Material Detail
Kernel Representations and Kernel Density Estimation
This video was recorded at Workshop on Sparsity and Inverse Problems in Statistical Theory and Econometrics, Berlin 2008. There has been a great deal of attention in recent times particularly in machine learning to representation of multivariate data points x by K(x, ·) where K is positive and symmetric and thus induces a reproducing kernel Hilbert space.The idea is then to use the matrix K(Xi , Xj )as a substitute for the empirical covariance matrix of a sample X1 , . . . , Xn for PCA and other inference.(Jordan and Fukumizu(2006) for instance. Nadler et. al(2006) connected this approach to one based on random walks and diffusion limits and indicated a connection to kernel density estimation.By making at least a formal connection to a multiplication operator on a function space we make further connection and show how clustering results of Beylkin ,Shih and Yu (2008) which apparently differ from Nadler et al. can be explained.
Quality
- User Rating
- Comments
- Learning Exercises
- Bookmark Collections
- Course ePortfolios
- Accessibility Info
More about this material
- Mobile Compatibility:
- Not specified at this time
- Language:
- English
- Cost Involved:
- No
- Source Code Available:
- No
- Creative Commons:
-
This work is licensed under a Attribution-NonCommercial-NoDerivs 3.0 United States
