*Article* **Nonnegative Matrix Factorization With Data-Guided Constraints For Hyperspectral Unmixing**

**Risheng Huang 1, Xiaorun Li 1 and Liaoying Zhao 2,\***


Received: 7 August 2017 ; Accepted: 18 October 2017; Published: 21 October 2017

**Abstract:** Hyperspectral unmixing aims to estimate a set of endmembers and corresponding abundances in pixels. Nonnegative matrix factorization (NMF) and its extensions with various constraints have been widely applied to hyperspectral unmixing. *<sup>L</sup>*1/2 and *L*2 regularizers can be added to NMF to enforce sparseness and evenness, respectively. In practice, a region in a hyperspectral image may possess different sparsity levels across locations. The problem remains as to how to impose constraints accordingly when the level of sparsity varies. We propose a novel nonnegative matrix factorization with data-guided constraints (DGC-NMF). The DGC-NMF imposes on the unknown abundance vector of each pixel with either an *<sup>L</sup>*1/2 constraint or an *L*2 constraint according to its estimated mixture level. Experiments on the synthetic data and real hyperspectral data validate the proposed algorithm.

**Keywords:** nonnegative matrix factorization; data-guided constraints; sparseness; evenness
