基于图正则化的加权低秩表示算法研究

Weighted low-rank representation algorithm based on graph regularization

低秩表示的目的是从整体上使得输入数据集的系数矩阵是低秩矩阵,但是它忽略数据集内部样本之间的关系,文中提出基于图正则化的低秩表示算法。在对传统低秩表示算法的求解中,通常是采用求解标准核范数的方式来近似矩阵的秩。标准核范数是计算矩阵的奇异值之和,然而矩阵的秩是计算非零奇异值的个数。因此,计算加权后的奇异值之和会更加接近矩阵的秩,进而文中提出基于图正则化的加权低秩表示模型。实验使用的是公开手写数字数据集,实验结果显示文中算法的聚类效果比低秩表示的提高了7.82%。

The low-rank representation is to make the coefficient matrix of the input data set as a low rank matrix as a whole, but it ignores the relationship between the samples in the data set. A low-rank repre- sentation algorithm based on the graph regularization is proposed. In the solution of the traditional low- rank representation algorithm, the value of the standard nuclear norm is usually taken to approximate the rank of the matrix. The standard nuclear norm is the sum of the singular values of the matrix, but the rank of the matrix is the number of nonzero singular values. Therefore, the sum of the singular values af- ter weighting is closer to the rank of the matrix, and then the weighted low-rank representation algorithm based on the graph normalization is proposed. A public handwritten digital data set is used in the experi- ment. Experimental results show that the algorithm is 7.82% higher than the low-rank representation.