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Attribute reduction is one of the most important preprocessing steps in machine learning and data mining. As a key step of attribute reduction, attribute evaluation directly affects classification performance, search time, and stopping criterion. The existing evaluation functions are greatly dependent on the relationship between objects, which makes its computational time and space more costly. To solve this problem, we propose a novel separability-based evaluation function and reduction method by using the relationship between objects and decision categories directly. The degree of aggregation (DA) of intraclass objects and the degree of dispersion (DD) of between-class objects are first defined to measure the significance of an attribute subset. Then, the separability of attribute subsets is defined by DA and DD in fuzzy decision systems, and we design a sequentially forward selection based on the separability (SFSS) algorithm to select attributes. Furthermore, a postpruning strategy is introduced to prevent overfitting and determine a termination parameter. Finally, the SFSS algorithm is compared with some typical reduction algorithms using some public datasets from UCI and ELVIRA Biomedical repositories. The interpretability of SFSS is directly presented by the performance on MNIST handwritten digits. The experimental comparisons show that SFSS is fast and robust, which has higher classification accuracy and compression ratio, with extremely low computational time. [ABSTRACT FROM AUTHOR]

Fuzzy rough sets (FRSs) are considered to be a powerful model for analyzing uncertainty in data. This model encapsulates two types of uncertainty: 1) fuzziness coming from the vagueness in human concept formation and 2) roughness rooted in the granulation coming with human cognition. The rough set theory has been widely applied to feature selection, attribute reduction, and classification. However, it is reported that the classical FRS model is sensitive to noisy information. To address this problem, several robust models have been developed in recent years. Nevertheless, these models do not consider a statistical distribution of data, which is an important type of uncertainty. Data distribution serves as crucial information for designing an optimal classification or regression model. Thus, we propose a data-distribution-aware FRS model that considers distribution information and incorporates it in computing lower and upper fuzzy approximations. The proposed model considers not only the similarity between samples, but also the probability density of classes. In order to demonstrate the effectiveness of the proposed model, we design a new sample evaluation index for prototype-based classification based on the model, and a prototype selection algorithm is developed using this index. Furthermore, a robust classification algorithm is constructed with prototype covering and nearest neighbor classification. Experimental results confirm the robustness and effectiveness of the proposed model. [ABSTRACT FROM PUBLISHER]

The fuzzy-rough set (FRS) methodology, as a useful tool to handle discernibility and fuzziness, has been widely studied. Some researchers studied on the rough approximation of fuzzy sets, while some others focused on studying one application of FRS: attribute reduction (i.e., feature selection). However, constructing classifier by using FRS, as another application of FRS, has been less studied. In this paper, we build a rule-based classifier by using one generalized FRS model after proposing a new concept named as "consistence degree" which is used as the critical value to keep the discernibility information invariant in the processing of rule induction. First, we generalized the existing FRS to a robust model with respect to misclassification and perturbation by incorporating one controlled threshold into knowledge representation of FRS. Second, we propose a concept named as "consistence degree" and by the strict mathematical reasoning, we show that this concept is reasonable as a critical value to reduce redundant attribute values in database. By employing this concept, we then design a discernibility vector to develop the algorithms of rule induction. The induced rule set can function as a classifier. Finally, the experimental results show that the proposed rule-based classifier is feasible and effective on noisy data. [ABSTRACT FROM AUTHOR]

The fuzzy rough set (FRS) model has been introduced to handle databases with real values. However, FRS was sensitive to misclassification and perturbation (here misclassification means error or missing values in classification, and perturbation means small changes of numerical data). The variable precision rough sets (VPRSs) model was introduced to handle databases with misclassification. However, it could not effectively handle the real-valued datasets. Now, it is valuable from theoretical and practical aspects to combine FRS and VPRS so that a powerful tool, which not only can handle numerical data but also is less sensitive to misclassification and perturbation, can be developed. In this paper, we set up a model named fuzzy VPRSs (FVPRSs) by combining FRS and VPRS with the goal of making FRS a special case. First, we study the knowledge representation ways of FRS and VPRS, and then, propose the set approximation operators of FVPRS. Second, we employ the discernibility matrix approach to investigate the structure of attribute reductions in FVPRS and develop an algorithm to find all reductions. Third, in order to overcome the NP-complete problem of finding all reductions, we develop some fast heuristic algorithms to obtain one near-optimal attribute reduction. Finally, we compare FVPRS with RS, FRS, and several flexible RS-based approaches with respect to misclassification and perturbation. The experimental comparisons show the feasibility and effectiveness of FVPRS. [ABSTRACT FROM AUTHOR]

