Dealing with non-metric dissimilarities in fuzzy central clustering algorithms

Clustering is the problem of grouping objects on the basis of a similarity measure among them. Relational clustering methods can be employed when a feature-based representation of the objects is not available, and their description is given in terms of pairwise (dis)similarities. This paper focuses on the relational duals of fuzzy central clustering algorithms, and their application in situations when patterns are represented by means of non-metric pairwise dissimilarities. Symmetrization and shift operations have been proposed to transform the dissimilarities among patterns from non-metric to metric. In this paper, we analyze how four popular fuzzy central clustering algorithms are affected by such transformations. The main contributions include the lack of invariance to shift operations, as well as the invariance to symmetrization. Moreover, we highlight the connections between relational duals of central clustering algorithms and central clustering algorithms in kernel-induced spaces. One among the presented algorithms has never been proposed for non-metric relational clustering, and turns out to be very robust to shift operations. (C) 2008 Elsevier Inc. All rights reserved

Graph ambiguity

In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved

Relational clustering models for knowledge discovery and recommender systems

Cluster analysis is a fundamental research field in Knowledge Discovery and Data Mining (KDD). It aims at partitioning a given dataset into some homogeneous clusters so as to reflect the natural hidden data structure. Various heuristic or statistical approaches have been developed for analyzing propositional datasets. Nevertheless, in relational clustering the existence of multi-type relationships will greatly degrade the performance of traditional clustering algorithms. This issue motivates us to find more effective algorithms to conduct the cluster analysis upon relational datasets. In this thesis we comprehensively study the idea of Representative Objects for approximating data distribution and then design a multi-phase clustering framework for analyzing relational datasets with high effectiveness and efficiency. The second task considered in this thesis is to provide some better data models for people as well as machines to browse and navigate a dataset. The hierarchical taxonomy is widely used for this purpose. Compared with manually created taxonomies, automatically derived ones are more appealing because of their low creation/maintenance cost and high scalability. Up to now, the taxonomy generation techniques are mainly used to organize document corpus. We investigate the possibility of utilizing them upon relational datasets and then propose some algorithmic improvements. Another non-trivial problem is how to assign suitable labels for the taxonomic nodes so as to credibly summarize the content of each node. Unfortunately, this field has not been investigated sufficiently to the best of our knowledge, and so we attempt to fill the gap by proposing some novel approaches. The final goal of our cluster analysis and taxonomy generation techniques is to improve the scalability of recommender systems that are developed to tackle the problem of information overload. Recent research in recommender systems integrates the exploitation of domain knowledge to improve the recommendation quality, which however reduces the scalability of the whole system at the same time. We address this issue by applying the automatically derived taxonomy to preserve the pair-wise similarities between items, and then modeling the user visits by another hierarchical structure. Experimental results show that the computational complexity of the recommendation procedure can be greatly reduced and thus the system scalability be improved

Mixed membership stochastic blockmodels

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.Comment: 46 pages, 14 figures, 3 table

Variational Bayesian modified adaptive Mamdani Fuzzy Modelling for use in condition monitoring

The paper proposes a new Adaptive Mamdani Fuzzy Model (AMFM) based system modelling methodology that improves on traditional Mamdani fuzzy rule based system (FRBS) techniques through use of alternative membership functions and a defuzzification mechanism that is ‘differentiable’, allowing a back error propagation (BEP) algorithm to refine the initial fuzzy model. Moreover, a variational Bayesian (VB) method is applied to simplify the results via automatic selection of the number of input rules so that redundant rules can be removed for the initial modelling phase. The efficacy of the proposed VB modified AMFM (VB-AMFM) approach is demonstrated through experimental trials using measurements from a compressor in an industrial gas turbine (IGT)