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Clustering Variable Length Sequences by
 In Lecture Notes in Computer Science
, 2004
"... We present a novel clustering method using HMM parameter space and eigenvector decomposition. Unlike the existing methods, our algorithm can cluster both constant and variable length sequences without requiring normalization of data. We show that the number of clusters governs the number of eige ..."
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We present a novel clustering method using HMM parameter space and eigenvector decomposition. Unlike the existing methods, our algorithm can cluster both constant and variable length sequences without requiring normalization of data. We show that the number of clusters governs the number
CLUSTER AUTOMORPHISMS AND COMPATIBILITY OF CLUSTER VARIABLES
, 2013
"... Abstract. In this paper, we introduce a notion of unistructural cluster algebras, for which the set of cluster variables uniquely determines the clusters. We prove that cluster algebras of Dynkin type and cluster algebras of rank 2 are unistructural, then prove that if A is unistructural or of Eucli ..."
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Cited by 2 (1 self)
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Abstract. In this paper, we introduce a notion of unistructural cluster algebras, for which the set of cluster variables uniquely determines the clusters. We prove that cluster algebras of Dynkin type and cluster algebras of rank 2 are unistructural, then prove that if A is unistructural
Estimating the number of clusters in a dataset via the Gap statistic
, 2000
"... We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference ..."
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Cited by 502 (1 self)
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principal components. 1 Introduction Cluster analysis is an important tool for \unsupervised" learning the problem of nding groups in data without the help of a response variable. A major challenge in cluster analysis is estimation of the optimal number of \clusters". Figure 1 (top right) shows
Denominators of cluster variables
"... Abstract. Associated to any acyclic cluster algebra is a corresponding triangulated ..."
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Cited by 12 (1 self)
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Abstract. Associated to any acyclic cluster algebra is a corresponding triangulated
BIPARTITE GRAPHS, QUIVERS, AND CLUSTER VARIABLES
, 2011
"... We explore connections between formulas for certain combinatorial and algebraic objects. In particular, given a planar bipartite graph G, we consider the cluster algebra A corresponding to a quiver obtained from its dual graph. We then obtain formulas for certain cluster variables in A in terms of ..."
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Cited by 2 (1 self)
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We explore connections between formulas for certain combinatorial and algebraic objects. In particular, given a planar bipartite graph G, we consider the cluster algebra A corresponding to a quiver obtained from its dual graph. We then obtain formulas for certain cluster variables in A in terms
Newton Polytopes of Cluster Variables of Type An
"... Abstract. We study Newton polytopes of cluster variables in type An cluster algebras, whose cluster and coefficient variables are indexed by the diagonals and boundary segments of a polygon. Our main results include an explicit description of the affine hull and facets of the Newton polytope of the ..."
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Cited by 1 (0 self)
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Abstract. We study Newton polytopes of cluster variables in type An cluster algebras, whose cluster and coefficient variables are indexed by the diagonals and boundary segments of a polygon. Our main results include an explicit description of the affine hull and facets of the Newton polytope
Mixtures of Probabilistic Principal Component Analysers
, 1998
"... Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a com ..."
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Cited by 532 (6 self)
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maximumlikelihood framework, based on a specific form of Gaussian latent variable model. This leads to a welldefined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context
ModelBased Analysis of Oligonucleotide Arrays: Model Validation, Design Issues and Standard Error Application
, 2001
"... Background: A modelbased analysis of oligonucleotide expression arrays we developed previously uses a probesensitivity index to capture the response characteristic of a specific probe pair and calculates modelbased expression indexes (MBEI). MBEI has standard error attached to it as a measure of ..."
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Cited by 775 (28 self)
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better ranking statistic for filtering genes. We can assign reliability indexes for genes in a specific cluster of interest in hierarchical clustering by resampling clustering trees. A software dChip implementing many of these analysis methods is made available. Conclusions: The modelbased approach
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 819 (28 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical
Results 1  10
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7,879