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Multiple-instance learning with pairwise instance similarity

Liming Yuan, Jiafeng Liu, Xianglong Tang (2014)

International Journal of Applied Mathematics and Computer Science

Multiple-Instance Learning (MIL) has attracted much attention of the machine learning community in recent years and many real-world applications have been successfully formulated as MIL problems. Over the past few years, several Instance Selection-based MIL (ISMIL) algorithms have been presented by using the concept of the embedding space. Although they delivered very promising performance, they often require long computation times for instance selection, leading to a low efficiency of the whole...

Multi-stage genetic fuzzy systems based on the iterative rule learning approach.

Antonio González, Francisco Herrera (1997)

Mathware and Soft Computing

Genetic algorithms (GAs) represent a class of adaptive search techniques inspired by natural evolution mechanisms. The search properties of GAs make them suitable to be used in machine learning processes and for developing fuzzy systems, the so-called genetic fuzzy systems (GFSs). In this contribution, we discuss genetics-based machine learning processes presenting the iterative rule learning approach, and a special kind of GFS, a multi-stage GFS based on the iterative rule learning approach, by...

Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces

Mihai Mihăilescu, Vicenţiu Rădulescu (2008)

Annales de l’institut Fourier

We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.

Neural methods for obtaining fuzzy rules.

José Manuel Benítez, Armando Blanco, Miguel Delgado, Ignacio Requena (1996)

Mathware and Soft Computing

In previous papers, we presented an empirical methodology based on Neural Networks for obtaining fuzzy rules which allow a system to be described, using a set of examples with the corresponding inputs and outputs. Now that the previous results have been completed, we present another procedure for obtaining fuzzy rules, also based on Neural Networks with Backpropagation, with no need to establish beforehand the labels or values of the variables that govern the system.

Neural network based identification of hysteresis in human meridian systems

Yonghong Tan, Ruili Dong, Hui Chen, Hong He (2012)

International Journal of Applied Mathematics and Computer Science

Developing a model based digital human meridian system is one of the interesting ways of understanding and improving acupuncture treatment, safety analysis for acupuncture operation, doctor training, or treatment scheme evaluation. In accomplishing this task, how to construct a proper model to describe the behavior of human meridian systems is one of the very important issues. From experiments, it has been found that the hysteresis phenomenon occurs in the relations between stimulation input and...

Neural network realizations of Bayes decision rules for exponentially distributed data

Igor Vajda, Belomír Lonek, Viktor Nikolov, Arnošt Veselý (1998)

Kybernetika

For general Bayes decision rules there are considered perceptron approximations based on sufficient statistics inputs. A particular attention is paid to Bayes discrimination and classification. In the case of exponentially distributed data with known model it is shown that a perceptron with one hidden layer is sufficient and the learning is restricted to synaptic weights of the output neuron. If only the dimension of the exponential model is known, then the number of hidden layers will increase...

Neural networks learning as a multiobjective optimal control problem.

Maciej Krawczak (1997)

Mathware and Soft Computing

The supervised learning process of multilayer feedforward neural networks can be considered as a class of multi-objective, multi-stage optimal control problem. An iterative parametric minimax method is proposed in which the original optimization problem is embedded into a weighted minimax formulation. The resulting auxiliary parametric optimization problems at the lower level have simple structures that are readily tackled by efficient solution methods, such as the dynamic programming or the error...

Neuro-fuzzy modelling based on a deterministic annealing approach

Robert Czabański (2005)

International Journal of Applied Mathematics and Computer Science

This paper introduces a new learning algorithm for artificial neural networks, based on a fuzzy inference system ANBLIR. It is a computationally effective neuro-fuzzy system with parametrized fuzzy sets in the consequent parts of fuzzy if-then rules, which uses a conjunctive as well as a logical interpretation of those rules. In the original approach, the estimation of unknown system parameters was made by means of a combination of both gradient and least-squares methods. The novelty of the learning...

Neuromorphic features of probabilistic neural networks

Jiří Grim (2007)

Kybernetika

We summarize the main results on probabilistic neural networks recently published in a series of papers. Considering the framework of statistical pattern recognition we assume approximation of class-conditional distributions by finite mixtures of product components. The probabilistic neurons correspond to mixture components and can be interpreted in neurophysiological terms. In this way we can find possible theoretical background of the functional properties of neurons. For example, the general...

New aspects on extraction of fuzzy rules using neural networks.

José Manuel Benítez, Armando Blanco, Miguel Delgado, Ignacio Requena (1998)

Mathware and Soft Computing

In previous works, we have presented two methodologies to obtain fuzzy rules in order to describe the behaviour of a system. We have used Artificial Neural Netorks (ANN) with the Backpropagation algorithm, and a set of examples of the system. In this work, some modifications which allow to improve the results, by means of an adaptation or refinement of the variable labels in each rule, or the extraction of local rules using distributed ANN, are showed. An interesting application on the assignement...

Non additive ordinal relations representable by lower or upper probabilities

Andrea Capotorti, Giulianella Coletti, Barbara Vantaggi (1998)

Kybernetika

We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non- additive (as the relations representable by a probability) and also not “partially monotone” (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immediately deducible by means...

Nonparametric recursive aggregation process

Elena Tsiporkova, Veselka Boeva (2004)

Kybernetika

In this work we introduce a nonparametric recursive aggregation process called Multilayer Aggregation (MLA). The name refers to the fact that at each step the results from the previous one are aggregated and thus, before the final result is derived, the initial values are subjected to several layers of aggregation. Most of the conventional aggregation operators, as for instance weighted mean, combine numerical values according to a vector of weights (parameters). Alternatively, the MLA operators...

Nonparametric statistical analysis for multiple comparison of machine learning regression algorithms

Bogdan Trawiński, Magdalena Smętek, Zbigniew Telec, Tadeusz Lasota (2012)

International Journal of Applied Mathematics and Computer Science

In the paper we present some guidelines for the application of nonparametric statistical tests and post-hoc procedures devised to perform multiple comparisons of machine learning algorithms. We emphasize that it is necessary to distinguish between pairwise and multiple comparison tests. We show that the pairwise Wilcoxon test, when employed to multiple comparisons, will lead to overoptimistic conclusions. We carry out intensive normality examination employing ten different tests showing that the...

Normal Subgroup of Product of Groups

Hiroyuki Okazaki, Kenichi Arai, Yasunari Shidama (2011)

Formalized Mathematics

In [6] it was formalized that the direct product of a family of groups gives a new group. In this article, we formalize that for all j ∈ I, the group G = Πi∈IGi has a normal subgroup isomorphic to Gj. Moreover, we show some relations between a family of groups and its direct product.

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