Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	王黎雯, 北京邮电大学
Inviter:	熊世峰
Title:	An Iterative Procedure for Nonlinear Dimensionality Reduction
Language:	Chinese
Time & Venue:	2023.08.21 09:00-10:00 思源楼813
Abstract:	This article proposes a nonlinear dimensionality reduction method using kernel reconstruction regression. We consider the problem of dimensionality reduction, where given high-dimensional data we want to estimate mapping between low and high dimension. We are interested in finding smooth function corresponding to minima of the distance between the data and the estimated model. Given function, we project data onto the function to find low-dimensional embedding vectors that minimizes distance, and for fixed low-dimensional embedding vectors, we use kernel reconstruction regression to estimate function that yields a minimum of distance. Besides, the initial function can be the principal components or other smooth functions, and the low-dimensional embedding vectors can be initialized to the output of a spectral method. The proposed method generalizes principal curves and surfaces, and avoids several of the problems that plague other methods: it can work with any dimension, it provides mappings, and it is not sensitive to noise. Experiments show that the method efficiently learns mapping from low to high dimension without being given intrinsic dimensionality in advance, even with very noisy data.