Clustering in high-dimensional spaces is nowadays a recurrent problem in many scientific domains but remains a difficult task from both the clustering accuracy and the result understanding points of view. This paper presents a discriminative latent mixture (DLM) model which fits the data in a latent orthonormal discriminative subspace with an intrinsic dimension lower than the dimension of the original space. By constraining model parameters within and between groups, a family of 12 parsimonious DLM models is exhibited which allows to fit onto various situations. An estimation algorithm, called the Fisher-EM algorithm, is also proposed for estimating both the mixture parameters and the discriminative subspace. Experiments on simulated and real datasets highlight the good performance of the proposed approach as compared to existing clustering methods while providing a useful representation of the clustered data. The method is as well applied to the clustering of mass spectrometry data.
Clustering is a traditional statistical problem which aims to divide a set of observations @math described by @math variables into @math homogeneous groups. The problem of clustering has been widely studied for years and the reader could refer to @cite_5 @cite_45 for reviews on the clustering problem. However, the interest in clustering is still increasing since more and more scientific fields require to cluster high-dimensional data. Moreover, such a task remains very difficult since clustering methods suffer from the well-known @cite_48 . Conversely, the @cite_14 , which refers to the fact that high-dimensional data do not fit the whole observation space but live in low-dimensional subspaces, gives hope to efficiently classify high-dimensional data. This section firstly reviews the framework of model-based clustering before exposing the existing approaches to deal with the problem of high dimension in clustering.
@cite_5 @cite_14 @cite_45 @cite_48
2011832962 145612104 1992419399
Cluster analysis is the automated search for groups of related observations in a dataset. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures, and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as how many clusters are there, which clustering method should be used, and how should outliers be handled. We review a general methodology for model-based clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, minefield detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology and discuss recent development... For the estimation of probability densities in dimensions past two, representational difficulties predominate. Experience indicates that we should investigate the locations of the modes and proceed to describe the unknown density using these as local origins. The scaling system to be employed should also be data determined. Using such a philosophy, density estimation has been successfully carried out in the three dimensional case. Color and motion can be used as enhancement devices so that estimation in dimensions past three becomes feasible. Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overviewof pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.