|| On the Role of Eigendecomposition in Kernel Embedding
||Jongha Jon Ryu, Jiun-Ting Huang, Young-Han Kim, University of California, San Diego, United States|
||D5-S1-T3: Kernels & Clustering
||Friday, 16 July, 22:00 - 22:20
||Friday, 16 July, 22:20 - 22:40
This paper proposes a special variant of Laplacian eigenmaps, whose solution is characterized by the underlying density and the eigenfunctions of the associated Hilbert--Schmidt operator of a similarity kernel function. In contrast to existing kernel-based spectral methods such as kernel principal component analysis and Laplacian eigenmaps, the new embedding algorithm only involves estimating density at each query point without any eigendecomposition of a matrix. A concrete example of dot-product kernels over hypersphere is provided to illustrate the applicability of the proposed framework.