关键词: 降维算法, 局部线性逼近, 流形学习, 局部线性嵌入

Abstract: Manifold learning is a nonlinear data dimensionality reduction method.It is proposed according to the manifold concept.The main idea of manifold leaning is to find a smooth low-dimensional manifold embedded in the high-dimensional data space.The Locally Linear Embedding（LLE） algorithm based on Manifold learning is introduced firstly in this paper,because the
conventional LLE algorithm will be ineffective when the source data is spare.,with that the manifold learning algorithm based on Locally Linear Approximating（LLA） is presented.At last,the results show the effectiveness of the LLA on the S-curse sampling
and testing.

Key words: dimensionality reduction algorithm, Locally Linear Approximating（LLA）, manifold learning, Locally Linear Embedding（LLE）