We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix used in f
orming the loss. This can be interpreted as a penalized kernel learning problem where indefinite kernel matrices are treated as a noisy observations of a true Mercer kernel. Our formulation keeps the problem convex and relatively large problems can be solved efficiently using the projected gradient or analytic center cutting plane methods. We compare the performance of our technique with other methods on several classic data sets.
We show how text from news articles can be used to predict intraday price movements of financial assets using support vector machines. Multiple kernel learning is used to combine equity returns with text as predictive features to increase classificat
ion performance and we develop an analytic center cutting plane method to solve the kernel learning problem efficiently. We observe that while the direction of returns is not predictable using either text or returns, their size is, with text features producing significantly better performance than historical returns alone.
In this paper, we study the application of sparse principal component analysis (PCA) to clustering and feature selection problems. Sparse PCA seeks sparse factors, or linear combinations of the data variables, explaining a maximum amount of variance
in the data while having only a limited number of nonzero coefficients. PCA is often used as a simple clustering technique and sparse factors allow us here to interpret the clusters in terms of a reduced set of variables. We begin with a brief introduction and motivation on sparse PCA and detail our implementation of the algorithm in dAspremont et al. (2005). We then apply these results to some classic clustering and feature selection problems arising in biology.
