关键词: 谱学习, 谱聚类, 缺失变量概率模型, 谱流形学习

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 learning. Compared 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