Belief fusion is the principle of combining separate beliefs or bodies of evidence originating from different sources. Depending on the situation to be modelled, different belief fusion methods can be applied. Cumulative and averaging belief fusion is defined for fusing opinions in subjective logic, and for fusing belief functions in general. The principle of fission is the opposite of fusion, namely to eliminate the contribution of a specific belief from an already fused belief, with the purpose of deriving the remaining belief. This paper describes fission of cumulative belief as well as fission of averaging belief in subjective logic. These operators can for example be applied to belief revision in Bayesian belief networks, where the belief contribution of a given evidence source can be determined as a function of a given fused belief and its other contributing beliefs.

Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. In this expository article, I discuss the main ideas behind these two types of methods, namely how to transform linear algorithms into nonlinear ones by using kernel functions, and how to make predictions with an ensemble or a collection of models rather than a single model. I also share my personal perspectives on how these ideas have influenced and shaped my own research. In particular, I present two recent algorithms that I have invented with my collaborators: LAGO, a fast kernel algorithm for unbalanced classification and rare target detection; and Darwinian evolution in parallel universes, an ensemble method for variable selection.

Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are different concepts. The former holds, given programs P and Q, iff P can be faithfully replaced by Q within any context R, while the latter holds iff P and Q provide the same output, that is, they have the same answer sets. Notions in between strong and ordinary equivalence have been introduced as theoretical tools to compare incomplete programs and are defined by either restricting the syntactic structure of the considered context programs R or by bounding the set A of atoms allowed to occur in R (relativized equivalence).For the latter approach, different A yield properly different equivalence notions, in general. For the former approach, however, it turned out that any ``reasonable'' syntactic restriction to R coincides with either ordinary, strong, or uniform equivalence. In this paper, we propose a parameterization for equivalence notions which takes care of both such kinds of restrictions simultaneously by bounding, on the one hand, the atoms which are allowed to occur in the rule heads of the context and, on the other hand, the atoms which are allowed to occur in the rule bodies of the context. We introduce a general semantical characterization which includes known ones as SE-models (for strong equivalence) or UE-models (for uniform equivalence) as special cases. Moreover,we provide complexity bounds for the problem in question and sketch a possible implementation method. To appear in Theory and Practice of Logic Programming (TPLP).

In this paper, we present a Mirroring Neural Network architecture to perform non-linear dimensionality reduction and Object Recognition using a reduced lowdimensional characteristic vector. In addition to dimensionality reduction, the network also reconstructs (mirrors) the original high-dimensional input vector from the reduced low-dimensional data. The Mirroring Neural Network architecture has more number of processing elements (adalines) in the outer layers and the least number of elements in the central layer to form a converging-diverging shape in its configuration. Since this network is able to reconstruct the original image from the output of the innermost layer (which contains all the information about the input pattern), these outputs can be used as object signature to classify patterns. The network is trained to minimize the discrepancy between actual output and the input by back propagating the mean squared error from the output layer to the input layer. After successfully training the network, it can reduce the dimension of input vectors and mirror the patterns fed to it. The Mirroring Neural Network architecture gave very good results on various test patterns.

This paper proposes an unsupervised learning technique by using Multi-layer Mirroring Neural Network and Forgy's clustering algorithm. Multi-layer Mirroring Neural Network is a neural network that can be trained with generalized data inputs (different categories of image patterns) to perform non-linear dimensionality reduction and the resultant low-dimensional code is used for unsupervised pattern classification using Forgy's algorithm. By adapting the non-linear activation function (modified sigmoidal function) and initializing the weights and bias terms to small random values, mirroring of the input pattern is initiated. In training, the weights and bias terms are changed in such a way that the input presented is reproduced at the output by back propagating the error. The mirroring neural network is capable of reducing the input vector to a great degree (approximately 1/30th the original size) and also able to reconstruct the input pattern at the output layer from this reduced code units. The feature set (output of central hidden layer) extracted from this network is fed to Forgy's algorithm, which classify input data patterns into distinguishable classes. In the implementation of Forgy's algorithm, initial seed points are selected in such a way that they are distant enough to be perfectly grouped into different categories. Thus a new method of unsupervised learning is formulated and demonstrated in this paper. This method gave impressive results when applied to classification of different image patterns.

