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Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The increasing need for learning sparse models in large-scale applications motivates the development of efficient, robust, and provably good dictionary learning algorithms. Algorithmic stability and generalizability are desirable characteristics for dictionary learning algorithms that aim to build global dictionaries, which can efficiently model any test data similar to the training samples. In this paper, we propose an algorithm to learn dictionaries for sparse representations from large scale data, and prove that the proposed learning algorithm is stable and generalizable asymptotically. The algorithm employs a 1-D subspace clustering procedure, the K-hyperline clustering, to learn a hierarchical dictionary with multiple levels. We also propose an information-theoretic scheme to estimate the number of atoms needed in each level of learning and develop an ensemble approach to learn robust dictionaries. Using the proposed dictionaries, the sparse code for novel test data can be computed using a low-complexity pursuit procedure. We demonstrate the stability and generalization characteristics of the proposed algorithm using simulations. We also evaluate the utility of the multilevel dictionaries in compressed recovery and subspace learning applications.

In complex visual recognition tasks, it is typical to adopt multiple descriptors, which describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a unified feature space in a principled manner using kernel methods. Sparse models that generalize well to the test data can be learned in the unified kernel space, and appropriate constraints can be incorporated for application in supervised and unsupervised learning. In this paper, we propose to perform sparse coding and dictionary learning in the multiple kernel space, where the weights of the ensemble kernel are tuned based on graph-embedding principles such that class discrimination is maximized. In our proposed algorithm, dictionaries are inferred using multiple levels of 1D subspace clustering in the kernel space, and the sparse codes are obtained using a simple levelwise pursuit scheme. Empirical results for object recognition and image clustering show that our algorithm outperforms existing sparse coding based approaches, and compares favorably to other state-of-the-art methods.

Vowel space area (VSA) is an attractive metric for the study of speech production deficits and reductions in intelligibility, in addition to the traditional study of vowel distinctiveness. Traditional VSA estimates are not currently sufficiently sensitive to map to production deficits. The present report describes an automated algorithm using healthy, connected speech rather than single syllables and estimates the entire vowel working space rather than corner vowels. Analyses reveal a strong correlation between the traditional VSA and automated estimates. When the two methods diverge, the automated method seems to provide a more accurate area since it accounts for all vowels. [ABSTRACT FROM AUTHOR]

We propose a method for characterizing sound activity in fixed spaces through segmentation, indexing, and retrieval of continuous audio recordings. Regarding segmentation, we present a dynamic Bayesian network (DBN) that jointly infers onsets and end times of the most prominent sound events in the space, along with an extension of the algorithm for covering large spaces with distributed microphone arrays. Each segmented sound event is indexed with a hidden Markov model (HMM) that models the distribution of example-based queries that a user would employ to retrieve the event (or similar events). In order to increase the efficiency of the retrieval search, we recursively apply a modified spectral clustering algorithm to group similar sound events based on the distance between their corresponding HMMs. We then conduct a formal user study to obtain the relevancy decisions necessary for evaluation of our retrieval algorithm on both automatically and manually segmented sound clips. Furthermore, our segmentation and retrieval algorithms are shown to be effective in both quiet indoor and noisy outdoor recording conditions. [ABSTRACT FROM AUTHOR]

A new speech analysis-synthesis approach that is based on a perceptually-motivated all-pole (PMAP) modeling is described. The main idea is to directly estimate the perceptually relevant pole locations using an auditory excitation pattern-matching method. The all-pole model is synthesized using the perceptual poles and produces improved spectral fitting. We show that the prediction residual obtained from the PMAP analysis has lower perceptual loudness relative to that of the conventional LP. [ABSTRACT FROM AUTHOR]

Abstract: Gradient-type adaptive channel equalizers can suffer from burst error problems under sustained fading and in the absence of sufficient excitation. To overcome this problem, we propose an algorithm called the gradient-with-projection-on-bounding-ellipsoid (GPrOBE). The main idea in the proposed GPrOBE algorithm is that the equalizer parameters are computed by projecting the gradient estimate onto a set that is updated using a priori information on the instantaneous error magnitude. Simulation results show an improvement in the performance of the GPrOBE algorithm over other gradient-based algorithms in terms of reduced error bursts. Normalized error energy (NEE) performance analysis highlights that the GPrOBE algorithm yields solutions that are close to minimum mean-square-error (MMSE), while providing instantaneous performance guarantees during periods of insufficient excitation. Bit error rate (BER) experiments reveal that the GPrOBE algorithm is more robust in channels with sustained fading. [Copyright &y& Elsevier]

Although adaptive gradient algorithms are relatively robust, they generally have poor performance in the absence of “rich” excitation. It is well known that the convergence speed of the LMS algorithm deteriorates when the condition number of the autocorrelation matrix of the input is large. This problem has been addressed using RLS, Weighted RLS (WRLS), as well as normalized frequency-domain algorithms. In this paper, we present an alternative approach that employs gradient projections in selected eigenvector subspaces to improve the convergence properties of LMS algorithms. We also use an auxiliary algorithm that iteratively updates selected eigensubspaces. The proposed algorithm is efficient in terms of complexity and its convergence speed approaches that of the WRLS for a certain class of excitation signals. [Copyright &y& Elsevier]

An optimum block modified covariance algorithm is developed for computing time-varying autoregressive (AR) parameters. The method presented here differs from those presented previously in that it derives optimally selected time-varying convergence factors such that the block mean square error is minimized from one iteration to the next. In particular, the algorithm developed here, called block modified covariance algorithm with individual adaptation of parameters (BMCAI), uses individual time-varying convergence factors computed using modified covariance matrix approximations along with the Gauss–Seidel method. Even though the BMCAI is gradient based, it retains the attractive spectral matching properties of fixed-window least-squares modified covariance algorithms while at the same time providing capabilities for time-varying spectral estimation. [Copyright &y& Elsevier]

Focuses on the interaction and integration of several components of a Mobile Ad-Hoc Network (MANET) using smart antenna systems. Description of adaptive signal processing algorithms; Information on the design of the antenna system; Simulation for the performance of the MANET.

Abstract: K-hyperline clustering is an iterative algorithm based on singular value decomposition and it has been successfully used in sparse component analysis. In this paper, we prove that the algorithm converges to a locally optimal solution for a given set of training data, based on Lloyd’s optimality conditions. Furthermore, the local optimality is shown by developing an Expectation-Maximization procedure for learning dictionaries to be used in sparse representations and by deriving the clustering algorithm as its special case. The cluster centroids obtained from the algorithm are proved to tessellate the space into convex Voronoi regions. The stability of clustering is shown by posing the problem as an empirical risk minimization procedure over a function class. It is proved that, under certain conditions, the cluster centroids learned from two sets of i.i.d. training samples drawn from the same probability space become arbitrarily close to each other, as the number of training samples increase asymptotically. [Copyright &y& Elsevier]