论文标题
稀疏可分离的非负基质分解
Sparse Separable Nonnegative Matrix Factorization
论文作者
论文摘要
我们提出了一种非负矩阵分解（NMF）的新变体，结合了可分离性和稀疏性假设。可分离性要求第一个NMF因子的列等于输入矩阵的列，而稀疏性要求第二个NMF因子的列稀疏。我们称这种变体稀疏可分离的NMF（SSNMF），我们被证明是NP完整的，而不是可分离的NMF，可以在多项式时间内解决。考虑这种新模型的主要动机是处理不确定的盲源分离问题，例如多光谱图像Unbixing。我们基于连续的非阴性投影算法（SNPA，一种可分离NMF的有效算法）和确切的稀疏非负最小二乘求解器的算法来求解SSNMF。我们证明，在无噪声的环境和在温和的假设下，我们的算法恢复了真正的潜在来源。关于合成数据集的实验和多光谱图像的不混合，这说明了这一点。
We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity requires that the columns of the second NMF factor are sparse. We call this variant sparse separable NMF (SSNMF), which we prove to be NP-complete, as opposed to separable NMF which can be solved in polynomial time. The main motivation to consider this new model is to handle underdetermined blind source separation problems, such as multispectral image unmixing. We introduce an algorithm to solve SSNMF, based on the successive nonnegative projection algorithm (SNPA, an effective algorithm for separable NMF), and an exact sparse nonnegative least squares solver. We prove that, in noiseless settings and under mild assumptions, our algorithm recovers the true underlying sources. This is illustrated by experiments on synthetic data sets and the unmixing of a multispectral image.
