Classifying Matrices with a Spectral Regularization
Ryota Tomioka - Dept. of Mathematical Informatics, IST, The University of Tokyo, Japan
Kazuyuki Aihara - Institute of Industrial Science, The University of Tokyo, Japan
We propose a method for the classification of matrices. We use a linear classifier with a novel regularization scheme based on the spectral 1-norm of its coefficient matrix. The spectral regularization not only provides a principled way of complexity control but also enables automatic determination of the rank of the coefficient matrix. Using the Linear Matrix Inequality technique, we formulate the inference task as a single convex optimization problem. We apply our method to the motor-imagery EEG classification problem. The method not only improves upon conventional methods in the classification performance but also determines a subspace in the signal that concentrates discriminative information without any additional feature extraction step. The method can be easily generalized to regression problems by changing the loss function. Connections to other methods are also discussed.