We report a result of perturbation analysis on decoding error of the belief propagation decoder for Gallager codes. The analysis is based on information geometry, and it shows that the principal term of decoding error at equilibrium comes from the m-embedding curvature of the log-linear submanifold spanned by the estimated pseudoposteriors, one for the full marginal, and K for partial posteriors, each of which takes a single check into account, where K is the number of checks in the Gallager code. It is then shown that the principal error term vanishes when the parity-check matrix of the code is so sparse that there are no two columns with overlap greater than 1.

The mystery of belief propagation (BP) decoder, especially of the turbo decoding, is studied from information geometrical viewpoint. The loopy belief network (BN) of turbo codes makes it difficult to obtain the true "belief" by BP, and the characteristics of the algorithm and its equilibrium are not clearly understood. Our study gives an intuitive understanding of the mechanism, and a new framework for the analysis. Based on the framework, we reveal basic properties of the turbo decoding.

We consider a problem of blind source separation from a set of instantaneous linear mixtures, where the mixing matrix is unknown. It was discovered recently, that exploiting the sparsity of sources in an appropriate representation according to some signal dictionary, dramatically improves the quality of separation. In this work we use the property of multi scale transforms, such as wavelet or wavelet packets, to decompose signals into sets of local features with various degrees of sparsity. We use this intrinsic property for selecting the best (most sparse) subsets of features for further separation. The performance of the algorithm is verified on noise-free and noisy data. Experiments with simulated signals, musical sounds and images demonstrate significant improvement of separation quality over previously reported results.

We propose a novel clustering method that is an extension of ideas inherent to scale-space clustering and support-vector clustering. Like the latter, it associates every data point with a vector in Hilbert space, and like the former it puts emphasis on their total sum, that is equal to the scalespace probability function. The novelty of our approach is the study of an operator in Hilbert space, represented by the Schrödinger equation of which the probability function is a solution. This Schrödinger equation contains a potential function that can be derived analytically from the probability function.

The way groups of auditory neurons interact to code acoustic information is investigated using an information theoretic approach. We develop measures of redundancy among groups of neurons, and apply them to the study of collaborative coding efficiency in two processing stations in the auditory pathway: the inferior colliculus (IC) and the primary auditory cortex (AI). Under two schemes for the coding of the acoustic content, acoustic segments coding and stimulus identity coding, we show differences both in information content and group redundancies between IC and AI neurons. These results provide for the first time a direct evidence for redundancy reduction along the ascending auditory pathway, as has been hypothesized for theoretical considerations [Barlow 1959,2001]. The redundancy effects under the single-spikes coding scheme are significant only for groups larger than ten cells, and cannot be revealed with the redundancy measures that use only pairs of cells. The results suggest that the auditory system transforms low level representations that contain redundancies due to the statistical structure of natural stimuli, into a representation in which cortical neurons extract rare and independent component of complex acoustic signals, that are useful for auditory scene analysis.

This paper describes a clustering algorithm for vector quantizers using a "stochastic association model". It offers a new simple and powerful softmax adaptation rule. The adaptation process is the same as the online K-means clustering method except for adding random fluctuation in the distortion error evaluation process. Simulation results demonstrate that the new algorithm can achieve efficient adaptation as high as the "neural gas" algorithm, which is reported as one of the most efficient clustering methods. It is a key to add uncorrelated random fluctuation in the similarity evaluation process for each reference vector. For hardware implementation of this process, we propose a nanostructure, whose operation is described by a single-electron circuit. It positively uses fluctuation in quantum mechanical tunneling processes.

A flexible pattern-matching analog classifier is presented in conjunction with a robust image representation algorithm called Principal Axes Projection (PAP). In the circuit, the functional form of matching is configurable in terms of the peak position, the peak height and the sharpness of the similarity evaluation. The test chip was fabricated in a 0.6-µm CMOS technology and successfully applied to handwritten pattern recognition and medical radiograph analysis using PAP as a feature extraction pre-processing step for robust image coding. The separation and classification of overlapping patterns is also experimentally demonstrated.

The information bottleneck method is an unsupervised model independent data organization technique. Given a joint distribution peA, B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are informative about B. In a recent paper, we introduced a general principled framework for multivariate extensions of the information bottleneck method that allows us to consider multiple systems of data partitions that are interrelated. In this paper, we present a new family of simple agglomerative algorithms to construct such systems of interrelated clusters. We analyze the behavior of these algorithms and apply them to several real-life datasets.

In the'missing data' approach to improving the robustness of automatic speech recognition to added noise, an initial process identifies spectraltemporal regions which are dominated by the speech source. The remaining regions are considered to be'missing'. In this paper we develop a connectionist approach to the problem of adapting speech recognition to the missing data case, using Recurrent Neural Networks. In contrast to methods based on Hidden Markov Models, RNNs allow us to make use of long-term time constraints and to make the problems of classification with incomplete data and imputing missing values interact. We report encouraging results on an isolated digit recognition task.

A new class of Support Vector Machine (SVM) that is applicable to sequential-pattern recognition such as speech recognition is developed by incorporating an idea of nonlinear time alignment into the kernel function. Since the time-alignment operation of sequential pattern is embedded in the new kernel function, standard SVM training and classification algorithms can be employed without further modifications. The proposed SVM (DTAK-SVM) is evaluated in speaker-dependent speech recognition experiments of hand-segmented phoneme recognition. Preliminary experimental results show comparable recognition performance with hidden Markov models (HMMs).