增量与演化流形学习综述

摘要

Manifold learning is to find the low-dimensional smooth manifold of observation data embedded in high-dimensional data space. In recent years, exploring the intrinsic low-dimensional manifold structure online or incrementally becomes a hot research topic in manifold learning area. This paper surveys the state of the art of incremental and evolutionary manifold learning, including the mechanisms and features of major existing incremental and evolutionary manifold learning methods, their advantages and disadvantages, and highlights the open research issues and future research directions.%流形学习的目标是发现观测数据嵌入在高维数据空间中的低维光滑流形.近年来,在线或增量地发现内在低维流形结构成为流形学习的研究热点.从增量学习和演化学习2个方面入手,对该领域已有研究进展进行综述.增量流形学习较之传统的批量流形学习方法具有动态增量的能力,而演化流形学习能够在线地发现海量动态数据的内在规律,有利于进行维数约简和数据分析.文中对主要的增量与演化流形学习算法的基本原理、特点进行了阐述,分析了各自的优点与不足,指出了该领域的开放问题,并对进一步的研究方向进行了展望.