-level problems, such as the training of large margin classifiers. In this paper, we describe these algorithms and the ideas that connect them.Publication Multiplicative updates for nonnegative quadratic programming in support vector machines(2002-12-10) Sha, Fei; Saul, Lawrence K; Lee, Daniel DWe derive multiplicative updates for solving the nonnegative quadratic programming problem in support vector machines (SVMs). The updates have a simple closed form, and we prove that they converge monotonically to the solution of the maximum margin hyperplane. The updates optimize the traditionally proposed objective function for SVMs. They do not involve any heuristics such as choosing a learning rate or deciding which variables to update at each iteration. They can be used to adjust all the quadratic programming variables in parallel with a guarantee of improvement at each iteration. We analyze the asymptotic convergence of the updates and show that the coefficients of non-support vectors decay geometrically to zero at a rate that depends on their margins. In practice, the updates converge very rapidly to good classifiers.Publication Multiband statistical learning for f0 estimation in speech(2004-05-17) Sha, Fei; Burgoyne, J. Ashley; Saul, Lawrence KWe investigate a simple algorithm that combines multiband processing and least squares fits to estimate f0 contours in speech. The algorithm is untraditional in several respects: it makes no use of FFTs or autocorrelation at the pitch period; it updates the pitch incrementally on a sample-by-sample basis; it avoids peak picking and does not require interpolation in time or frequency to obtain high resolution estimates; and it works reliably, in real time, without the need for postprocessing to produce smooth contours. We show that a baseline implementation of the algorithm, though already quite accurate, is significantly improved by incorporating a model of statistical learning into its final stages. Model parameters are estimated from training data to minimize the likelihood of gross errors in f0 as well as errors in classifying voiced versus unvoiced speech. Experimental results on several databases confirm the benefits of statistical learning.Publication Modeling Distances in Large-Scale Networks by Matrix Factorization(2004-10-25) Mao, Yun; Saul, Lawrence KIn this paper, we propose a model for representing and predicting distances in large-scale networks by matrix factorization. The model is useful for network distance sensitive applications, such as content distribution networks, topology-aware overlays, and server selections. Our approach overcomes several limitations of previous coordinates-based mechanisms, which cannot model sub-optimal routing or asymmetric routing policies. We describe two algorithms -- singular value decomposition (SVD) and nonnegative matrix factorization (NMF) -- for representing a matrix of network distances as the product of two smaller matrices. With such a representation, we build a scalable system -- Internet Distance Estimation Service (IDES) -- that predicts large numbers of network distances from limited numbers of measurements. Extensive simulations on real-world data sets show that IDES leads to more accurate, efficient and robust predictions of latencies in large-scale networks than previous approaches.Publication Learning High Dimensional Correspondences from Low Dimensional Manifolds(2003-08-21) Lee, Daniel D; Ham, Ji Hun; Saul, Lawrence KMany different high dimensional data sets are characterized by the same underlying modes of variability. When these modes of variability are continuous and few in number, they can be viewed as parameterizing a low dimensional manifold. The manifold provides a compact shared representation of the data, suggesting correspondences between the high dimensional examples from different data sets. These correspondences, though naturally induced by the underlying manifold, are difficult to learn using traditional methods in supervised learning. In this paper, we generalize three methods in unsupervised learning—principal components analysis, factor analysis, and locally linear embedding—to discover subspaces and manifolds that provide common low dimensional representations of different high dimensional data sets. We use the shared representations discovered by these algorithms to put high dimensional examples from different data sets into correspondence. Finally, we show that a notion of "self-correspondence" between examples in the same data set can be used to improve the performance of these algorithms on small data sets. The algorithms are demonstrated on images and text.Publication Real time voice processing with audiovisual feedback : toward autonomous agents with perfect pitch(2002-12-09) Saul, Lawrence K; Lee, Daniel D; Isbell, Charles L; LeCun, YannWe have implemented a real time front end for detecting voiced speech and estimating its fundamental frequency. The front end performs the signal processing for voice-driven agents that attend to the pitch contours of human speech and provide continuous audiovisual feedback. The algorithm we use for pitch tracking has several distinguishing features: it makes no use of FFTs or autocorrelation at the pitch period; it updates the pitch incrementally on a sample-by-sample basis; it avoids peak picking and does not require interpolation in time or frequency to obtain high resolution estimates; and it works reliably over a four octave range, in real time, without the need for postprocessing to produce smooth contours. The algorithm is based on two simple ideas in neural computation: the introduction of a purposeful nonlinearity, and the error signal of a least squares fit. The pitch tracker is used in two real time multimedia applications: a voice-to-MIDI player that synthesizes electronic music from vocalized melodies, and an audiovisual Karaoke machine with multimodal feedback. Both applications run on a laptop and display the user’s pitch scrolling across the screen as he or she sings into the computer.Publication Unsupervised learning of image manifolds by semidefinite programming(2004-06-27) Weinberger, Kilian Q; Saul, Lawrence KCan we detect low dimensional structure in high dimensional data sets of images and video? The problem of dimensionality reduction arises often in computer vision and pattern recognition. In this paper, we propose a new solution to this problem based on semidefinite programming. Our algorithm can be used to analyze high dimensional data that lies on or near a low dimensional manifold. It overcomes certain limitations of previous work in manifold learning, such as Isomap and locally linear embedding. We illustrate the algorithm on easily visualized examples of curves and surfaces, as well as on actual images of faces, handwritten digits, and solid objects.