Repository logo

Residual Component Analysis

Accepted version


Conference Object

Change log


Kalaitzis, Alfredo A 
Lawrence, Neil David  ORCID logo


Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. 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 factors, e.g. covariates of interest, or temporal correlations leaving some residual variance. We decompose the residual variance into its components through a generalized eigenvalue problem, which we call residual component analysis (RCA). We show that canonical covariates analysis (CCA) is a special case of our algorithm and explore a range of new algorithms that arise from the framework. We illustrate the ideas on a gene expression time series data set and the recovery of human pose from silhouette.



stat.ML, stat.ML, cs.AI, math.ST, stat.CO, stat.TH, 62J10 (Primary), 62-09, 62H25, G.1.3; G.3; I.2.6; I.5.1

Journal Title

Proceedings of the 29th International Coference on International Conference on Machine Learning

Conference Name

International Conference on Machine Learning

Journal ISSN

Volume Title



All rights reserved