A semi-supervised hidden Markov tree (HMT) model is developed for texture analysis, incorporating both labeled and unlabeled data for training; the optimal balance between labeled and unlabeled data is estimated via the homotopy method. In traditional EM-based semi-supervised modeling, this balance is dictated by the relative size of labeled and unlabeled data, often leading to poor performance. Semi-supervised modeling may be viewed as a source allocation problem between labeled and unlabeled data, controlled by a parameter λ ∈ [0, 1], where λ = 0 and 1 correspond to the purely supervised HMT model and purely unsupervised HMT-based clustering, respectively. We consider the homotopy method to track a path of fixed points starting from λ = 0, with the optimal source allocation identified as a critical transition point where the solution is unsupported by the initial labeled data. Experimental results on real textures demonstrate the superiority of this method compared to the EM-based semi-supervised HMT training.

We propose an approximate Bayesian approach for unsupervised feature selection and density estimation, where the importance of the features for clustering is used as the measure for feature selection. Traditional maximum-likelihood (ML) model-parameter optimization schemes estimate the feature saliencies for a fixed model structure (i.e., a fixed number of clusters). In practice, the number of clusters present in the data for mixture-based modeling is unknown. In an ML framework, the number of clusters typically needs to be ascertained prior to estimating the feature saliencies. We propose a density estimation scheme that addresses model complexity (number of clusters present) and model-parameter estimation (feature saliencies) in a single optimization framework. The approximate Bayesian approach presented here, based on the expectation propagation method, obtains a full posterior distribution on the saliency of the features, along with full posterior distribution of other model parameters (including the number of clusters) that represent the underlying statistics of the data. The performance of the algorithm, is analyzed based on its ability to identify the features salient for clustering the multivariate data.

Time-reversal imaging (TRI) is analogous to matched-field processing, although TRI is typically very wideband and is capable of performing target classification (in addition to localization). We apply the time-reversal technique to locate man-made cylindrical targets moving in a shallow ocean channel at long range, as well as to classify them from natural false targets like a school of fish. We present imaging and classification on simulated scattering data, for both target classes. In addition to the imaging, we explore extraction of features from the time-reversal data, with these applied to subsequent target classification. Time-reversal implementation requires a fast forward model, which we implement by a normal-mode model. We present the underlying theory of TRI, feature extraction and target classification via a relevance vector machine (RVM).

Wavelet-domain hidden Markov tree (HMT) modeling provides a powerful approach to capture the underlying statistics of the wavelet coefficients. We develop a mutual information-based information-theoretic approach to quantify the interactions between the wavelet coefficients within a wavelet tree. This graphical method enables the design of a context-specific hidden Markov tree (HMT) by adding or deleting links from the traditional tree structure. The performance of the model is demonstrated on segmenting two-dimensional synthetic textures having intricate substructures, although the method can be used for signals of arbitrary dimensions.

Time-reversal imaging is addressed for sensing an elastic target situated in an acoustic waveguide. It is demonstrated that the channel parameters associated with a given measurement may be determined via a genetic-algorithm (GA) search in parameter space. Target classification based on time-reversal imagery is considered, with this implemented via a relevance-vector machine.

The DNA microarray technique offers an ability to analyze the expression profile of a genome. The complex correlation between the large number of genes present in the genome undermines straightforward understanding of their functionality. In this paper, we have proposed a pair of modeling schemes to recognize the functional identities of the known genes. In Independent Component Analysis (ICA), each of the microarray signals is modeled as a linear combination of some underlying independent components having specific biological interpretation. The second algorithm, Partial Least Squares (PLS) is proposed to identify the latent functional units contributing to drug sensitivity from the microarray data. Applications of this research include prediction of drug responses based on gene expressions, and also to identify the function(s) of a new gene. We consider the Rosetta compendium data set with yeast gene profiles, and the NCI-60 data set of human gene expressions as a function of drug type (cancer drugs are considered).

We consider several sequential processing algorithms for identifying genes in human DNA, based on detecting CpG ("C proceeds G") islands. The algorithms are designed to capture the underlying statistical structure in a DNA sequence. Sequential processing using a Markov model and a hidden Markov model are shown to identify most CpG islands in annotated (marked) DNA subsequences available from publicly available DNA datasets. We also consider a wavelet-based hidden Markov tree (HMT). In the context of the HMT, we address design of adaptive wavelets matched to CpG islands, this accomplished via lifting and genetic-algorithm optimization.

It has been demonstrated that hidden Markov models (HMM) provide an effective architecture for classification of distinct targets from multiple target-sensor orientations. We present a methodology for designing class-based HMM that are well suited to the identification of targets with common physical attributes. This approach provides a means to form associations between existing target classes and data from targets never observed in training. After performing a wavefront-resonance matching-pursuits feature extraction, we present an information theoretic tree-based state-parsing algorithm to define the HMM state structure for each target class. In training, class association is determined by minimizing the statistical divergence between the target under consideration and each existing class, with a new class defined when the target is poorly matched to each existing class The class-based HMM are trained with data from the members of its corresponding class, and tested on previously unobserved data. Results are presented for simulated acoustic scattering data.

Biorthogonal wavelets are applied to parse multiaspect transient scattering data in the context of signal classification. A language-based genetic algorithm is used to design wavelet filters that enhance classification performance. The biorthogonal wavelets are implemented via the lifting procedure and the optimization is carried out using a classification-based cost function. Example results are presented for target classification using measured scattering data.