Generalization Bounds for Subspace Selection and Hyperbolic PCA

We present a method which uses example pairs of equal or unequal class labels to select a subspace with near optimal metric properties in a kernel-induced Hilbert space. A representation of …nite dimensional projections as bounded linear functionals on a space of HilbertSchmidt operators leads to PAC-type performance guarantees for the resulting feature maps. The proposed algorithm returns the projection onto the span of the principal eigenvectors of an empirical operator constructed in terms of the example pairs. It can be applied to metalearning environments and experiments demonstrate an e¤ective transfer of knowledge between di¤erent but related learning tasks.

• Type: Conference
• Year: 2005
• Where: SLSFS
• Authors: Andreas Maurer
• Keywords: Example Pairs, Optimal Metric Properties, Pattern Recognition, SLSFS 2005, Unequal Class Labels