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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.

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.

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.