基于Gamma的有序均值聚类及其在基因表达分析中的应用

Composite likelihood inference in a discrete latent variable model for two-way "clustering-by-segmentation" problems

We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or segments, along the other (e.g. consecutively ordered times or locations). The model relies on a hidden Markov structure but, given its complexity, cannot be estimated by full maximum likelihood. We therefore introduce composite likelihood methodology based on considering different subsets of the data. The proposed approach is illustrated by simulation, and with an…

Model-based clustering of Gaussian copulas for mixed data

Clustering task of mixed data is a challenging problem. In a probabilistic framework, the main difficulty is due to a shortage of conventional distributions for such data. In this paper, we propose to achieve the mixed data clustering with a Gaussian copula mixture model, since copulas, and in particular the Gaussian ones, are powerful tools for easily modelling the distribution of multivariate variables. Indeed, considering a mixing of continuous, integer and ordinal variables (thus all having a cumulative distribution function), this copula mixture model defines intra-component dependencies …

基于正则化谱聚类的潜在类别分析

Latent class analysis by regularized spectral clustering

本文提出基于正则化拉普拉斯矩阵的两种新算法，用于有序分类数据的潜在类别模型参数估计，并给出理论收敛速率、类别数确定度量及模拟与真实数据验证。

Scalable Model Selection for Staged Trees: Mean-posterior Clustering and Binary Trees

Several structure-learning algorithms for staged trees, asymmetric extensions of Bayesian networks, have been proposed. However, these either do not scale efficiently as the number of variables considered increases, a priori restrict the set of models, or they do not find comparable models to existing methods. Here, we define an alternative algorithm based on a totally ordered hyperstage. We demonstrate how it can be used to obtain a quadratically-scaling structural learning algorithm for staged trees that restricts the model space a-posteriori. Through comparative analysis, we show that throu…

Dimension reduction for model-based clustering

We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and, depending on the estimated mixture model, on the variation on group covariances. The proposed method aims at reducing the dimensionality by identifying a set of linear combinations, ordered by importance as quantified by the associated eigenvalues, of the original features which capture most of the cluster structure contained in the data. Observations may then b…

Clustering, Classification, Discriminant Analysis, and Dimension Reduction via Generalized Hyperbolic Mixtures

A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of model-based clustering, classification, or discriminant analysis. A reduced subspace of the data is derived by considering the extent to which group means and group covariances vary. The members of the subspace arise through linear combinations of the original data, and are ordered by importance via the associated eigenvalues. The observations can be projected …