Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
A kernel view of the dimensionality reduction of manifolds
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Learning with non-positive kernels
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Feature Discovery in Non-Metric Pairwise Data
The Journal of Machine Learning Research
DISTATIS: The Analysis of Multiple Distance Matrices
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops - Volume 03
Pattern Recognition
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
Restricted deep belief networks for multi-view learning
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
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Most manifold learning methods consider only one similarity matrix to induce a low-dimensional manifold embedded in data space. In practice, however, we often use multiple sensors at a time so that each sensory information yields different similarity matrix derived from the same objects. In such a case, manifold integration is a desirable task, combining these similarity matrices into a compromise matrix that faithfully reflects multiple sensory information. A small number of methods exists for manifold integration, including a method based on reproducing kernel Krein space (RKKS) or DISTATIS, where the former is restricted to the case of only two manifolds and the latter considers a linear combination of normalized similarity matrices as a compromise matrix. In this paper we present a new manifold integration method, Markov random walk on multiple manifolds (RAMS), which integrates transition probabilities defined on each manifold to compute a compromise matrix. Numerical experiments confirm that RAMS finds more informative manifolds with a desirable projection property.