论文标题
与稀疏性约束的正交非负矩阵分解
Orthogonal Nonnegative Matrix Factorization with Sparsity Constraints
论文作者
论文摘要
本文提出了一种新的方法，可以解决稀疏性受限的正交非负矩阵分解（SCONMF）问题，该问题需要将非负数据矩阵分解为两个低级别非级矩阵的产物，x = wh，x = wh，在其中混合矩阵H具有正通的元素，同时又符合正式的元素。 排。通过将SCONMF重新定义为容量约束的设施解决问题（CCFLP），该方法自然会整合非负，正交性和稀疏性约束。具体而言，我们的方法集成了用于动态最佳控制设计问题的基于控制式屏障功能（CBF）的框架，该框架与最大透镜基本的框架用于设施位置问题，以实施这些约束，同时确保可靠的分解。此外，这项工作还引入了一种定量方法，用于确定``w或h的true''等级，相当于``true''特征的数量 - ``true''特征的数量 - 在特征数量未知的ONMF应用程序中的关键方面。各种数据集上的模拟表明，重建误差较低（高达150次），同时严格满足所有约束，超出了对所有约束的影响，从而显着改善了因素化，这表现优于现有的方法，这些方法在平衡准确性和约束依从性方面遇到了困难。
This article presents a novel approach to solving the sparsity-constrained Orthogonal Nonnegative Matrix Factorization (SCONMF) problem, which requires decomposing a non-negative data matrix into the product of two lower-rank non-negative matrices, X=WH, where the mixing matrix H has orthogonal rows HH^T=I, while also satisfying an upper bound on the number of nonzero elements in each row. By reformulating SCONMF as a capacity-constrained facility-location problem (CCFLP), the proposed method naturally integrates non-negativity, orthogonality, and sparsity constraints. Specifically, our approach integrates control-barrier function (CBF) based framework used for dynamic optimal control design problems with maximum-entropy-principle-based framework used for facility location problems to enforce these constraints while ensuring robust factorization. Additionally, this work introduces a quantitative approach for determining the ``true" rank of W or H, equivalent to the number of ``true" features - a critical aspect in ONMF applications where the number of features is unknown. Simulations on various datasets demonstrate significantly improved factorizations with low reconstruction errors (as small as by 150 times) while strictly satisfying all constraints, outperforming existing methods that struggle with balancing accuracy and constraint adherence.
