动态增殖流形学习算法

A Dynamically Incremental Manifold Learning Algorithm

流形学习的主要目标是发现高维观测数据空间中的低维光滑流形.目前,流形学习已经成为机器学习和数据挖掘领域的研究热点.为了从高维数据流和大规模海量数据集中探索有价值的信息,迫切需要增殖地发现内在低维流形结构.但是,现有流形学习算法不具有增殖能力,并且不能有效处理海量数据集.针对这些问题,系统定义了增殖流形学习的概念,这有利于解释人脑中稳态感知流形的动态形成过程,且可以指导符合人脑增殖学习机理的流形学习算法的研究.以此为指导原则,提出了动态增殖流形学习算法,并在实验中验证了算法的有效性.

The main goal of manifold learning is to find a smooth low-dimensional manifold embedded in high-dimensional data space. At present, manifold learning has become a hot issue in the field of machine learning and data mining. In order to seek valuable information from high-dimensional data stream and large-scale data set, it is urgently necessary to incrementally find intrinsic low-dimensional manifold structure in such observation data set. But, current manifold learning algorithms have no incremental ability and also can not process the giant data set effectively. Aiming at these problems, the concept of incremental manifold learning is firstly defined systematically in this paper. It is advantageous to interpret the dynamic process of developing a stable perception manifold and to guide the research of manifold learning algorithms which fit to incremental learning mechanism in man brain. According to the guiding principles of incremental manifold learning, a dynamically incremental manifold learning algorithm is then proposed, which can effectively process the increasing data sets and the giant data set sampled from the same manifold. The novel method can find the global low-dimensional manifold by integrating the lowdimensional coordinates of different neighborhood observation data sets. Finally, the experimental results on both synthetic ＂Swiss-roll＂ data set and real face data set show that the algorithm is feasible.