Orthogonal discriminant neighborhood analysis for tumor classification

An important application of gene expression data is tumor classification. Dimensionality reduction is a key step of tumor classification as gene expression data have the so-called large and small problem. To reduce the dimensionality of the microarray data, in this paper, a novel algorithm called orthogonal discriminant neighborhood analysis (ODNA) is proposed for tumor classification, which can reduce the effect resulting from over-fitting by pre-selecting a small subset of genes. Given a set of data points in the ambient space, a neighbor weight matrix is firstly built to describe the relationship among the data samples. Secondly, optimal between-class scatter matrix and within-class scatter matrix are defined such that the neighborhood structure can be preserved. To improve the discriminating ability, a new method is presented to orthogonalize the basis eigenvectors. The experimental results with two public microarray datasets demonstrate that the proposed ODNA is quite effective and feasible for tumor classification.