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Principal component analysis (PCA) is an exploratory tool widely used in dataanalysis to uncover dominant patterns of variability within a population.Despite its ability to represent a data set in a low-dimensional space, theinterpretability of PCA remains limited. However, in neuroimaging, it isessential to uncover clinically interpretable phenotypic markers that wouldaccount for the main variability in the brain images of a population. Recently,some alternatives to the standard PCA approach, such as Sparse PCA, have beenproposed, their aim being to limit the density of the components. Nonetheless,sparsity alone does not entirely solve the interpretability problem, since itmay yield scattered and unstable components. We hypothesized that theincorporation of prior information regarding the structure of the data may leadto improved relevance and interpretability of brain patterns. We thereforepresent a simple extension of the popular PCA framework that adds structuredsparsity penalties on the loading vectors in order to identify the few stableregions in the brain images accounting for most of the variability. Suchstructured sparsity can be obtained by combining l1 and total variation (TV)penalties, where the TV regularization encodes higher order information aboutthe structure of the data. This paper presents the structured sparse PCA(denoted SPCA-TV) optimization framework and its resolution. We demonstrate theefficiency and versatility of SPCA-TV on three different data sets. The gainsof SPCA-TV over unstructured approaches are significant,since SPCA-TV revealsthe variability within a data set in the form of intelligible brain patternsthat are easy to interpret, and are more stable across different samples.

Structured Sparse Principal Components Analysis with the TV-Elastic Net penalty