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Probabilistic principal component analysis (PPCA) seeks a low dimensionalrepresentation of a data set in the presence of independent spherical Gaussiannoise. The maximum likelihood solution for the model is an eigenvalue problemon the sample covariance matrix. In this paper we consider the situation wherethe data variance is already partially explained by other actors, for examplesparse conditional dependencies between the covariates, or temporalcorrelations leaving some residual variance. We decompose the residual varianceinto its components through a generalised eigenvalue problem, which we callresidual component analysis (RCA). We explore a range of new algorithms thatarise from the framework, including one that factorises the covariance of aGaussian density into a low-rank and a sparse-inverse component. We illustratethe ideas on the recovery of a protein-signaling network, a gene expressiontime-series data set and the recovery of the human skeleton from motion capture3-D cloud data.

Residual Component Analysis: Generalising PCA for more flexible inference in linear-Gaussian models