  Big data applications, such as medical imaging and genetics, typically
generate datasets that consist of few observations n on many more variables p,
a scenario that we denote as p>>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 p>>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 p>>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.
