We start with a locally defined principal curve definition for a given probability density function (pdf) and define a pairwise manifold score based on local derivatives of the...
We present a manifold learning approach to dimensionality
reduction that explicitly models the manifold as a mapping
from low to high dimensional space. The manifold is
represen...
We describe techniques to establish local frames over point-sampled manifold surfaces. The tangential alignment of local frames is determined using a wave front algorithm starting...
Dimensionality reduction plays a fundamental role in data processing, for which principal component analysis (PCA) is widely used. In this paper, we develop the Laplacian PCA (LPC...
Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high dimensional spaces. We consider the case where data is drawn from sampling...
Xiaofei He, Deng Cai, Shuicheng Yan, HongJiang Zha...