The EM Algorithm for Mixtures of Factor Analyzers
نویسنده
چکیده
Factor analysis, a statistical method for modeling the covariance structure of high dimensional data using a small number of latent variables, can be extended by allowing di erent local factor models in di erent regions of the input space. This results in a model which concurrently performs clustering and dimensionality reduction, and can be thought of as a reduced dimension mixture of Gaussians. We present an exact Expectation{Maximization algorithm for tting the parameters of this mixture of factor analyzers.
منابع مشابه
Mixtures of common t-factor analyzers for clustering high-dimensional microarray data
MOTIVATION Mixtures of factor analyzers enable model-based clustering to be undertaken for high-dimensional microarray data, where the number of observations n is small relative to the number of genes p. Moreover, when the number of clusters is not small, for example, where there are several different types of cancer, there may be the need to reduce further the number of parameters in the speci...
متن کاملMaximum likelihood estimation in constrained parameter spaces for mixtures of factor analyzers
Mixtures of factor analyzers are becoming more and more popular in the area of model based clustering of multivariate data. According to the likelihood approach in data modeling, it is well known that the unconstrained likelihood function may present spurious maxima and singularities. To reduce such drawbacks, in this paper we introduce a procedure for parameter estimation of mixtures of factor...
متن کاملSignal Modeling and Classification Using a Robust Latent Space Model Based on t Distributions
Factor analysis is a statistical covariance modeling technique based on the assumption of normally distributed data. A mixture of factor analyzers can be hence viewed as a special case of Gaussian (normal) mixture models providing a mathematically sound framework for attribute space dimensionality reduction. A significant shortcoming of mixtures of factor analyzers is the vulnerability of norma...
متن کاملAdaptive Mixtures of Factor Analyzers
A mixture of factor analyzers is a semi-parametric density estimator that generalizes the well-known mixtures of Gaussians model by allowing each Gaussian in the mixture to be represented in a different lower-dimensional manifold. This paper presents a robust and parsimonious model selection algorithm for training a mixture of factor analyzers, carrying out simultaneous clustering and locally l...
متن کاملnr . IAS - UVA - 02 - 01 Procrustes Analysis to Coordinate Mixtures of Probabilistic Principal Component Analyzers
Mixtures of Probabilistic Principal Component Analyzers can be used to model data that lies on or near a low dimensional manifold in a high dimensional observation space, in effect tiling the manifold with local linear (Gaussian) patches. In order to exploit the low dimensional structure of the data manifold, the patches need to be localized and oriented in a low dimensional space, so that 'loc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996