On the Role of Eigendecomposition in Kernel Embedding
J. Jon Ryu, Jiun-Ting Huang, Younghan Kim · 2021
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.