Abstract: It is well known that the manifold structure of data will greatly affect final results about dimensionality reduction. However, most of the existing multiple kernel learning for dimensionality reduction does not consider the problem of maintaining the original manifold structure of data. This paper proposes a new multiple kernel learning for dimensionality reduction method to overcome the possibly distorted manifold structure of data. The core idea of the proposed method is to combine all or partial features of the original data into the multiple kernel expression such that the degree of such distortion is reduced. The combination of original information and feature information will eventually be expressed as a coupling between kernels, and this problem can be optimized through the original multiple kernel learning framework to get its kernel weight coefficients. Experimental results show that the proposed method can achieve a promising result with both a smaller amount of feature descriptor and less running time, in contrast to that of original method this paper based on.

Key words: manifold learning, kernel method, multiple kernel learning, original data, mapping space

摘要： 对于一些降维算法来说，数据的流形结构会对其降维效果造成很大影响。针对已有的多核学习降维算法没有考虑到保持数据流形结构这一问题，在其基础上提出了一种新的多核学习降维方法。其实质是由于数据通过映射函数投影到高维空间，在这个过程中可能会造成数据流形结构的扭曲，为了保持原数据的流形结构，从原数据中选择全部或局部信息与映射空间信息进行组合，从而使得在高维投影空间中能够较好地保存原数据的流形结构，减小因数据在映射空间中产生扭曲而对降维结果造成的影响。原信息与特征信息组合的方法最终将表示为核之间的耦合，并可以通过原多核学习框架的优化方法进行优化得到其核权重系数。实验证明，通过使用新方法，使用少量的特征也能够达到不错的效果，同时在时间效率上较原多核学习框架的方法也有所提高。

关键词: 流形学习, 核方法, 多核学习, 原信息, 映射空间