Classification and Feature Selection on Matrix Data with Application to Gene-Expression Analysis

with Application to Gene-Expression Analysis Sepp Hochreiter [email protected] Klaus Obermayer Fakultät für Elektrotechnik und Informatik Technische Universität Berlin Franklinstr. 28/29, 10587 Berlin, Germany [email protected] We consider the classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects where row and column objects may be from different sets and column objects are labeled. Data matrix entries express relationships between row and column objects and are produced by an unknown kernel. These kernels represent dot products in some (unknown) feature space. In this feature space a linear column object classifier should be constructed. However the dot products between column objects are not available. Therefore standard support vector techniques cannot be utilized. We derive a new objective function for model selection in such a feature space according to the principle of structural risk minimization. The new objective allows the analysis of matrices which are not positive definite, and not even symmetric or square. Because row objects can be interpreted as features and our method assigns support vector weights to the row objects can be used for feature selection. An additional constraint, which imposes sparseness on the row objects resulting in few selected features. We analyse data obtained from DNA microarrays, where “column” objects correspond to samples, “row” objects correspond to genes and matrix elements correspond to expression levels. Benchmarks are conducted using standard one-gene classification and support vector machines and K-nearest neighbors after standard feature selection. Our new method extracts a sparse set of genes and provides superior classification results. Introduction Many data in the real world are characterized by matrices, e.g. data in Microsoft Excel tables, transaction data or micro arrays. Rows and columns of these matrices indicate the relationship between objects. One typical case are so-called pairwise data, where rows as well as columns of the matrix represent the objects of the dataset (Fig. 1a) and where the entries of the matrix denote similarity values. Another typical case occurs, if objects are described by a set of features (Fig. 1b). In this case, the column objects are the objects to be characterized, the row objects correspond to their features and the matrix elements denote the strength with which a feature is expressed in a particular object. 0.2 -0.9 0.2 0.4 -0.3 -0.5 -0.7 -0.3 -0.1