Diffusion Representation for Asymmetric Kernels
We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work we study data sets in which its geometry structure is induced by an asymmetric kernel. We use a priori coordinate system to represent this geometry and, thus, be able to improve the computational complexity of reducing the dimensionality of data sets. A coordinate system connected to the tensor product of Fourier basis is used to represent the underlying geometric structure obtained by the diffusion-map, thus reducing the dimensionality of the data set and making use of the speedup provided by the two-dimensional Fast Fourier Transform algorithm (2-D FFT). We compare our results with those obtained by other eigenvalue expansions, and verify the efficiency of the algorithms with synthetic data, as well as with real data from applications including climate change studies.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Diffusion Representation for Asymmetric Kernels via Magnetic Transform
As a nonlinear dimension reduction technique, the diffusion map (DM) has been widely used. In DM, kernels play an important role for capturing the nonlinear relationship of data. However, only symmetric kernels can be u…
Learning with Asymmetric Kernels: Least Squares and Feature Interpretation
Asymmetric kernels naturally exist in real life, e.g., for conditional probability and directed graphs. However, most of the existing kernel-based learning methods require kernels to be symmetric, which prevents the use …
Semi-Supervised Learning on Graphs through Reach and Distance Diffusion
Semi-supervised learning (SSL) is an indispensable tool when there are few labeled entities and many unlabeled entities for which we want to predict labels. With graph-based methods, entities correspond to nodes in a gra…
Nonlinear SVD with Asymmetric Kernels: feature learning and asymmetric Nyström method
Asymmetric data naturally exist in real life, such as directed graphs. Different from the common kernel methods requiring Mercer kernels, this paper tackles the asymmetric kernel-based learning problem. We describe a non…
Random Fourier Features for Asymmetric Kernels
The random Fourier features (RFFs) method is a powerful and popular technique in kernel approximation for scalability of kernel methods. The theoretical foundation of RFFs is based on the Bochner theorem that relates sym…
Computational Efficiency