对称局部保持的半监督维数约简算法

A Symmetric Locally-Preserving Semi-Supervised Dimensionality Reduction Algorithm

针对自然界较多图像具有对称的特点以及数据分布大多呈一定的流形结构情况,提出了一种对称局部保持的半监督维数约减(SLPSDR)算法.该算法使用矩阵定义维数约减映射矩阵元素之间的关系,使图像中对称的像素点对应的映射矩阵的值之间的差别最小;同时为了利用无标签训练样本保持数据的流形结构,要求低维空间中每个点的邻域关系与高维空间中的邻域关系相似.在CMU PIE、Extend Yale B、ORL、AR人脸数据库上的实验结果表明,图像数据明显的对称特点使得SLPSDR算法优于其他对比的维数约减算法.

As many natural images are symmetrical and most of data distributions exhibit a manifold structure, a symmetric locally-preserving semi-supervised dimensionality reduction （ SLPSDR） algorithm is proposed. In the algorithm, a matrix is used to define the relationship between dimensionality reduction mapping matrix elements, so as to minimize the difference between the matrix elements of symmetric pixel points in an image. In order to keep the manifold structure of data by using the training samples without a label, it is required that the neighborhood relationship of each point in a low-dimension space is similar to that in a high-dimension space. The experimental results on CMU PIE, Extend YaleB, ORL and AR face databases show that the symmetric feature of image data causes the SLPSDR algorithm to be superior to other contrastive dimensionality reduction algorithms.