Many methods based on rough sets to deal with incomplete information system have been proposed in recent years. However, they are only suitable for the nominal datasets. So far only a few methods based on rough sets t...
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Many methods based on rough sets to deal with incomplete information system have been proposed in recent years. However, they are only suitable for the nominal datasets. So far only a few methods based on rough sets to deal with incomplete information system with continuous-attributes have been proposed. In this paper we propose one generalized model of rough sets to reduce continuous-attributes in an incomplete information system. The definition of a relative discernible measure is firstly proposed, which is the underlying concept to redefine the concepts of knowledge reduction such as the reduct and core. The advantage of the proposed method is that instead of preprocessing continuous data by discretization or fuzzification, we can reduce an incomplete information system directly based on the generalized model of rough sets. Finally, a numerical example is given to show the feasibility of our proposed method.
The generalization error bounds for the entire input space found by current error models using the number of effective parameters of a classifier and the number of training samples are usually very loose. But classifi...
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The generalization error bounds for the entire input space found by current error models using the number of effective parameters of a classifier and the number of training samples are usually very loose. But classifiers such as SVM, RBFNN and MLPNN, are really local learningmachines used for many application problems, which consider unseen samples close to the training samples more important. In this paper, we propose a localized generalization error model which bounds above the generalization error within a neighborhood of the training samples using stochastic sensitivity measure (expectation of the squared output perturbations). It is then used to develop a model selection technique for a classifier with maximal coverage of unseen samples by specifying a generalization error threshold. Experiments by using eight real world datasets show that, in comparison with cross-validation, sequential learning, and two other ad-hoc methods, our technique consistently yields the best testing classification accuracy with fewer hidden neurons and less training time.
Since its introduction, rough set theory has demonstrated its usefulness in many applications where imprecise and inconsistent information is involved. An important area of its application is in the induction of decis...
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Since its introduction, rough set theory has demonstrated its usefulness in many applications where imprecise and inconsistent information is involved. An important area of its application is in the induction of decision rules for decision problems. Recently, there are studies for applying rough set theory in decision related to ordering where items are ordered by assigning to them an ordinal class label such as excellent, good, fair, bad. In this paper we examine a particular situation of ordinal decision which has not been considered in previous studies. We introduce some new concepts in relation to reducts of such ordinal decision systems and proposed a way to find these reducts using a concept similar to discernibility matrix.
It has been shown that the optimal solution for the matching problem in multi-target tracking, when both estimated measuring bearing data and actual measuring data are known, can be found from among N different matchi...
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It has been shown that the optimal solution for the matching problem in multi-target tracking, when both estimated measuring bearing data and actual measuring data are known, can be found from among N different matchings. This paper shows by experiment that the costs of the N different possible solutions constitute a bimodal sequence, which suggests an algorithm of O(N-logN) complexity for the matching, lower than most known algorithms. An improved algorithm for the whole process of the multi-target tracking problem is obtained, and an improved performance is shown.
Bayesian Networks are one of the most popular formalisms for reasoning under uncertainty. Hierarchical Bayesian Networks (HBNs) are an extension of Bayesian Networks that are able to deal with structured domains, usin...
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The Minimax Probability machine Classification (MPMC) framework [Lanckriet et al., 2002] builds classifiers by minimizing the maximum probability of misclassification, and gives direct estimates of the probabilistic a...
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ISBN:
(纸本)0262201526
The Minimax Probability machine Classification (MPMC) framework [Lanckriet et al., 2002] builds classifiers by minimizing the maximum probability of misclassification, and gives direct estimates of the probabilistic accuracy bound Ω. The only assumptions that MPMC makes is that good estimates of means and covariance matrices of the classes exist. However, as with Support Vector machines, MPMC is computationally expensive and requires extensive cross validation experiments to choose kernels and kernel parameters that give good performance. In this paper we address the computational cost of MPMC by proposing an algorithm that constructs nonlinear sparse MPMC (SMPMC) models by incrementally adding basis functions (i.e. kernels) one at a time - greedily selecting the next one that maximizes the accuracy bound Ω. SMPMC automatically chooses both kernel parameters and feature weights without using computationally expensive cross validation. Therefore the SMPMC algorithm simultaneously addresses the problem of kernel selection and feature selection (i.e. feature weighting), based solely on maximizing the accuracy bound Ω. Experimental results indicate that we can obtain reliable bounds Ω, as well as test set accuracies that are comparable to state of the art classification algorithms.
We present a novel method for approximate inference in Bayesian models and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of conditional probab...
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ISBN:
(纸本)0262201526
We present a novel method for approximate inference in Bayesian models and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of conditional probabilities in factorizing distributions, much akin to Minka's Expectation Propagation. In the jointly normal case, it coincides with the latter and belief propagation, whereas in the general case, it provides an optimization strategy containing Support Vector chunking, the Bayes Committee machine, and Gaussian Process chunking as special cases.
Fuzzy Extension Matrix induction is an extraction technique of fuzzy rules, which can be used in handling ambiguous classification problems related to human's thought and sense. The entire process of building heur...
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ISBN:
(纸本)0780384032
Fuzzy Extension Matrix induction is an extraction technique of fuzzy rules, which can be used in handling ambiguous classification problems related to human's thought and sense. The entire process of building heuristic algorithm based on Fuzzy Extension Matrix is dependent of three specified parameters that seriously affect the computational effort and the rule extraction accuracy. Since the value of three parameters is usually given in terms of human experience or real requirements, it is very difficult to determine its optimal value. This paper makes an initial attempt to give some guidelines of how to automatically choose these parameters by analyzing the relationship between the values of parameters and the number of rules generated.
Decision trees and extension matrixes are two methodologies for (fuzzy) rule generation. This paper gives an initial study on the comparison between the two methodologies. Their computational complexity and the qualit...
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ISBN:
(纸本)0780384032
Decision trees and extension matrixes are two methodologies for (fuzzy) rule generation. This paper gives an initial study on the comparison between the two methodologies. Their computational complexity and the quality of rule generation are analyzed. The experimental results show that the number of generated rules of the heuristic algorithm based on extension matrix is fewer than the decision tree algorithm. Moreover, regarding the testing accuracy (i.e., the generalization capability for unknown cases), experiments also show that the extension matrix method is better than the other.
This paper brings together two strands of machinelearning of increasing importance: kernel methods and highly structured data. We propose a general method for constructing a kernel following the syntactic structure o...
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This paper brings together two strands of machinelearning of increasing importance: kernel methods and highly structured data. We propose a general method for constructing a kernel following the syntactic structure of the data, as defined by its type signature in a higher-order logic. Our main theoretical result is the positive definiteness of any kernel thus defined. We report encouraging experimental results on a range of real-world data sets. By converting our kernel to a distance pseudo-metric for 1-nearest neighbour, we were able to improve the best accuracy from the literature on the Diterpene data set by more than 10%.
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