Publications

Principal curves, as a nonlinear generalization of principal components, are a common tool used in multivariate analysis for ends like dimensionality reduction and feature extraction. However, one of the difficulties that arise when utilizing this technique is that efficiency of existing principal curves algorithms is often low when dealing with large data set owing to high computational complexity. In the paper, a new method based on the idea of "information granulation and fuzzy sets" is proposed to improve efficiency and noise robustness. First, large amounts of numerical data are granulated into C interval (granular) data based on the fuzzy C-means cluster and two criteria of granulation, which significantly reduces the amount of data that is to be processed in the later step. Then granular principal curves are constructed according to the upper and the lower bounds of the interval data. Finally we introduce a quantitative index based on the parameter α to evaluate the fuzziness of granular principal curves output, where α is a positive parameter delivering some flexibility when optimizing the information granule. A series of numeric studies completed for synthetic data set provide a useful insight into the effectiveness of the proposed algorithm.

Classifying magnetic resonance spectra is often difficult due to the curse of dimensionality; a high-dimensional feature space couple with a small sample size. We present an aggregation strategy that combines predicted disease states from multiple classifiers with the anticipated outcome that the aggregated predictions are superior to any individual classifier prediction. Multiple classifiers are presented with different, randomly selected, subsets of spectral features. The fuzzy integration results are compared against the best individual classifier operating on a spectral feature subset.

Under the assumption of rational economics, the opinions of decision makers should exhibit some transitivity properties. It is an important issue on how to measure the transitivity properties of the provided preference relations over a set of alternatives. In this study, we report the methods for measuring weak consistency (w-consistency) and weak transitivity (w-transitivity) of pairwise comparison matrices (PCMs) originating from the analytic hierarchy process (AHP). First, some interesting properties of PCMs with w-consistency and w-transitivity are studied. Second, novel methods are proposed to construct the quantification indices of w-consistency and w-transitivity of PCMs, respectively. Some comparisons with the existing methods are offered to illustrate the novelty of the proposed ones. Third, an optimization model is put forward to modify a PCM without any transitivity property to a new one with w-consistency and w-transitivity, respectively. The particle swarm optimization (PSO) algorithm is adopted to solve the nonlinear optimization problems. A novel decision-making model is established by considering the w-transitivity as the minimum requirement. Some numerical examples are carried out to illustrate the developed methods and models. It is observed that the proposed indices can be computed efficiently and reflect the inherent relations of the entries in a PCM with w-consistency and w-transitivity, respectively.

This study extends the web classification approach through a proximity-based fuzzy clustering sensible to the influence of the page. The proximity-based fuzzy clustering works in an unsupervised manner, augmented by a certain auxiliary supervision mechanism. The supervision scheme is realized via a number of proximity “hints” (constraints) that specify an extent to which some pairs of patterns are regarded similar or different. The hints are provided externally to the clustering algorithm and improve the searching activity by customizing the user’s navigation. In this paper we focus on the feature spaces corresponding to the Web data characterizing the context analysis and we discuss how the knowledge extraction process identifies the right context.