Unsupervised spectral mixture analysis of highly mixed data with hopfield neural network

Hopfield Neural Network (HNN) has been demonstrated to be an effective tool for Spectral Mixture Analysis (SMA). However, the spectrum of pure ground objects, known as endmember, must be known previously. In this paper, the HNN is utilized to solve unsupervised SMA, in which Endmember Extraction (EE) and Abundance Estimation (AE) are performed iteratively. Two different HNNs are constructed to solve such multiplicative updating procedure, respectively. The proposed HNN based unsupervised SMA framework is then applied to solve three second-order constrained Nonnegative Matrix Factorization (NMF) models for SMA, including Minimum Distance Constrained NMF (MDC-NMF), Minimum endmember-wise Distance Constrained NMF (MewDC-NMF), and Minimum Dispersion Constrained NMF (MiniDisCo-NMF). As a result, our proposed HNN based algorithms are able to perform unsupervised SMA and extract virtual endmembers without assuming the presence of spectrally pure constituents in highly mixed hyperspectral data. Experimental results on both synthetic and real hyperspectral images demonstrate that our proposed HNN based algorithms clearly outperform traditional Projected Gradient (PG) based solutions for these constrained NMF based SMA.