Classification of Big Data With Application to Imaging Genetics

Abstract

Big data applications, such as medical imaging and genetics, typically generate datasets that consist of few observations ${\boldsymbol n}$ on many more variables ${\boldsymbol p}$ , a scenario that we denote as ${\boldsymbol p}\gg{\boldsymbol n}$ . Traditional data processing methods are often insufficient for extracting information out of big data. This calls for the development of new algorithms that can deal with the size, complexity, and the special structure of such datasets. In this paper, we consider the problem of classifying ${\boldsymbol p}\gg{\boldsymbol n}$ data and propose a classification method based on linear discriminant analysis (LDA). Traditional LDA depends on the covariance estimate of the data, but when ${\boldsymbol p}\gg{\boldsymbol n}$ , the sample covariance estimate is singular. The proposed method estimates the covariance by using a sparse version of noisy principal component analysis (nPCA). The use of sparsity in this setting aims at automatically selecting variables that are relevant for classification. In experiments, the new method is compared to state-of-the art methods for big data problems using both simulated datasets and imaging genetics datasets.