Training Invariant Support Vector Machines
Machine Learning
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Optimizing the kernel in the empirical feature space
IEEE Transactions on Neural Networks
Shape based appearance model for kernel tracking
Image and Vision Computing
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Scale-space representation of an image is a significant way to generate features for classification. However, for a specific classification task, the entire scale-space may not be useful; only a part of it is typically effective. Toward this end, we design a data dependent classification kernel function, which is a weighted mixture of kernels defined on individual scales. In order to choose the optimum weights in the mixture kernel function (MKF), we propose an optimization criterion that leads to the minimization of Raleigh quotient in the positive orthant. This optimization is in general a difficult, non-convex, quadratically constrained quadratic programming. Utilizing a property of ratio of functions, we reduce the aforementioned optimization into a novel binary search, which is essentially a series of quadratic programming. As an application we choose a significant detection problem in oil sands mining called large lump detection from videos. Employing support vector classifier with our MKF yields encouraging results on these difficult-to-process images and compares favorably against the kernel alignment method [1] as well as Fisher criterion adopted in [2].