Multidimensional fitting for multivariate data analysis

Large multidimensional data matrices are frequent in biology. However, statistical methods often have difficulties dealing with such matrices because they contain very complex data sets. Consequently variable selection and dimensionality reduction methods are often used to reduce matrix complexity, although at the expense of information conservation. A new method derived from multidimensional scaling (MDS) is presented for the case where two matrices are available to describe the same population. The presented method transforms one of the matrices, called the target matrix, with some constraints to make it fit with the second matrix, referred to as the reference matrix. The fitting to the reference matrix is performed on the distances computed for the two matrices, and the transformation depends on the problem at hand. A special feature of this method is that a variable can be only partially modified. The method is applied on the exclusive-or (XOR) problem and then on a biological application with large-scale gene expression data.