We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in each one state. We employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. Analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules is required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. Techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems.

Chemotaxis can be defined as an innate behavioural response by an organism to a directional stimulus, in which bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals in their environment. This is important for bacteria to find food (e.g., glucose) by swimming towards the highest concentration of food molecules, or to flee from poisons. Based on self-organized computational approaches and similar stigmergic concepts we derive a novel swarm intelligent algorithm. What strikes from these observations is that both eusocial insects as ant colonies and bacteria have similar natural mechanisms based on stigmergy in order to emerge coherent and sophisticated patterns of global collective behaviour. Keeping in mind the above characteristics we will present a simple model to tackle the collective adaptation of a social swarm based on real ant colony behaviors (SSA algorithm) for tracking extrema in dynamic environments and highly multimodal complex functions described in the well-know De Jong test suite. Later, for the purpose of comparison, a recent model of artificial bacterial foraging (BFOA algorithm) based on similar stigmergic features is described and analyzed. Final results indicate that the SSA collective intelligence is able to cope and quickly adapt to unforeseen situations even when over the same cooperative foraging period, the community is requested to deal with two different and contradictory purposes, while outperforming BFOA in adaptive speed. Results indicate that the present approach deals well in severe Dynamic Optimization problems.

The generation of meaningless "words" matching certain statistical and/or linguistic criteria is frequently needed for experimental purposes in Psycholinguistics. Such stimuli receive the name of pseudowords or nonwords in the Cognitive Neuroscience literatue. The process for building nonwords sometimes has to be based on linguistic units such as syllables or morphemes, resulting in a numerical explosion of combinations when the size of the nonwords is increased. In this paper, a reactive tabu search scheme is proposed to generate nonwords of variables size. The approach builds pseudowords by using a modified Metaheuristic algorithm based on a local search procedure enhanced by a feedback-based scheme. Experimental results show that the new algorithm is a practical and effective tool for nonword generation.

This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of statistical learning theory forged by Vladimir Vapnik. Using convex analysis on the set of posterior probability measures, we show how to get local measures of the complexity of the classification model involving the relative entropy of posterior distributions with respect to Gibbs posterior measures. We then discuss relative bounds, comparing the generalization error of two classification rules, showing how the margin assumption of Mammen and Tsybakov can be replaced with some empirical measure of the covariance structure of the classification model.We show how to associate to any posterior distribution an effective temperature relating it to the Gibbs prior distribution with the same level of expected error rate, and how to estimate this effective temperature from data, resulting in an estimator whose expected error rate converges according to the best possible power of the sample size adaptively under any margin and parametric complexity assumptions. We describe and study an alternative selection scheme based on relative bounds between estimators, and present a two step localization technique which can handle the selection of a parametric model from a family of those. We show how to extend systematically all the results obtained in the inductive setting to transductive learning, and use this to improve Vapnik's generalization bounds, extending them to the case when the sample is made of independent non-identically distributed pairs of patterns and labels. Finally we review briefly the construction of Support Vector Machines and show how to derive generalization bounds for them, measuring the complexity either through the number of support vectors or through the value of the transductive or inductive margin.

Contributing to the rigorous understanding of BP, in this paper we relate the convergence of BP to spectral properties of the graph. This encompasses a result for random graphs with a ``planted'' solution; thus, we obtain the first rigorous result on BP for graph coloring in the case of a complex graphical structure (as opposed to trees). In particular, the analysis shows how Belief Propagation breaks the symmetry between the $3!$ possible permutations of the color classes.