Dimensionality reduction by sparse orthogonal projection with applications to miRNA expression analysis and cancer prediction

Background: High dimensionality, i.e. p>n, is an inherent feature of machine learning. Fitting a classification model directly to p-dimensional data risks overfitting and a reduction in accuracy. Thus, dimensionality reduction is necessary to address overfitting and high dimensionality. Results: We present a novel dimensionality reduction method which uses sparse, orthogonal projections to discover linear separations in reduced dimension space. The technique is applied to miRNA expression analysis and cancer prediction. We use least squares fitting and orthogonality constraints to find a set of orthogonal directions which are highly correlated to the class labels. We also enforce L^1 norm sparsity penalties, to prevent overfitting and remove the uninformative features from the model. Our method is shown to offer a highly competitive classification performance on synthetic examples and real miRNA expression data when compared to similar methods from the literature which use sparsity ideas and orthogonal projections. %Specifically, our method offers a more consistent performance in terms of sensitivity and AUC, particularly in the case $p>n$, and when the training samples are weighted towards one class. Discussion: A novel technique is introduced here, which uses sparse, orthogonal projections for dimensionality reduction. The approach is shown to be highly effective in reducing the dimension of miRNA expression data. The application of focus in this article is miRNA expression analysis and cancer prediction. The technique may be generalizable, however, to other high dimensionality datasets.