基于局部约束字典学习的数据降维和重构方法  

Dimensionality reduction and reconstruction method based on locality constrained dictionary learning

作　　者：刘丽娜[1,2] 马世伟[1] 温加睿 

机构地区：[1]上海大学机电工程与自动化学院,上海210072 [2]山东理工大学电气与电子工程学院,淄博255049

出　　处：《仪器仪表学报》2016年第1期99-108,共10页Chinese Journal of Scientific Instrument

摘　　要：针对目前已有的非线性降维算法存在计算复杂度高、难以处理大型数据集和增量化降维问题,本文提出了一种基于局部约束字典学习的非线性降维算法。该方法通过重构一些潜在标志点的局部内在流形,并在数据处理过程中将训练数据和未知数据一起嵌入到内在流形中,使得数据的内在几何结构特征得以保持。与已有非线性降维方法相比,该算法具有计算复杂度低、存储空间小和通用性强的特点,可以很好地解决增量化降维问题,易于处理大型数据集。另外,该算法也可以解决高维数据的重构问题,与已有重构方法相比具有计算简单、重构误差较低的特点。实验结果表明了算法的有效性。Since the computational complexity of current existing nonlinear dimensionality reduction algorithm is high, it is difficult to deal with large - scale data sets and out-of-sample extension problem. A nonlinear dimensionality reduction algorithm is presented based on locality constrained dictionary learning. This method maintains the local intrinsic manifold through reconstructing the local intrinsic manifold of some potential landmarks and embedding the training datasets and unknown datasets into the intrinsic manifold, and the intrinsic local geometric construction feature of the datasets are maintained. Compared with the existing methods, it has the characteristics of lower computational complexity, smaller storage space and stronger generality. It can be used to solve sample extension and large-scale data sets problems. In addition, the proposed algorithm can also be used to deal with the high dimensional data reconstruction problem. It has the characteristics of simple calculation and lower reconstruction error. The experimental result verifies the efficiency of the proposed algorithm.

关 键 词：字典学习 局部约束 数据降维 数据重构 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] TH89[自动化与计算机技术—计算机科学与技术]