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.
26197775
Using Neural Networks to Determine Sugeno Measures by Statistics
Abstract To replace the traditional weighted average method, Choquet integrals or Sugeno integrals with respect to fuzzy measures are used to obtain a synthetic evaluation of a given object (or its quality, function, etc. respectively) with multi-attribute. Generally, it is not easy to determine fuzzy measures in real problems due to the subjectivity of human thinking. It is even much more difficult than determining weights in the weighted average method, because of the nonadditivity of fuzzy measures. This paper uses a neural network algorithm to optimize the inverse problem of synthetic evaluation, and thus to determine Sugeno measures by the Choquet integral and statistics of given data. Since the Choquet integral is a generalization of the weighted average method, this technology has a broad applicability in areas of multivariate analysis, decision making, pattern recognition, image and speech processing and expert systems. Copyright © 1996 Elsevier Science Ltd.
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.
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.
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.
12805492
PFB-Integrals and PFA-Integrals with Respect to Monotone Set Functions
A pair of new integrals, a PFB-integral and a PFA-integral, are introduced. Given a measurable space, these integrals are defined for nonnegative functions with respect to monotone set functions, and they are generalizations of both the Lebesgue integral and the fuzzy integral. Some primary properties of the PFB-integral and PFA-integral are discussed and an inequality between them is established in this paper.
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
2647804
Extended DBP for (m, k)-Firm Based QoS
In this paper, an extended DBP (E_DBP) scheme is studied for (m,k)-firm constraint. The basic idea of the proposed algorithm takes into account the distance to exit a failure state, which is a symmetrical notion of distance to fall into a failure state in DBP. Quality of Service (QoS) in terms of dynamic failure and delay is evaluated. Simulation results reveal the effectiveness of E_DBP to provide better QoS.
6164572
Video quality assessment using structural distortion measurement
Objective image/video quality measures play important roles in various image/video processing applications, such as compression, communication, printing, analysis, registration, restoration and enhancement. Most proposed quality assessment approaches in the literature are error sensitivity-based methods. We follow a new philosophy in designing image/video quality metrics, which uses structural distortion as an estimation of perceived visual distortion. We develop a new approach for video quality assessment. Experiments on the video quality experts group (VQEG) test data set shows that the new quality measure has higher correlation with subjective quality measurement than the proposed methods in VQEG's Phase I tests for full-reference video quality assessment.
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.
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.