Misaligned principal components analysis: Application to gene expression time series analysis

Principal Component Analysis (PCA) is a widely applied method for extracting structure from samples of high dimensional biological data. Often there exist misalignments between different samples and this can cause severe problems in PCA if not properly taken into account. For example, subject-dependent temporal differences in gene expression response to a treatment will create relative time shifts in the samples that decohere the PCA analysis. Depending on the characteristics of the underlying signal, the sensitivity of PCA to such misalignments is severe, leading to a phase transition phenomenon that can be studied using the spectral theory of autocorrelation matrices. With this as motivation, we propose a new method of PCA, called MisPCA, that explicitly accounts for the effects of misalignments in the samples. We illustrate MisPCA on clustering longitudinal temporal gene expression data.