一种基于局部保持的隐变量模型

A Latent Variable Model Based on Local Preservation

隐变量模型是一类有效的降维方法,但是由非线性核映射建立的隐变量模型不能保持数据空间的局部结构.为了克服这个缺点,文中提出一种保持数据局部结构的隐变量模型.该算法充分利用局部保持映射的保局性质,将局部保持映射的目标函数作为低维空间中数据的先验信息,对高斯过程隐变量中的低维数据进行约束,建立局部保持的隐变量.实验结果表明,相比原有的高斯过程隐变量,文中算法较好地保持数据局部结构的效果.

Latent variable model （LVM） is a kind of efficient nonlinear dimensionality reduction algorithm through establishing smooth kernel mappings from the latent space to the data space. However, this kind of mappings cannot keep the points close in the latent space even they are close in data space. A LVM is proposed based on locality preserving projection （LPP） which can preserve the locality structure of dataset. The objective function of LPP is considered as a prior of the variables in the Gaussian process latent variable model （GP-LVM）. The proposed locality preserving GP-LVM is built with the constrained term of the objective function. Compared with the traditional LPP and GP-LVM, experimental results show that the proposed method performs better in preserving local structure on common data sets.