基于张量的稀疏保持投影降维方法

传统的基于向量的降维算法需要将图像数据进行向量化处理。然而，向量表示难以考虑数据各维度上的变化，容易丢失有效的结构信息和判别信息。为此，从数据的张量表示出发，将新近提出的稀疏保持投影方法（sparsity preserving projections，SPP）推广到张量空间中，提出了基于张量的稀疏保持投影降维方法。该方法可直接将图像数据作为张量目标进行运算，保留了数据的完整性以及数据的原始结构和判别信息。降维的同时保持了原始张量空间中数据样本的稀疏重构信息。人脸数据库的识别实验结果表明，基于张量的稀疏保持投影降维方法能有效地提高识别率。

A novel dimensionality reduction method based on tensor and sparsity preserving projections

The traditional vector-based dimensionality reduction algorithms require to reshape,the image data into vectors. However, it is well understood that reshaping breaks the natural structure and correlation of the original data, and is likely to lose poten- tially more compact or useful representations. This paper extends the sparsity preserving projections （SPP） method to the tensor space, and presents the tensor sparsity preserving projections method. This method regards the image data as a tensor object, which reserves the original structure, discriminating information, and the integrity of data. During the dimensionality reduction process, it preserves the sparse reconstructive relationship of the data in tensor space. The feasibility and effectiveness of the proposed method have been verified by the recognition experiment on two popular face databases.