Support vector machines (SVMs), which were originally designed for binary classifications, are an excellent tool for machine learning. For the multiclass classifications, they are usually converted into binary ones before they can be used to classify the examples. In the one-against-one algorithm with SVMs, there exists an unclassifiable region where the data samples cannot be classified by its decision function. This paper extends the one-against-one algorithm to handle this problem. We also give the convergence and computational complexity analysis of the proposed method. Finally, one-against-one, fuzzy decision function (FDF), and decision-directed acyclic graph (DDAG) algorithms and our proposed method are compared using five University of California at Irvine (UCI) data sets. The results report that the proposed method can handle the unclassifiable region better than others. [ABSTRACT FROM AUTHOR]

Fuzzy rough sets are the generalization of traditional rough sets to deal with both fuzziness and vagueness in data. The existing researches on fuzzy rough sets are mainly concentrated on the construction of approximation operators. Less effort has been put on the attributes reduction of databases with fuzzy rough sets. This paper mainly focuses on the attributes reduction with fuzzy rough sets. After analyzing the previous works on attributes reduction with fuzzy rough sets, we introduce formal concepts of attributes reduction with fuzzy rough sets and completely study the structure of attributes reduction. An algorithm using discernibility matrix to compute all the attributes reductions is developed. Based on these lines of thought, we set up a solid mathematical foundation for attributes reduction with fuzzy rough sets. The experimental results show that the idea in this paper is feasible and valid. [ABSTRACT FROM AUTHOR]

Multiple Classifier System (MCS) is a very popular research topic in recent years. It has been proved theoretically and empirically to be better than single classifiers in many scenarios. Creating diverse sets of classifier is one of the key issues in building MCSs. Feature grouping is one of the methods to create diverse classifiers and it has been shown to improve the accuracy of an MCS. In this paper, we propose a new feature grouping method based on Genetic Algorithm (GA) with the localized Generalization Error Model as the evaluation criterion. The combined individual classifiers using the weighted sum are examined in this paper. Moreover, several feature grouping methods are compared with the proposed method in this work. The experimental results on benchmark dataset show that the MCS trained by the proposed method is promising. [ABSTRACT FROM AUTHOR]

We had developed the localized generalization error model for supervised learning with minimization of Mean Square Error. In this work, we extend the error model to Single Layer Perceptron Neural Network (SLPNN) and Support Vector Machine (SVM) with sigmoid kernel function. For a trained SLPNN or SVM and a given training dataset, the proposed error model bounds above the error for unseen samples which are similar to the training samples. As the major component of the localized generalization error model, the stochastic sensitivity measure formula for perceptron neural network derived in this work has relaxed the assumptions of same distribution for all inputs and each sample perturbed only once in previous works. These make the sensitivity measure applicable to pattern classification problems. The stochastic sensitivity measure of SVM with Sigmoid kernel is also derived in this work as a component of the localized generalization error model. At the end of this paper, we discuss the advantages of the proposed error bound over existing error bound. [ABSTRACT FROM AUTHOR]

This paper investigates the convergence theorems that are associated with a Discrete Hopfield Neural Network (DHNN) with delay. We present two updating rules, one for serial mode and the other for parallel mode. The speed of convergence of these proposed updating rules is faster than all of the existing updating rules. It has been proved in this paper that a DHNN with delay will converge to a stable state when operating in a serial mode if the matrix of weights of the no-delay term is symmetric. In addition, it has been proved that they will converge to a stable state when operating in a parallel mode if the matrix of weights of the no-delay term is a symmetric and non-negative definite matrix. The condition for convergence of a DHNN without delay can been relaxed from the need to have a symmetric matrix to an even weaker condition of having a quasi-symmetric matrix. The results in this paper extend both the existing results concerning the convergence of a DHNN without delay and our previous findings. By means of the new network structure and its convergence theorems, we propose a local searching algorithm for combinatorial optimization. We also relate the maximum value of a bivariate energy function to the stable states of a DHNN with delay, which generalizes Hopfield's energy function. Moreover, for the serial model we give the relationship between the convergence of the energy function and the convergence of the corresponding network. One application is presented to demonstrate the higher rate of convergence and the accuracy of the classification using our algorithm. [ABSTRACT FROM AUTHOR]

The one-class classification problem aims to distinguish a target class from outliers. The spherical one-class classifier (SOCC) solves this problem by finding a hypersphere with minimum volume that contains the target data while keeping outlier samples outside. SOCC achieves satisfactory performance only when the target samples have the same distribution tendency in all orientations. Therefore, the performance of the SOCC is limited in the way that many superfluous outliers might be mistakenly enclosed. The authors propose to exploit target data structures obtained via unsupervised methods such as agglomerative hierarchical clustering and use them in calculating a set of hyperellipsoidal separating boundaries. This method is named the structured one-class classifier (TOCC). The optimization problem in TOCC can be formulated as a series of second-order cone programming problems that can be solved with acceptable efficiency by primal-dual interior-point methods. The experimental results on artificially generated data sets and benchmark data sets demonstrate the advantages of TOCC. [ABSTRACT FROM AUTHOR]

