Residual Component Analysis: Generalising PCA for more flexible inference in linear-Gaussian models
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situat...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
18.06.2012
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Subjects | |
Online Access | Get full text |
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Summary: | Probabilistic principal component analysis (PPCA) seeks a low dimensional
representation of a data set in the presence of independent spherical Gaussian
noise. The maximum likelihood solution for the model is an eigenvalue problem
on the sample covariance matrix. In this paper we consider the situation where
the data variance is already partially explained by other actors, for example
sparse conditional dependencies between the covariates, or temporal
correlations leaving some residual variance. We decompose the residual variance
into its components through a generalised eigenvalue problem, which we call
residual component analysis (RCA). We explore a range of new algorithms that
arise from the framework, including one that factorises the covariance of a
Gaussian density into a low-rank and a sparse-inverse component. We illustrate
the ideas on the recovery of a protein-signaling network, a gene expression
time-series data set and the recovery of the human skeleton from motion capture
3-D cloud data. |
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DOI: | 10.48550/arxiv.1206.4560 |