谱机器学习研究综述

ISSN 1673-9418CODEN JKYTA8

Journal of Frontiers of Computer Science and Technology 1673-9418/2015/09(12)-1409-11doi:10.3778/j.issn.1673-9418.1505049E-mail:fcst@https://www.360docs.net/doc/4a11581102.html, https://www.360docs.net/doc/4a11581102.html, Tel:+86-10-89056056谱机器学习研究综述*

尹宏伟，李凡长+

苏州大学计算机科学与技术学院，江苏苏州215000

Survey on Spectral Machine Learning *

YIN Hongwei,LI Fanzhang +

College of Computer Science and Technology,Soochow University,Suzhou,Jiangsu 215000,China

+Corresponding author:E-mail:lfzh@https://www.360docs.net/doc/4a11581102.html,.

YIN Hongwei,LI Fanzhang.Survey on spectral machine learning.Journal of Frontiers of Computer Science and Technology,2015,9(12)：1409-1419.

Abstract:There are many problems in the fields of natural science which are difficult to be resolved due to continuous variation.These complex problems can be expressed as the combination of a series of simple problems which are distributed among the discrete spaces.The approximate solution of the complex problems can be obtained by solving the simple problems.In recent years,the spectral learning based on spectral mathematic theory is attracting more and more attention in machine https://www.360docs.net/doc/4a11581102.html,pared with traditional learning methods,it can not only preserve the latent structure in the data,but also obtain a global optimization solution.This paper firstly introduces the basic theory of spectral learning,then shows some typical algorithms including spectral clustering,spectral learning of latent variable probabilistic model and spectral manifold learning,and finally presents some worthy perspectives according to the current researches.

Key words:spectral learning;spectral clustering;latent variable probabilistic model;spectral manifold learning

摘要：在自然科学研究领域存在众多因连续变化而难以解决的问题。这些复杂问题可以通过谱方法表示为一系列离散空间上的简单问题的组合，通过求解这些简单问题获得其近似解。谱学习算法是近年来国际上机器学习领域的一个研究热点。谱学习算法建立在谱数学理论基础上，与传统的学习算法相比，一方面能保持*The National Natural Science Foundation of China under Grant Nos.61033013,60775045(国家自然科学基金);the Soochow Scholar Program of Soochow University under Grant No.14317360(苏州大学东吴学者计划).

Received 2015-05,Accepted 2015-08.

CNKI 网络优先出版：2015-09-01,https://www.360docs.net/doc/4a11581102.html,/kcms/detail/11.5602.TP.20150901.1503.002.html 尹宏伟，李凡长.谱机器学习研究综述[J].计算机科学与探索，2015，9（12）：

1409-1419.