The paper studies the possibility of giving a general multiplicity of the fractional Fourier transform (FRFT) with the intention of combining existing finite versions of the FRFT. We introduce a new class of FRFT that includes the conventional fractional Fourier transforms (CFRFTs) and the weighted-type fractional Fourier transforms (WFRFTs) as special cases. The class is structurally well organized because these new FRFTs, which are called general multifractional Fourier transform (GMFRFTs), are related with one another by the Generalized Permutation Matrix Group (GPMG), and their kernels are related with that of CFRFTs as the finite combination by the recursion of matrix. In addition, we have computer simulations of some GMFRFTs on a rectangular function as a simple application of GMFRFTs to signal processing. [ABSTRACT FROM AUTHOR]

Feature selection is a difficult but important issue in the field of machine learning and pattern recognition. In this paper, features for Chinese character recognition are selected by using inductive learning algorithms. The existing inductive learning method based on extension matrix requires precise consistency between positive example and negative example sets, which is very difficult to maintain in most practical cases. The traditional decision tree algorithm ID3 considers only the performance of the discriminating power while selecting features. However, in actual practice the consideration of the associated cost of feature extraction may become a significant concern. In addressing these problems we propose a modified extension matrix approach to select feature subset from the training example set with noises. A decision tree algorithm based on information gain and cost evaluation is also proposed to facilitate cost consideration. The comparative experiments show that the proposed algorithms perform better than the existing inductive learning algorithms to a certain extent. [ABSTRACT FROM AUTHOR]

When fuzzy production rules are used to approximate reasoning, interaction exists among rules that have the same consequent. Due to this interaction, the weighted average model frequently used in approximate reasoning does not work well in many real-world problems. In order to model and handle this interaction, this paper proposes to use a nonadditive nonnegative set function to replace the weights assigned to rules having the same consequent, and to draw the reasoning conclusion based on an integral with respect to the nonadditive nonnegative set function, rather than on the weighted average model. Handling interaction in fuzzy production rule reasoning hi this way can lead to a good understanding of the rules base and an improvement of reasoning accuracy. This paper also investigates how to determine from data the nonadditive set function that cannot be specified by a domain expert. [ABSTRACT FROM AUTHOR]

Fuzzy production rules (FPRs) have been used for years to capture and represent fuzzy, vague, imprecise and uncertain domain knowledge in many fuzzy systems. There have been a lot of researches on how to generate or obtain FPRs. There exist two methods to obtain FPRs. One is by painstakingly, repeatedly and time-consuming interviewing domain experts to extract the domain knowledge. The other is by using some machine learning techniques to generate and extract FPRs from some training samples. These extracted rules, however, are found to be nonoptimal and sometimes redundant. Furthermore, these generated rules suffer from the problem of low accuracy of classifying or recognizing unseen examples. The reasons for having these problems are 1) the FPRs generated are not powerful enough to represent the domain knowledge, 2) the techniques used to generate FPRs are pre-matured, ad-hoc or may not be suitable for the problem, and 3) further refinement of the extracted rules has not been done. In this paper we look into the solutions of the above problems by 1) enhancing the representation power of FPRs by including local and global weights, 2) developing a fuzzy neural network (FNN) with enhanced learning algorithm, and 3) using this FNN to refine the local and global weights of FPRs. By experimenting our method with some existing benchmark examples, the proposed method is found to have high accuracy in classifying unseen samples without increasing the number of the FPRs extracted and the time required to consult with domain experts is greatly reduced. [ABSTRACT FROM AUTHOR]

Proposes a framework for interpreting imprecise linguistic expressions of a fuzzy set theory. Description of linguistic term by the compatibility ordering induced in some universe of discourse; Reflection of the membership function in fuzzy set theory; Investigation of qualitative reasoning without the extensive scale and common scale assumptions.

