Cluster ensembles, quantization and the dilogarithm

Cluster ensemble is a pair of positive spaces (X, A) related by a map p: A -> X. It generalizes cluster algebras of Fomin and Zelevinsky, which are related to the A-space. We develope general properties of cluster ensembles, including its group of symmetries - the cluster modular group, and a relation with the motivic dilogarithm. We define a q-deformation of the X-space. Formulate general duality conjectures regarding canonical bases in the cluster ensemble context. We support them by constructing the canonical pairing in the finite type case. Interesting examples of cluster ensembles are provided the higher Teichmuller theory, that is by the pair of moduli spaces corresponding to a split reductive group G and a surface S defined in math.AG/0311149. We suggest that cluster ensembles provide a natural framework for higher quantum Teichmuller theory.Comment: Version 7: Final version. To appear in Ann. Sci. Ecole Normale. Sup. New material in Section 5. 58 pages, 11 picture

A CLUE for CLUster Ensembles

Cluster ensembles are collections of individual solutions to a given clustering problem which are useful or necessary to consider in a wide range of applications. The R package clue provides an extensible computational environment for creating and analyzing cluster ensembles, with basic data structures for representing partitions and hierarchies, and facilities for computing on these, including methods for measuring proximity and obtaining consensus and "secondary" clusterings.

A Method to Improve the Analysis of Cluster Ensembles

Clustering is fundamental to understand the structure of data. In the past decade the cluster ensembleproblem has been introduced, which combines a set of partitions (an ensemble) of the data to obtain a singleconsensus solution that outperforms all the ensemble members. However, there is disagreement about which arethe best ensemble characteristics to obtain a good performance: some authors have suggested that highly differentpartitions within the ensemble are beneï¬ cial for the ï¬ nal performance, whereas others have stated that mediumdiversity among them is better. While there are several measures to quantify the diversity, a better method toanalyze the best ensemble characteristics is necessary. This paper introduces a new ensemble generation strategyand a method to make slight changes in its structure. Experimental results on six datasets suggest that this isan important step towards a more systematic approach to analyze the impact of the ensemble characteristics onthe overall consensus performance.Fil: Pividori, Milton Damián. Universidad Tecnologica Nacional. Facultad Regional Santa Fe. Centro de Investigacion y Desarrollo de Ingenieria en Sistemas de Informacion; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Stegmayer, Georgina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; Argentina. Universidad Tecnologica Nacional. Facultad Regional Santa Fe. Centro de Investigacion y Desarrollo de Ingenieria en Sistemas de Informacion; ArgentinaFil: Milone, Diego Humberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; Argentin

LinkCluE: A MATLAB Package for Link-Based Cluster Ensembles

Cluster ensembles have emerged as a powerful meta-learning paradigm that provides improved accuracy and robustness by aggregating several input data clusterings. In particular, link-based similarity methods have recently been introduced with superior performance to the conventional co-association approach. This paper presents a MATLAB package, LinkCluE, that implements the link-based cluster ensemble framework. A variety of functional methods for evaluating clustering results, based on both internal and external criteria, are also provided. Additionally, the underlying algorithms together with the sample uses of the package with interesting real and synthetic datasets are demonstrated herein.

Invariant Functions On Cluster Ensembles

We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type of invariant ring and give many new examples. We show that these invariants have geometric and number theoretic interpretations, and classify them for ensembles associated to affine Dynkin diagrams.Comment: 26 pages, 16 figure