基于近邻图改进的块对角子空间聚类算法

块对角表示（BDR）模型可以通过利用线性表示对数据有效地进行聚类，却无法很好地利用高维数据常见的非线性流形结构信息。针对这一问题，提出了基于近邻图改进的块对角子空间聚类（BDRNG）算法来通过近邻图来线性拟合高维数据的局部几何结构，并通过块对角约束来生成具有全局信息的块对角结构。BDRNG同时学习全局信息以及局部数据结构，从而获得更好的聚类表现。由于模型包含近邻图算子和非凸的块对角表示范数，BDRNG 采用了交替最小化来优化求解算法。实验结果如下：在噪声数据集上，BDRNG能够生成稳定的块对角结构系数矩阵，这说明了BDRNG对于噪声数据具有鲁棒性；在标准数据集上，BDRNG的聚类表现均优于BDR，尤其在人脸数据集上，相较于BDR，BDRNG的聚类准确度提高了8%。

Improved block diagonal subspace clustering algorithm based on neighbor graph

Block Diagonal Representation(BDR)model can efficiently cluster data by using linear representation,but it cannot make good use of non-linear manifold information commonly appeared in high-dimensional data.To solve this problem,the improved Block Diagonal Representation based on Neighbor Graph(BDRNG)clustering algorithm was proposed to perform the linear fitting of the local geometric structure by the neighbor graph and generate the block-diagonal structure by using the block-diagonal regularization.In BDRNG algorithm,both global information and local data structure were learned at the same time to achieve a better clustering performance.Due to the fact that the model contains the neighbor graph and non-convex block-diagonal representation norm,the alternative minimization was adopted by BDRNG to optimize the solving algorithm.Experimental results show that:on the noise dataset,BDRNG can generate the stable coefficient matrix with block-diagonal form,which proves that BDRNG is robust to the noise data;on the standard datasets,BDRNG has better clustering performance than BDR,especially on the facial dataset,BDRNG has the clustering accuracy 8%higher than BDR.