Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

This chapter introduces the subject of statistical pattern recognition (SPR). It starts by considering how features are defined and emphasizes that the nearest neighbor algorithm achieves error rates comparable with those of an ideal Bayes’ classifier. The concepts of an optimal number of features, representativeness of the training data, and the need to avoid overfitting to the training data are stressed. The chapter shows that methods such as the support vector machine and artificial neural networks are subject to these same training limitations, although each has its advantages. For neural networks, the multilayer perceptron architecture and back-propagation algorithm are described. The chapter distinguishes between supervised and unsupervised learning, demonstrating the advantages of the latter and showing how methods such as clustering and principal components analysis fit into the SPR framework. The chapter also defines the receiver operating characteristic, which allows an optimum balance between false positives and false negatives to be achieved.

Statistical Pattern Recognition

We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorithms do not consider such temporal correlation and thus their performance degrades significantly with the correlation. In this paper, we propose a block sparse Bayesian learning framework which models the temporal correlation. We derive two sparse Bayesian learning (SBL) algorithms, which have superior recovery performance compared to existing algorithms, especially in the presence of high temporal correlation. Furthermore, our algorithms are better at handling highly underdetermined problems and require less row-sparsity on the solution matrix. We also provide analysis of the global and local minima of their cost function, and show that the SBL cost function has the very desirable property that the global minimum is at the sparsest solution to the MMV problem. Extensive experiments also provide some interesting results that motivate future theoretical research on the MMV model.

Sparse Signal Recovery With Temporally Correlated Source Vectors Using Sparse Bayesian Learning

/pdf/analysis-of-observed-chaotic-data-3spe9uweeb.pdf

Analysis of observed chaotic data

The VLDB journal : the international journal on very large data bases.

This paper presents a new rotation-invariant image retrieval method, which extends a recently introduced classification technique based on steerable wavelet transforms. In the proposed procedure, the feature extraction step consists of estimating the covariations (lower-order cross-correlations) between the wavelet subband coefficients, which are modeled as subGaussian random vectors. The similarity measurement is carried out first by employing norms calculating the distance between the covariation matrices representing two distinct images and second by evaluating the Kullback-Leibler Distance (KLD) between their corresponding subGaussian distributions. We provide analytical expressions relating the subGaussian features corresponding to a rotated image from the features of the original image. Finally, we relate the employed optimal lower-order correlation (p/spl les/2) to the degree of nonGaussianity of the wavelet coefficients, and we demonstrate the effectiveness of our method using real texture images.

/pdf/subgaussian-rotation-invariant-features-for-steerable-52h9f9m18y.pdf

SubGaussian rotation-invariant features for steerable wavelet-based image retrieval

A novel statistical scheme for the characterization of underwater acoustic signals is tested in a shallow water environment for the classification of the bottom properties The scheme is using the statistics of the 1-D wavelet coefficients of the transformed signal For geoacoustic inversions based on optimization procedures, an appropriate norm is defined, based on the Kullback-Leibler divergence (KLD), expressing the difference between two statistical distributions Thus the similarity of two environments is determined by means of an appropriate norm expressing the difference between two acoustical signals The performance of the proposed inversion method is studied using synthetic acoustic signals generated in a shallow water environment over a fluid bottom

http://users.ics.forth.gr/~tsakalid/PAPERS/CNFRS/2005-ICTCA.pdf

Characterization of an underwater acoustic signal using the statistics of the wavelet subband coefficients

Graph denoising of impulsive EEG signals and the effect of their graph representation

Sensor networks gather an enormous amount of data over space and time to derive an estimate of a parameter or function. Several constraints, such as limited power, bandwidth, and storage capacity, motivate the need for a new paradigm for sensor data processing in order to extend the network's lifetime, while also obtaining accurate estimates. In a companion paper [1], we proposed a novel iterative algorithm for reconstructing non-negative sparse signals in highly impulsive background by modeling their prior distribution using symmetric alpha-stable distributions. In the present work, we extend this algorithm in the framework of distributed compressed sensing using duality theory and the method of subgradients for the optimization of the associated cost function. The experimental results show that our proposed distributed method maintains the reconstruction performance of its centralized counterpart, while also achieving a highly sparse basis configuration, thus reducing the total amount of data handled by each sensor.

Distributed compressed sensing of non-negative signals using symmetric alpha-stable distributions

Financial time series usually exhibit non-stationarity and time-varying volatility. Extraction and analysis of compli- cated patterns, such as trends and transient changes, are at the core of modern financial data analytics. Furthermore, efficient and timely analysis is often hindered by large volumes of raw data, which are supplied and stored nowadays. In this paper, the power of learned dictionaries in adapting accurately to the underlying micro-local structures of time series is exploited to extract sparse patterns, aiming at compactly capturing the meaningful information of volatile financial data. Specifically, our proposed method relies on sparse representations of the original time series in terms of dictionary atoms, which are learned and updated from the available data directly in a rolling-window fashion. In contrast to previous methods, our extracted sparse patterns enable both compact storage and highly accurate reconstruction of the original data. Equally importantly, financial analytics, such as volatility clustering, can be performed on the sparse patterns directly, thus reducing the overall computational cost, without deteriorating accuracy. Experimental evaluation on 12 market indexes reveals a superior performance of our approach against a modified symbolic representation and a well-established wavelet transform-based technique, in terms of information compactness, reconstruction accuracy, and volatility clustering efficiency.

George Tzagkarakis

Papers

SubGaussian rotation-invariant features for steerable wavelet-based image retrieval

Characterization of an underwater acoustic signal using the statistics of the wavelet subband coefficients

Graph denoising of impulsive EEG signals and the effect of their graph representation

Distributed compressed sensing of non-negative signals using symmetric alpha-stable distributions

Sparse modeling of volatile financial time series via low-dimensional patterns over learned dictionaries