不完整张量上基于流形学习和张量分解的特征提取

Feature Extraction Based on Manifold Learning and Tensor Decomposition for Incomplete Tensors

针对不完整张量数据的特征提取问题,传统的“两步走”方法,即先张量补全再特征提取,难以避免无关特征增大填补误差,进而影响特征提取的效果;而近年提出的TDVM方法尽管可以同时进行张量补全和特征提取,但由于没有考虑数据的局部结构特点,特征提取效果仍不理想.因此,本文提出一个基于流形学习和张量分解的不完整张量特征提取方法:MLTD.首先,利用“部分距离法”和非负对称矩阵分解得到完整的样本相似矩阵,进而得到样本近邻图;然后,根据近邻图建立基于流形学习和张量分解的特征提取模型,主要思想是将方差最大化和局部保持投影策略融入张量分解中.该方法可以直接从不完整张量中提取有效特征,同时保留数据的局部结构特点.本文在4个图像数据集上与5种较新的方法进行对比.实验结果表明,新提出的方法在张量补全和利用所提取的特征进行分类时性能上都有显著的优越性.

Aiming at the feature extraction from incomplete tensor data, the traditional ″two-step″ technique, i.e.,tensor completion and then feature extraction, is unable to avoid the increase of the imputation errors caused by irrelevant features, which will affect the effect of the following feature extraction.Although the recently proposed method, TDVM,can perform tensor completion and feature extraction simultaneously, it does not consider the local structure of the data, which results the extracted features are still unsatisfactory.Therefore, in this paper, we propose a feature extraction method for incomplete tensors based on manifold learning and tensor decomposition: MLTD.Firstly, complete sample similarity matrix is obtained by utilizing ″partial distance″ and non-negative symmetric matrix factorization, and the adjacency graph can be given from the similarity matrix;Secondly, a feature extraction model based on manifold learning and tensor decomposition is established according to the adjacency graph, which incorporates variance maximization and local preserving projection into tensor decomposition.This model can directly extract effective features from the incomplete tensors, while preserving the local structure of the data.The comparative experiments have been conducted on four image datasets with five state-of-the-art methods.Experimental results show that the proposed method has significant advantages in performing both tensor completion and classification by extracted features.