Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the pairwise constraints from the local perspective, i.e., they either directly refine the similarity matrix element-wisely or restrain the distance of the decomposed vectors in pairs according to the pairwise constraints, which overlook the global perspective, i.e., in the ideal case, the pairwise constraint matrix and the ideal similarity matrix possess the same low-rank structure. To this end, we first propose a novel semi-supervised SNMF model by seeking low-rank representation for the tensor synthesized by the pairwise constraint matrix and a similarity matrix obtained by the product of the embedding matrix and its transpose, which could strengthen those two matrices simultaneously from a global perspective. We then propose an enhanced SNMF model, making the embedding matrix tailored to the above tensor low-rank representation. We finally refine the similarity matrix by the strengthened pairwise constraints. We repeat the above steps to continuously boost the similarity matrix and pairwise constraint matrix, leading to a high-quality embedding matrix. Extensive experiments substantiate the superiority of our method. The code is available at https://github.com/JinaLeejnl/TSNMF.

我们提出了一种新的半监督对称非负矩阵分解模型，通过为通过对称约束矩阵和嵌入矩阵转置的乘积得到的相似度矩阵合成的张量寻找低秩表示，同时从全局角度加强这两个矩阵，然后通过增强的SNMF模型使嵌入矩阵适应此张量低秩表示，最终通过强化的相似约束来改进相似度矩阵，重复上述步骤进一步提升相似度矩阵和约束矩阵，从而得到高质量的嵌入矩阵。我们的方法在大量实验证明了其优越性。

低秩张量表示的半监督对称矩阵分解