Robust EM algorithm for model-based curve clustering

Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful approaches in cluster analysis. The mixture density estimation is generally performed by maximizing the observed-data log-likelihood by using the expectation-maximization (EM) algorithm. However, it is well-known that the EM algorithm initialization is crucial. In addition, the standard EM algorithm requires the number of clusters to be known a priori. Some solutions have been provided in [31, 12] for model-based clustering with Gaussian mixture models for multivariate data. In this paper we focus on model-based curve clustering approaches, when the data are curves rather than vectorial data, based on regression mixtures. We propose a new robust EM algorithm for clustering curves. We extend the model-based clustering approach presented in [31] for Gaussian mixture models, to the case of curve clustering by regression mixtures, including polynomial regression mixtures as well as spline or B-spline regressions mixtures. Our approach both handles the problem of initialization and the one of choosing the optimal number of clusters as the EM learning proceeds, rather than in a two-fold scheme. This is achieved by optimizing a penalized log-likelihood criterion. A simulation study confirms the potential benefit of the proposed algorithm in terms of robustness regarding initialization and funding the actual number of clusters.Comment: In Proceedings of the 2013 International Joint Conference on Neural Networks (IJCNN), 2013, Dallas, TX, US

Generalized topographic block model

Co-clustering leads to parsimony in data visualisation with a number of parameters dramatically reduced in comparison to the dimensions of the data sample. Herein, we propose a new generalized approach for nonlinear mapping by a re-parameterization of the latent block mixture model. The densities modeling the blocks are in an exponential family such that the Gaussian, Bernoulli and Poisson laws are particular cases. The inference of the parameters is derived from the block expectation–maximization algorithm with a Newton–Raphson procedure at the maximization step. Empirical experiments with textual data validate the interest of our generalized model

Methods of Hierarchical Clustering

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference

Compositional generative mapping for tree-structured data - Part II: Topographic projection model

We introduce GTM-SD (Generative Topographic Mapping for Structured Data), which is the first compositional generative model for topographic mapping of tree-structured data. GTM-SD exploits a scalable bottom-up hidden-tree Markov model that was introduced in Part I of this paper to achieve a recursive topographic mapping of hierarchical information. The proposed model allows efficient exploitation of contextual information from shared substructures by a recursive upward propagation on the tree structure which distributes substructure information across the topographic map. Compared to its noncompositional generative counterpart, GTM-SD is shown to allow the topographic mapping of the full sample tree, which includes a projection onto the lattice of all the distinct subtrees rooted in each of its nodes. Experimental results show that the continuous projection space generated by the smooth topographic mapping of GTM-SD yields a finer grained discrimination of the sample structures with respect to the state-of-the-art recursive neural network approach

A Hybrid Artificial Neural Network Model For Data Visualisation, Classification, And Clustering [QP363.3. T253 2006 f rb].

Tesis ini mempersembahkan penyelidikan tentang satu model hibrid rangkaian neural buatan yang boleh menghasilkan satu peta pengekalan-topologi, serupa dengan penerangan teori bagi peta otak, untuk visualisasi, klasifikasi dan pengklusteran data. In this thesis, the research of a hybrid Artificial Neural Network (ANN) model that is able to produce a topology-preserving map, which is akin to the theoretical explanation of the brain map, for data visualisation, classification, and clustering is presented

Swarm-Organized Topographic Mapping

Topographieerhaltende Abbildungen versuchen, hochdimensionale oder komplexe Datenbestände auf einen niederdimensionalen Ausgaberaum abzubilden, wobei die Topographie der Daten hinreichend gut wiedergegeben werden soll. Die Qualität solcher Abbildung hängt gewöhnlich vom eingesetzten Nachbarschaftskonzept des konstruierenden Algorithmus ab. Die Schwarm-Organisierte Projektion ermöglicht eine Lösung dieses Parametrisierungsproblems durch die Verwendung von Techniken der Schwarmintelligenz. Die praktische Verwendbarkeit dieser Methodik wurde durch zwei Anwendungen auf dem Feld der Molekularbiologie sowie der Finanzanalytik demonstriert

Self-Organization of Topographic Mixture Networks Using Attentional Feedback

This paper proposes a biologically-motivated neural network model of supervised learning. The model possesses two novel learning mechanisms. The first is a network for learning topographic mixtures. The network's internal category nodes are the mixture components, which learn to encode smooth distributions in the input space by taking advantage of topography in the input feature maps. The second mechanism is an attentional biasing feedback circuit. When the network makes an incorrect output prediction, this feedback circuit modulates the learning rates of the category nodes, by amounts based on the sharpness of their tuning, in order to improve the network's prediction accuracy. The network is evaluated on several standard classification benchmarks and shown to perform well in comparison to other classifiers. Possible relationships are discussed between the network's learning properties and those of biological neural networks. Possible future extensions of the network are also discussed.Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409