基于局部线性逼近的流形学习算法

A Manifold Learning Algorithm Based on Locally Linear Approximating

流形学习方法是根据流形的定义提出的一种非线性数据降维方法,主要思想是发现嵌入在高维数据空间的低维光滑流形。局部线性嵌入算法是应用比较广泛的一种流形学习方法,传统的局部线性嵌入算法的一个主要缺点就是在处理稀疏源数据时会失效,而实际应用中很多情况还要面对处理源数据稀疏的问题。在分析局部线性嵌入算法的基础上提出了基于局部线性逼近思想的流形学习算法,其通过采用直接估计梯度值的方法达到局部线性逼近的目的,从而实现高维非线性数据的维数约简,最后在S-曲线上进行稀疏采样测试取得良好降维效果。

Manifold learning is a kind of nonlinear data dimensionality reduction method based on the definition of manifold.The main concept is to find out the low-dimensional smooth manifold embedded in the high-dimensional data space.The Locally Linear Embedding（LLE） Algorithm is applied widely,and one main disadvantage of the traditional Locally Linear Embedding method is that it will turn invalid when it deals with the spare source data,but in practice dealing with the problem of source data sparsity has to be confronted with in many cases.This paper comes up with the manifold learning algorithm based on locally linear approximating by analyzing the LLE Algorithm.It reaches the aim of locally linear approximating through adopting the way of assessing the grads directly,thus realizing the dimensionality reduction of the high-dimensional nonlinear data and finally achieves the fine effect of dimensionality reduction while sampling on the S-curve to test the sparsity.