In nonnegative matrix factorization (NMF), minimum-volume-constrained NMF is a widely used framework for identifying the solution of NMF by making basis vectors as similar as possible. This typically induces sparsity in the coefficient matrix, with each row containing zero entries. Consequently, minimum-volume-constrained NMF may fail for highly mixed data, where such sparsity does not hold. Moreover, the estimated basis vectors in minimum-volume-constrained NMF may be difficult to interpret as they may be mixtures of the ground truth basis vectors. To address these limitations, in this paper we propose a new NMF framework, called maximum-volume-constrained NMF, which makes the basis vectors as distinct as possible. We further establish an identifiability theorem for maximum-volume-constrained NMF and provide an algorithm to estimate it. Experimental results demonstrate the effectiveness of the proposed method.

翻译：在非负矩阵分解（NMF）中，最小体积约束的NMF是一种广泛使用的框架，通过使基向量尽可能相似来辨识NMF的解。这通常会导致系数矩阵具有稀疏性，其中每行包含零元素。因此，最小体积约束的NMF可能无法处理高度混合的数据，因为此类数据不满足这种稀疏性。此外，最小体积约束NMF中估计的基向量可能难以解释，因为它们可能是真实基向量的混合。针对这些局限，本文提出了一种新的NMF框架——最大体积约束NMF，该框架使基向量尽可能不同。我们进一步建立了最大体积约束NMF的可辨识性定理，并给出了一种估计算法。实验结果验证了所提方法的有效性。