Multi-objective clustering ensemble for gene expression data analysis

In this paper, we present an algorithm for cluster analysis that integrates aspects from cluster ensemble and multi-objective clustering. The algorithm is based on a Pareto-based multi-objective genetic algorithm, with a special crossover operator, which uses clustering validation measures as objective functions. The algorithm proposed can deal with data sets presenting different types of clusters, without the need of expertise in cluster analysis. its result is a concise set of partitions representing alternative trade-offs among the objective functions. We compare the results obtained with our algorithm, in the context of gene expression data sets, to those achieved with multi-objective Clustering with automatic K-determination (MOCK). the algorithm most closely related to ours. (C) 2009 Elsevier B.V. All rights reserved.

Quality indices for (practical) clustering evaluation

Clustering quality or validation indices allow the evaluation of the quality of clustering in order to support the selection of a specific partition or clustering structure in its natural unsupervised environment, where the real solution is unknown or not available. In this paper, we investigate the use of quality indices mostly based on the concepts of clusters` compactness and separation, for the evaluation of clustering results (partitions in particular). This work intends to offer a general perspective regarding the appropriate use of quality indices for the purpose of clustering evaluation. After presenting some commonly used indices, as well as indices recently proposed in the literature, key issues regarding the practical use of quality indices are addressed. A general methodological approach is presented which considers the identification of appropriate indices thresholds. This general approach is compared with the simple use of quality indices for evaluating a clustering solution.

Physical properties of palm fruits processed with tools by wild bearded capuchins (Cebus libidinosus)

Habitually, capuchin monkeys access encased hard foods by using their canines and premolars and/or by pounding the food on hard surfaces. Instead, the wild bearded capuchins (Cebus libidinosus) of Boa Vista (Brazil) routinely crack palm fruits with tools. We measured size, weight, structure, and peak-force-at-failure of the four palm fruit species most frequently processed with tools by wild capuchin monkeys living in Boa Vista. Moreover, for each nut species we identify whether peak-force-at-failure was consistently associated with greater weight/volume, endocarp, thickness, and structural complexity. The goals of this study were (a) to investigate whether these palm fruits are difficult, or impossible, to access other than with tools and (b) to collect data on the physical properties of palm fruits that are comparable to those available for the nuts cracked open with tools by wild chimpanzees. Results showed that the four nut species differ in terms of peak-force-at-failure and that peak-force-at-failure is positively associated with greater weight (and consequently volume) and apparently with structural complexity (i.e. more kernels and thus more partitions); finally for three out of four nut species shell thickness is also positively associated with greater volume. The finding that the nuts exploited by capuchins with tools have very high resistance values support the idea that tool use is indeed mandatory to crack them open. Finally, the peak-force-at-failure of the piassava nuts is similar to that reported for the very tough panda nuts cracked open by wild chimpanzees; this highlights the ecological importance of tool use for exploiting high resistance foods in this capuchin species.

Weak hypergraph regularity and linear hypergraphs

We consider conditions which allow the embedding of linear hypergraphs of fixed size. In particular, we prove that any k-uniform hypergraph H of positive uniform density contains all linear k-uniform hypergraphs of a given size. More precisely, we show that for all integers l >= k >= 2 and every d > 0 there exists Q > 0 for which the following holds: if His a sufficiently large k-uniform hypergraph with the property that the density of H induced on every vertex subset of size on is at least d, then H contains every linear k-uniform hypergraph F with l vertices. The main ingredient in the proof of this result is a counting lemma for linear hypergraphs, which establishes that the straightforward extension of graph epsilon-regularity to hypergraphs suffices for counting linear hypergraphs. We also consider some related problems. (C) 2009 Elsevier Inc. All rights reserved.

Decomposability problem on branched coverings

Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected closed surface N with chi(N) <= 0. This shows that decomposable and indecomposable realizations may coexist. Moreover, we characterize the branch data of a decomposable primitive branched covering. Bibliography: 20 titles.