In this paper, the Hopfield neural network with delay (HNND) is studied from the standpoint of regarding it as an optimizing computational model. Two general updating rules for networks with delay (GURD) are given based on Hopfield-type neural networks with delay for optimization problems and characterized by dynamic thresholds. It is proved that in any sequence of updating rule modes, the GURD monotonously converges to a stable state of the network. The diagonal elements of the connection matrix are shown to have an important influence on the convergence process, and they represent the relationship of the local maximum value of the energy function to the stable states of the networks. All the ordinary discrete Hopfield neural network (DHNN) algorithms are instances of the GURD. It can be shown that the convergence conditions of the GURD may be relaxed in the context of applications, for instance, the condition of nonnegative diagonal elements of the connection matrix can be removed from the original convergence theorem. A new updating rule mode and restrictive conditions can guarantee the network to achieve a local maximum of the energy function with a step-by-step algorithm. The convergence rate improves evidently when compared with other methods. For a delay item considered as a noise disturbance item, the step-by-step algorithm demonstrates its efficiency and a high convergence rate. Experimental results support our proposed algorithm. [ABSTRACT FROM AUTHOR]

Support vector machines (SVMs), which were originally designed for binary classifications, are an excellent tool for machine learning. For the multiclass classifications, they are usually converted into binary ones before they can be used to classify the examples. In the one-against-one algorithm with SVMs, there exists an unclassifiable region where the data samples cannot be classified by its decision function. This paper extends the one-against-one algorithm to handle this problem. We also give the convergence and computational complexity analysis of the proposed method. Finally, one-against-one, fuzzy decision function (FDF), and decision-directed acyclic graph (DDAG) algorithms and our proposed method are compared using five University of California at Irvine (UCI) data sets. The results report that the proposed method can handle the unclassifiable region better than others.

The support vector machine (SVM) has been demonstrated to be a very effective classifier in many applications, but its performance is still limited as the data distribution information is underutilized in determining the decision hyperplane. Most of the existing kernels employed in nonlinear SVMs measure the similarity between a pair of pattern images based on the Euclidean inner product or the Euclidean distance of corresponding input patterns, which ignores data distribution tendency and makes the SVM essentially a "local" classifier. In this paper, we provide a step toward a paradigm of kernels by incorporating data specific knowledge into existing kernels. We first find the data structure for each class adaptively in the input space via agglomerative hierarchical clustering (AHC), and then construct the weighted Mahalanobis distance (WMD) kernels using the detected data distribution information. In WMD kernels, the similarity between two pattern images is determined not only by the Mahalanobis distance (MD) between their corresponding input patterns but also by the sizes of the clusters they reside in. Although WMD kernels are not guaranteed to be positive definite (pd) or conditionally positive definite (cpd), satisfactory classification results can still be achieved because regularizers in SVMs with WMD kernels are empirically positive in pseudo-Euclidean (pE) spaces. Experimental results on both synthetic and real-world data sets show the effectiveness of "plugging" data structure into existing kernels.

The generalization error bounds found by current error models using the number of effective parameters of a classifier and the number of training samples are usually very loose. These bounds are intended for the entire input space. However, support vector machine (SVM), radial basis function neural network (RBFNN), and multilayer perceptron neural network (MLPNN) are local learning machines for solving problems and treat unseen samples near the training samples to be more important. In this paper, we propose a localized generalization error model which bounds from above the generalization error within a neighborhood of the training samples using stochastic sensitivity measure. It is then used to develop an architecture selection technique for a classifier with maximal coverage of unseen samples by specifying a generalization error threshold. Experiments using 17 University of California at Irvine (UCI) data sets show that, in comparison with cross validation (CV), 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.

The one-class classification problem aims to distinguish a target class from outliers. The spherical one-class classifier (SOCC) solves this problem by finding a hypersphere with minimum volume that contains the target data while keeping outlier samples outside. SOCC achieves satisfactory performance only when the target samples have the same distribution tendency in all orientations. Therefore, the performance of the SOCC is limited in the way that many superfluous outliers might be mistakenly enclosed. The authors propose to exploit target data structures obtained via unsupervised methods such as agglomerative hierarchical clustering and use them in calculating a set of hyperellipsoidal separating boundaries. This method is named the structured one-class classifier (TOCC). The optimization problem in TOCC can be formulated as a series of second-order cone programming problems that can be solved with acceptable efficiency by primal-dual interior-point methods. The experimental results on artificially generated data sets and benchmark data sets demonstrate the advantages of TOCC.

In this paper, we propose a new approach to detect activated time series in functional MRI using support vector clustering (SVC). We extract Fourier coefficients as the features of fMRI time series and cluster these features by SVC. In SVC, these features are mapped from their original feature space to a very high dimensional kernel space. By finding a compact sphere that encloses the mapped features in the kernel space, one achieves a set of cluster boundaries in the feature space. The SVC is an effective and robust fMRI activation detection method because of its advantages in (1) better discovery of real data structure since there is no cluster shape restriction, (2) high quality detection results without explicitly specifying the number of clusters, (3) the stronger robustness due to the mechanism in outlier elimination. Experimental results on simulated and real fMRI data demonstrate the effectiveness of SVC.