A novel dimensionality reduction technique based on independent component analysis for modeling microarray gene expression data

DNA microarray experiments generating thousands of gene expression measurements, are being used to gather information from tissue and cell samples regarding gene expression differences that will be useful in diagnosing disease. But one challenge of microarray studies is the fact that the number n of samples collected is relatively small compared to the number p of genes per sample which are usually in thousands. In statistical terms this very large number of predictors compared to a small number of samples or observations makes the classification problem difficult. This is known as the ”curse of dimensionality problem”. An efficient way to solve this problem is by using dimensionality reduction techniques. Principle Component Analysis(PCA) is a leading method for dimensionality reduction of gene expression data which is optimal in the sense of least square error. In this paper we propose a new dimensionality reduction technique for specific bioinformatics applications based on Independent component Analysis(ICA). Being able to exploit higher order statistics to identify a linear model result, this ICA based dimensionality reduction technique outperforms PCA from both statistical and biological significance aspects. We present experiments on NCI 60 dataset to show this result

A study of the classification of low-dimensional data with supervised manifold learning

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of supervised manifold learning for classification. We consider nonlinear dimensionality reduction algorithms that yield linearly separable embeddings of training data and present generalization bounds for this type of algorithms. A necessary condition for satisfactory generalization performance is that the embedding allow the construction of a sufficiently regular interpolation function in relation with the separation margin of the embedding. We show that for supervised embeddings satisfying this condition, the classification error decays at an exponential rate with the number of training samples. Finally, we examine the separability of supervised nonlinear embeddings that aim to preserve the low-dimensional geometric structure of data based on graph representations. The proposed analysis is supported by experiments on several real data sets