Motivation : Graph on labeled and unlabeled data W; Laplacian

1. (Semi-Supervised Kernels via Convex Optimization with Order Constraints) zhuxj@cs.cmu.edu • Motivation: • Graph on labeled and unlabeled data W; Laplacian • Graph kernels for semisupervised learning • r( ) turns eigenvalues “upside down”, emphasizes smooth  (small ) • diffusion kernel • Gaussian field kernel • What parametric form r( )? Is it flexible enough? we can do better Nonparametric Transforms of Graph Kernels for Semi-Supervised LearningXiaojin Zhu†Jaz Kandola‡ Zoubin Ghahramani†‡ John Lafferty† • Method: • Forget about parametric form r( ). • Optimize i’s to maximize kernel alignment to labels • Constrain the order to respect the smoothness assumptions encoded in the graph. • Convex optimization, QCQP. • Improvement: do not constrain 0 if 0 constant (bias). • Result: • Novel graph kernels for semi-supervised learning. • Computationally feasible • Improved classification accuracy †School of Computer Science, Carnegie Mellon University. ‡ Gatsby Computational Neuroscience Unit, University College London Preprint: http://www.cs.cmu.edu/~zhuxj/pub/flex.pdf Contact: zhuxj@cs.cmu.edu