The relational approach to dependency estimation entails the selection of a sufficiently compact 'relevance' subset of training-set objects with which any newly occurring object may be compared in order to estimate its hidden target characteristics. If several comparison modalities are available, a 'relevance' subset of these may additionally have to be chosen via an appropriate selection criterion. Typically, the level of selectivity will constitute a free parameter, and in traditional approaches, multiple training repetitions would be required to determine this value via cross-validation. To avoid this, we seek to algorithmically emulate the cross-validation process using conservative assumptions as to the nature of the unknown probability distribution that produced the training set. We term this approach 'non-enumerative cross-validation', and demonstrate that the classical Akaike Information Criterion is a specific case of it under naive assumptions. The application of this non-enumerative cross-validation strategy is demonstrated on the standard multikernel data set, "chicken-pieces", treated from the perspective of relational discriminant analysis.

This paper proposes a definition and a solution of the problem of finding a hyper cavity as a data-free hyper sphere of maximum radius. This problem is formulated here as a multiextremal problem under constraints in a linear feature space and in a linear space produced by a kernel function. In accordance with the proposed approach, just as in the one-class SVM, the center of the hyper sphere is sought for as a linear combination of some small quantity of so called "support" objects. Experiments with smulated points in a 2-dimensional feature space and with symbolic sequences modeling a global evolutionary process have demonstrated correctness of the obtained solution.

In multimodal biometric information fusion, it is common to encounter missing modalities in which matching cannot be performed. As a result, at the match score level, this implies that scores will be missing. We address the multimodal fusion problem involving missing modalities (scores) using support vector machines (SVMs) with the neutral point substitution (NPS) method. The approach starts by processing each modality using a kernel. When a modality is missing, at the kernel level, the missing modality is substituted by one that is unbiased with regards to the classification, called a neutral point. Critically, unlike conventional missing-data substitution methods, explicit calculation of neutral points may be omitted by virtue of their implicit incorporation within the SVM training framework. Experiments based on the publicly available Biosecure DS2 multimodal (scores) data set show that the SVM-NPS approach achieves very good generalization performance compared to the sum rule fusion, especially with severe missing modalities.

The problem of finding the most appropriate subset of features or regressors is the generic challenge of Machine Learning problems like regression estimation or pattern recognition. We consider the problem of time-varying regression estimation, which implies also the inevitable necessity to choose the individual appropriate levels of model volatility in each of regressors, ranging from the full stationarity of instant models to their absolute independence in time. The problem is considered from the Bayesian point of view as that of estimating the sequence of regression coefficients associated with the hidden vector state of a stochastic linear dynamic system, whose a priori model includes parameters responsible for both the size of the subset of active regressors and the time-volatility factors of regression coefficients at them. The proposed technique of adaptive time varying regression estimation is built as that of estimating both the state and parameters of the hidden state-space model.

The problem of signature verification is considered within the bounds of the kernel-based methodology of pattern recognition, more specifically, SVM principle of machine learning. A kernel in the set of signatures can be defined in different ways and it is impossible to choose the most appropriate kernel a priori. We propose a principle of fusing several on-line and off-line kernels into an entire training and verification technique. Experiments with signature database SVC2004 have shown that the multi-kernel approach essentially decreases the error rate in comparison with verification based on single kernels.

Multi-modal pattern recognition must frequently truncate the set of initially available modalities. When a kernel-based approach is adopted within each modality, the problem of modality selection becomes mathematically analogous to that of wrapper-based feature selection. In this paper, we revise two implicitly wrapper based methods of SVM-embedded selective kernel combination, the Relevance and Support Kernel Machines, so as to equip them with the ability to preset the desired level of feature-selectivity. Hence, a continuous axis of nested feature selection models is obtained, ranging from the absence of selectivity to the selection of single features. We thus unite the distinct processes of selection and classification within the two techniques in manner suitable for general application within Kernel-based multi-modal pattern recognition.

The problem of prospecting oil and gas reserves in the crystalline basement of the Earth mantle by way of a combined interpretation of seismic data registered on the daylight surface and direct information from a sparse net of exploratory wells is considered as pattern recognition problem in which the role of objects whose class membership is to be recovered is played by points of the three-dimensional underground medium. Local properties of reflected seismic signals serve as features of the membership of the respective rock mass zones in the class of collectors, i.e. spatial areas capable of accumulating fluids, whereas direct data obtained from exploratory wells serve as trainer's information. A new spatial approach to supervised pattern recognition is proposed which makes use of the fact that objects to be recognized are arranged in an array in space. Along with the additional assumption that immediately adjacent points offer a tendency to belong to the same class, this fact allows for drawing reliable decisions from relatively unreliable features.

A class of signal and image processing problems is considered from the standpoint of treating them as those of coordinating the local data-dependent information and model-based smoothness constraints. Such a generalized problem is set as the formal problem of minimization of a separable objective function defined on an appropriate neighborhood graph of data array elements.

Under the generalized smoothing of a signal or image, a wider class of operations is understood than the plain suppression of noise. A variational approach to the generalized edge-preserving smoothing is considered on the basis of treating the sought-for result of processing as the minimum point of an objective function.

Four problems of image processing, namely, those of smoothing. texture image segmentation, matching two images of similar structure, and building the local texture orientation map, are considered jointly as problems which can be treated as those of transforming the original image into another function on the image plane. We generalized statistical image processing procedure is aimed at finding a compromise between the local image-dependent information on the values of the hidden function at each pixel and the a priori information expressed in the form of some Markov smoothness constraints. For attaining a higher computation speed, instead of a full unitary prior Markov model of the hidden field, a compromise composite model is used which consists of a set of independent identical tree-like Markov neighborhood graphs.