中文摘要：

结合现实中数据表现出复杂的多流形特点，对多流形假设下的学习算法进行了研究。利用多种聚类算法对不同类型的数据进行聚类分析，得出每种数据类型下的最优聚类方法。仿真结果表明，采用规范化切割谱聚类方法可将独立子空间高维数据成功分类；SSC算法对线性子空间聚类效果表现最佳；引入LLE的Ncut聚类算法和SMMC算法对于非线性数据的多流形聚类具有较好的效果；SSC算法和SMR算法对高维子空间聚类问题表现出较好的适用性。

英文摘要：

According to the complex multi-manifold characteristics of real data, the learning algorithm with multi-manifold assumption is mainly studied. The different types of data are analyzed by using a variety of clustering algorithms to get the best clustering method for each type of data. Simulation results show that in- dependent subspace high dimensional data will be classified successfully by a standardized cutting spectral clustering method; SSC algorithm is the best choice to cluster the linear subspace; NCUT clustering algo- rithm of LLE and SMMC algorithm will make better effect on multi-manifold clustering for nonlineaer data; SSC algorithm and SMR algorithm are suitable for higher dimensional subspace clustering problems.