11,029 research outputs found
Self-weighted Multiple Kernel Learning for Graph-based Clustering and Semi-supervised Classification
Multiple kernel learning (MKL) method is generally believed to perform better
than single kernel method. However, some empirical studies show that this is
not always true: the combination of multiple kernels may even yield an even
worse performance than using a single kernel. There are two possible reasons
for the failure: (i) most existing MKL methods assume that the optimal kernel
is a linear combination of base kernels, which may not hold true; and (ii) some
kernel weights are inappropriately assigned due to noises and carelessly
designed algorithms. In this paper, we propose a novel MKL framework by
following two intuitive assumptions: (i) each kernel is a perturbation of the
consensus kernel; and (ii) the kernel that is close to the consensus kernel
should be assigned a large weight. Impressively, the proposed method can
automatically assign an appropriate weight to each kernel without introducing
additional parameters, as existing methods do. The proposed framework is
integrated into a unified framework for graph-based clustering and
semi-supervised classification. We have conducted experiments on multiple
benchmark datasets and our empirical results verify the superiority of the
proposed framework.Comment: Accepted by IJCAI 2018, Code is availabl
Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images
We present a novel kernel regression framework for smoothing scalar surface
data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel
constructed from the eigenfunctions, we formulate a new bivariate kernel
regression framework as a weighted eigenfunction expansion with the heat kernel
as the weights. The new kernel regression is mathematically equivalent to
isotropic heat diffusion, kernel smoothing and recently popular diffusion
wavelets. Unlike many previous partial differential equation based approaches
involving diffusion, our approach represents the solution of diffusion
analytically, reducing numerical inaccuracy and slow convergence. The numerical
implementation is validated on a unit sphere using spherical harmonics. As an
illustration, we have applied the method in characterizing the localized growth
pattern of mandible surfaces obtained in CT images from subjects between ages 0
and 20 years by regressing the length of displacement vectors with respect to
the template surface.Comment: Accepted in Medical Image Analysi
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