Kernel principal component analysis
Advances in kernel methods
The Effect of the Input Density Distribution on Kernel-based Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Learning Mixtures of Gaussians
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The spectral method for general mixture models
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Kernel current source density method
Neural Computation
EigenSpokes: surprising patterns and scalable community chipping in large graphs
PAKDD'10 Proceedings of the 14th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part II
Semi-supervised classification by probabilistic relaxation
CIARP'11 Proceedings of the 16th Iberoamerican Congress conference on Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Semi-supervised learning from a translation model between data distributions
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Fast mining and forecasting of complex time-stamped events
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
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In this paper we develop a spectral framework for estimating mixture distributions, specifically Gaussian mixture models. In physics, spectroscopy is often used for the identification of substances through their spectrum. Treating a kernel function K(x, y) as "light" and the sampled data as "substance", the spectrum of their interaction (eigenvalues and eigenvectors of the kernel matrix K) unveils certain aspects of the underlying parametric distribution p, such as the parameters of a Gaussian mixture. Our approach extends the intuitions and analyses underlying the existing spectral techniques, such as spectral clustering and Kernel Principal Components Analysis (KPCA). We construct algorithms to estimate parameters of Gaussian mixture models, including the number of mixture components, their means and covariance matrices, which are important in many practical applications. We provide a theoretical framework and show encouraging experimental results.