基于有效距离的低秩表示

低秩表示（Low-Rank Representation，LRR）在探索数据中的低维子空间结构方面具有良好的效果，近年来引起了人们的广泛关注。然而，传统的LRR方法通常使用欧氏距离来度量样本的相似性，仅考虑相邻样本两两之间的距离信息，对于具有流形结构的数据往往不能反映其固有的几何结构。最近的研究表明，概率激励距离测量（即有效距离）可以有效地对数据的全局信息进行建模，来度量样本间的相似性。在此基础上，提出了一种基于有效距离的低秩表示模型。该方法用稀疏表示方法计算样本之间的有效距离来构造拉普拉斯矩阵，并将其进行低秩表示拉普拉斯正则化约束，该模型不仅能表示全局低维结构，而且能捕获流形结构数据中的几何结构信息。为了评估方法的有效性，在三个公开数据集上进行了分类实验。实验结果表明，该方法比基于传统欧氏距离的方法，具有更高的分类性能和更强的鲁棒性。

Effective Distance Based Low-Rank Representation

Low-Rank Representation（LRR） has recently attracted a great deal of attention due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. However, conventional LRR-based methods simply use Euclidean distance to measure the similarity of samples, where cannot reflect the inherent geometric structure of data with manifold structure. Meanwhile, recent studies have shown that a probabilistically motivated distance measurement（called effective distance） can effectively model the global information of data to measure the similarity between samples. To this end, this paper proposes an Effective Distance Based Low-Rank Representation（EDLRR） model, which firstly uses the sparse representation method to calculate the effective distance between samples for constructing a Laplacian matrix, and then develops a Laplacian regularized low-rank representation term. Low rank representation model. This method can not only represent the global low-dimensional structure, but also capture the geometric structure information in the data of the manifold structure. To evaluate the effectiveness of the proposed method, this paper conducts classification experiments by using three public datasets. Experimental results show that the proposed EDLRR method has higher classification performance and stronger robustness than the traditional Euclidean distance based methods.