Abstract A novel optimization framework for joint unsupervised clustering and kernel learning is derived. Sparse nonnegative matrix factorization of kernel covariance matrices is utilized to categorize data according to their information content. It is demonstrated that a pertinent kernel covariance matrix for clustering can be constructed such that it is block diagonal within arbitrary row and column permutations, while each diagonal block has rank one. To achieve this, a linear combination of a dictionary of kernels is sought such that it has rank equal to the number of clusters while a certain kernel eigenvalue is maximized by a novel difference of convex functions formulation. We establish that the proposed algorithm converges to a stationary solution. Numerical tests with different datasets demonstrate the effectiveness of the proposed scheme whose performance is very close to supervised methods, and performs better than unsupervised alternatives without the need of painstaking parameter tuning.

中文翻译：

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关于无监督同步内核学习和数据聚类

摘要 推导出了一种用于联合无监督聚类和核学习的新优化框架。核协方差矩阵的稀疏非负矩阵分解用于根据数据的信息内容对数据进行分类。证明可以构造用于聚类的相关核协方差矩阵，使其在任意行和列排列中是块对角线，而每个对角线块的秩为 1。为了实现这一点，寻求内核字典的线性组合，使得它的秩等于集群的数量，而某个内核特征值通过凸函数公式的新差异最大化。我们确定所提出的算法收敛到一个平稳的解决方案。