基于子空间字典低秩表示的流形投影学习

Manifold Projection Learning via Low-Rank Representation with Subspace Dictionary

低秩表示(Low-Rank Representation,LRR)能够将每个数据点表示为若干个基的线性组合,是一种获取样本底层低维结构的方法。然而,大多数LRR方法使用原始数据集作为字典,这不能揭示数据的真实分割。本文提出了基于子空间字典低秩表示的流形投影学习:该方法学习最优子空间作为LRR问题的字典,而不是使用原始数据集;利用基数最少的方案,低秩表示矩阵能很好地恢复原始数据;通过对投影矩阵施加行稀疏约束,该方法不仅可以选择鉴别性特征并忽略冗余特征,而且使子空间学习具有很好的解释性。此外,通过引入流形结构保持约束,使得样本的原始表示和距离信息在投影下保持不变。在多个真实世界数据集上的实验结果表明,该方法优于最近提出的一些相关方法。

Low-Rank Representation(LRR)allows for the representation of each data point as a linear combination of bases,making it a promising approach for capturing underlying low-dimensional structures.However,most LRR methods use the original dataset as a dictionary,which cannot reveal the true segmentation of the data.In this paper,we propose an unsupervised projection learning method,called Manifold Projection Learning via Low-Rank Representation with Subspace Dictionary(MPL-LRRSD).MPL-LRRSD learns an optimal subspace as the dictionary for the LRR problem instead of using the original dataset.The original data can be well recovered by low-rank matrix using minimal bases.Meanwhile,by imposing row sparse constraint on the projection matrix,MPL-LRRSD not only selects discriminative features and eliminates the redundant features,but also makes the subspace learning well interpretable.Furthermore,we introduce manifold structure preserving constraint to preserve both original representation and distance information of the samples under projection.Extensive experiment results on various real-world datasets demonstrate the superiority over the state-of-the-art methods.