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• We propose hypothetical distribution models with theoretical method to compute the optimal number of query labels. • We present clustering-based practical statistical method for the same issue. • We design the cost-sensitive active learning through statistical methods (CATS) algorithm. • Results of significance test verify the superiority of CATS to state-of-the-art algorithms. Clustering-based active learning splits the data into a number of blocks and queries the labels of most the representative instances. When the cost of labeling and misclassification are considered, we also face a key issue: How many labels should be queried for a given block. In this paper, we present theoretical and practical statistical methods to handle this issue. The theoretical statistical method calculates the optimal number of query labels for a predefined label distribution. Considering label distributions for different clustering qualities, we obtain three hypothetical models, namely Gaussian, Uniform, and V models. The practical statistical method calculates empirical label distribution of the cluster blocks. Considering four popular clustering algorithms, we use symmetry and curve fitting techniques on 30 datasets to obtain empirical distributions. Inspired by three-way decision, we design an algorithm called the cost-sensitive active learning through statistical methods (CATS). Experiments were performed on 12 binary-class datasets for both the distribution evaluation and learning task. The results of significance tests verify the effectiveness of CATS and its superior performance with respect to state-of-the-art cost-sensitive active learning algorithms. [ABSTRACT FROM AUTHOR]

In multicriteria decision tasks, certain features are linearly ordered according to the decision and are called criteria, whereas others, called regular attributes, are not. In practice, regular attributes and criteria coexist in most classification tasks. In this paper, we propose a rank-inconsistent rate that distinguishes attributes from criteria. Furthermore, it represents the directions of the monotonic relationships between criteria and decisions. We design a partially monotonic decision tree algorithm to extract decision rules for partially monotonic classification tasks. Experimental results show that the proposed algorithm is effective and efficient. [ABSTRACT FROM AUTHOR]

In this paper, conditions for n -argument functions to preserve diverse types of fuzzy orders during aggregation process are presented. Namely, the following fuzzy orders are studied: total preorder, total order, strict total order, partial preorder, partial order, strict partial order, interval order or semiorder and their preservation in aggregation process along with other connections between input fuzzy relations and the aggregated one are presented. Moreover, dependencies between diverse classes and also among the given class of fuzzy orders are presented. The considered fuzzy orders are compound properties depending in their definitions on arbitrary binary operations on [0, 1], including fuzzy conjunctions and disjunctions (with special cases of triangular norms and triangular conorms). Finally, an application of the obtained result is presented by the given algorithm. [ABSTRACT FROM AUTHOR]

Abstract: K-local hyperplane distance nearest neighbor (HKNN) classifier is an improved K-nearest neighbor (KNN) algorithm that has been successfully applied to pattern classification. This paper embeds the decision rule of HKNN classifier into the discriminant analysis model to develop a new feature extractor. The obtained feature extractor is called K-local hyperplane distance nearest neighbor classifier oriented local discriminant analysis (HOLDA), in which a regularization item is imposed on the original HKNN algorithm to obtain a more reliable distance metric. Based on this distance metric, the homo-class and hetero-class local scatters are characterized in HOLDA. By maximizing the ratio of the hetero-class local scatter to the homo-class local scatter, we obtain a subspace which is suitable for feature extraction and classification. In general, this paper provides a framework for building a feature extractor from the decision rule of a classifier. By this means, the feature extractor and classifier can be seamlessly integrated. Experimental results on four databases demonstrate that the integrated pattern recognition system is effective. [Copyright &y& Elsevier]

Indecision constitutes a frequent and significant problem among decision makers (DMs). The substantial amount of potential choices available, the subjectivity and imprecision inherent in the information received, and the limited capacity of DMs to assimilate the information available are generally blamed for the resulting indecisiveness. We consider the problem of a DM who must rank a set of alternatives in a way that there are no two alternatives equally ranked. Each alternative is quantitatively and qualitatively described by a different information sender (IS). That is, the DM cannot observe the alternatives directly, he has to subjectively infer and evaluate them on the basis of the information provided by the ISs. The current paper introduces a novel algorithm that generates a strict order over the alternatives when DMs cannot decide among them. The proposed algorithm defines a lexicographic choice rule that is implementable over different evaluation loops. This algorithm complements and extends previous research on subjective evaluations and exchange reliability where the ISs–DMs interaction does not guarantee that DMs are able to make a unique most-preferred choice. We illustrate how this algorithm can also be adapted to account for the strategic manipulation of the information provided by the ISs and for different attitudes towards uncertainty on the side of the DMs. [ABSTRACT FROM AUTHOR]

The identification of communities is crucial to an understanding of the structural and functional properties of a complex network. Many methods and algorithms have been developed to detect overlapping communities. A problem that has not been addressed satisfactorily is the relationship or difference between vertices in overlapping regions during the formation and growth of communities. This paper investigates methods that not only detect the overlapping communities but also refine the overlapping regions. We give a three-way representation of a community by using interval sets and re-formalize the problem of community detection as three-way clustering. We suggest four macro types and eight micro types of vertices to characterize members in overlapping regions for their refinement. We propose an overlapping community detection algorithm by classifying the vertices into core vertices, bone vertices, and trivial vertices. The main strategy of this algorithm is to find an initial cluster core, to expand the core to a preliminary community according to a new fitness function, and to merge trivial vertices based on three-way decision strategies. The experimental results on both real-world social networks and computer-generated artificial networks show the effectiveness and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, the notion of homogeneity is extended to the interval-valued setting. In particular, we focus on the case of interval-valued t-norms and t-conorms and we characterize interval-valued homogeneous t-norms and t-conorms of interval-valued order. We also introduce the notions of interval-valued pseudo-homogeneous t-norm and interval pseudo-homogeneous t-conorm are introduced and characterized. We illustrate our results with two examples, one in image processing and the other one in decision making. [ABSTRACT FROM AUTHOR]