2059324
Choquet integrals and natural extensions of lower probabilities
Abstract Both the Choquet integral with respect to monotone set functions and the natural extensions of lower probabilities are generalizations of the Lebesgue integral with respect to σ-additive measures. The relation between these generalizations is investigated. We show that the Choquet integral with respect to a belief measure is always greater than or equal to the corresponding natural extension. Also, we compare some concepts introduced in the theory of imprecise probabilities with concepts established in fuzzy measure theory, capacity theory, and Dempster-Shafer theory.
29035045
Genetic algorithms for determining fuzzy measures from data
A synthetic evaluation of a given object in terms of multiple factors that contribute to some feature of the object (quality, performance, etc.) may be regarded as a system with multiple inputs and one output. Traditionally, the output is expressed as the weighted average of the inputs. Unfortunately, this method is severely limited as it cannot capture any inherent relation among the factors involved. This limitation can be overcome by using the Choquet integral or the fuzzy integral with respect to a fuzzy measure that captures the relation among the factors. The crux of this method is to determine the right fuzzy measure. In this paper, we describe an efficient genetic algorithm for constructing a suitable fuzzy measure from relevant input-output data. This algorithm has a broad applicability in various problem areas, such as decision making, cluster analysis, pattern recognition, image and speech processing, and expert systems.
8746593
Modal logic interpretation of Dempster-Shafer theory: An infinite case
Abstract A modal logic interpretation of belief and plausibility measures defined on infinite sets is established. As a special case, a modal logic interpretation of necessity and possibility measures defined on infinite sets is also established. It is proven in both cases that the interpretation is complete. These results establish, in effect, modal logic interpretations of the Dempster-Shafer theory and possibility theory.
2505136
Indeterminate integrals with respect to nonadditive measures
Recently, nonadditive set functions have been used in information fusion and data mining to describe the interaction among the predictive attributes. In this case, replacing the traditional weighted average or, more generally, the linear mapping from a higher dimensional space to a one-dimensional space, relevant nonlinear integrals should be used as the aggregation tool to express how the objective attribute depends on predictive attributes. Several different types of nonlinear integral, such as the Choquet integral and the Wang integral, have been discussed in literature. In these models, the objective attribute is the integral, while the predictive attributes are the integrand. In this paper, a new concept of indeterminate integral is introduced when the universe of discourse is finite. It is a family of integrals including nonlinear integrals mentioned above and, therefore, possesses a large adaptability as a new aggregation tool. Each specified type of indeterminate integral can be obtained from the family of indeterminate integrals by specifying a decomposition of the integrand. Such a new aggregation tool can be used in information fusion and data mining as well as in expert systems.
28890
Extension of Lower Probabilities and Coherence of Belief Measures
Coherence is an important concept which is introduced and discussed in a new mathematics branch, Imprecise Probability Theory. By using the Choquet integral, belief measures can be extended to be coherent lower previsions on the linear space consisting of all bounded functions. As a special case, we establish that all belief measures are coherent imprecise probabilities.
1885677
Learning nonlinear multiregression networks based on evolutionary computation
This paper describes a novel knowledge discovery and data mining framework dealing with nonlinear interactions among domain attributes. Our network-based model provides an effective and efficient reasoning procedure to perform prediction and decision making. Unlike many existing paradigms based on linear models, the attribute relationship in our framework is represented by nonlinear nonnegative multiregressions based on the Choquet integral. This kind of multiregression is able to model a rich set of nonlinear interactions directly. Our framework involves two layers. The outer layer is a network structure consisting of network elements as its components, while the inner layer is concerned with a particular network element modeled by Choquet integrals. We develop a fast double optimization algorithm (FDOA) for learning the multiregression coefficients of a single network element. Using this local learning component and multiregression-residual-cost evolutionary programming (MRCEP), we propose a global learning algorithm, called MRCEP-FDOA, for discovering the network structures and their elements from databases. We have conducted a series of experiments to assess the effectiveness of our algorithm and investigate the performance under different parameter combinations, as well as sizes of the training data sets. The empirical results demonstrate that our framework can successfully discover the target network structure and the regression coefficients.
32491059
Speech Driven MPEG-4 Based Face Animation via Neural Network
In this paper, some clustering and machine learning methods are combined together to learn the correspondence between speech acoustic and MPEG-4 based face animation parameters. The features of audio and image sequences can be extracted from the large recorded audio-visual database. The face animation parameter (FAP) sequences can be computed and then clustered to FAP patterns. An artificial neural network (ANN) was trained to map the linear predictive coefficients (LPC) and some prosodic features of an individual's natural speech to FAP patterns. The performance of our system shows that the proposed learning algorithm is suitable, which can greatly improve the realism of real time face animation during speech.
18764674
Image information restoration based on long-range correlation
A new class of image information restoration algorithms, virtually different from traditional techniques, is proposed. In comparison with other approaches, our methods use not only the information in local areas, but also that in the remote regions of the image. The methods originate from the idea that there exists abundant long-range correlation within natural images and the human vision system, composed of our eyes and brains, can sufficiently utilize such types of information redundancy to implement the functions of image interpretation, representation, restoration, enhancement and error concealment. Our general approach can be summarized as five basic steps: fetching, searching, matching, competing and recovering. The experimental results on several practical applications show that our methods perform substantially better than many other state-of-the-art methods.
17056192
Automatic Alignment of High-Resolution NMR Spectra Using a Bayesian Estimation Approach
Nuclear magnetic resonance (NMR) spectral analysis has recently become one of the major means for the detection and recognition of metabolic changes of disease state, physiological alteration, and natural biological variation. For the pattern recognition tasks in which two or more NMR spectra need to be compared, it is critical to properly align the spectra for the subsequent pattern recognition analysis. Previous spectral alignment methods do not consider any baseline intensity variation between the spectra and disregard the effect of noise. Here we formulate the spectra alignment problem in a Bayesian statistical framework, which allows us to simultaneously and efficiently estimate the spectral shift and the baseline intensity variation in the existence of independent additive noise. Experimental results with real high-resolution NMR spectral data from human plasma demonstrate the effectiveness and robustness of the proposed approach
10182592
A Software Component Model and Its Preliminary Formalisation
A software component model should define what components are, and how they can be composed. That is, it should define a theory of components and their composition. Current software component models tend to use objects or port-connector type architectural units as components, with method calls and port-to-port connections as composition mechanisms. However, these models do not provide a proper composition theory, in particular for key underlying concepts such as encapsulation and compositionality. In this paper, we outline our notion of these concepts, and give a preliminary formalisation of a software component model that embodies these concepts.
1450237
An Improved Constructive Neural Network Ensemble Approach to Medical Diagnoses
Neural networks have played an important role in intelligent medical diagnoses. This paper presents an Improved Constructive Neural Network Ensemble (ICNNE) approach to three medical diagnosis problems. New initial structure of the ensemble, new freezing criterion, and a different error function are presented. Experiment results show that our ICNNE approach performed better for most problems.