Hyperspectral Unmixing Based on Clustered Multitask Networks
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Hyperspectral remote sensing is a prominent research topic in data processing. Most of the spectral unmixing algorithms are developed by adopting the linear mixing models. Nonnegative matrix factorization (NMF) and its developments are used widely for estimation of signatures and fractional abundances in the SU problem. Sparsity constraints was added to NMF, and was regularized by $ L_ {q} $ norm. In this paper, at first hyperspectral images are clustered by fuzzy c- means method, and then a new algorithm based on sparsity constrained distributed optimization is used for spectral unmixing. In the proposed algorithm, a network including clusters is employed. Each pixel in the hyperspectral images considered as a node in this network. The proposed algorithm is optimized with diffusion LMS strategy, and then the update equations for fractional abundance and signature matrices are obtained. Simulation results based on defined performance metrics illustrate advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods.Keywords:
Non-negative Matrix Factorization
Spectral signature
The non-negative matrix factorization (NMF) has been found an effective clustering algorithm and it outperforms the classical k-means algorithm. Existing researches mainly focus on the problem of reducing the decomposition error between two decomposition matrices and the original matrix. In this paper, inspired by the power k-means algorithm and the hierarchical alternating least square NMF, we propose a novel NMF algorithm called power NMF (PHALS-NMF), which introduces the power mean to reduce decomposition error. Massive experiments on several datasets show the feasibility and effectiveness of PHALS-NMF.
Non-negative Matrix Factorization
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Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role in solving this problem. In this article, we present a comprehensive survey of the NMF-based methods proposed for hyperspectral unmixing. Taking the NMF model as a baseline, we show how to improve NMF by utilizing the main properties of HSIs (e.g., spectral, spatial, and structural information). We categorize three important development directions including constrained NMF, structured NMF, and generalized NMF. Furthermore, several experiments are conducted to illustrate the effectiveness of associated algorithms. Finally, we conclude the article with possible future directions with the purposes of providing guidelines and inspiration to promote the development of hyperspectral unmixing.
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Detection of Brain Activity in Functional Magnetic Resonance Imaging Data using Matrix Factorization
Non-negative matrix factorization (NMF) is becoming a popular tool for decomposition of data in the field of signal and image processing like Independent Component Analysis (ICA). In this study we are relaxing the requirement of non-negative data for NMF making the update equations simple and thus making it Matrix Factorization (MF) and implementing it on simulated Functional Magnetic Resonance Imaging (fMRI) data for detection of neuronal activity. Simulated fMRI data is processed to detect the hidden sources of task related activity, functional activity and artifacts using the proposed MF technique. Performance of the proposed scheme is better than NMF in terms of average correlation results of the extracted sources/time courses with the actual sources/time courses. Similarly proposed MF is computationally cost effective and converges fast as compared to NMF. Also extracted sources obey no permutation which is the limitation of ICA and NMF.
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Hyperspectral unmixing is one of the most important techniques in remotely sensed image processing.Nonnegative matrix factorization(NMF) based hyper spectral unmixing has been developed in recent years.NMF based spectral mixture analysis assumes that the spectrum must have a constant spectral signature.However,spectral variability always exists in practical situations,which reduces the accuracy of mixed pixel decomposition.In order to solve the problem,the spectral data were translated by Fisher discriminant analysis(FDA),and then using the transformed hyperspectral data a new hyper spectral unmixing method is proposed by combining FDA with NMF.Experiments show that the proposed method can improve both accuracy and efficiency of mixed pixels decomposition.
Non-negative Matrix Factorization
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Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data. It was successfully applied to learn spectral features from EEG data. However, the size of a data matrix grows, NMF suffers from 'out of memory' problem. In this paper we present a memory-reduced method where we downsize the data matrix using CUR decomposition before NMF is applied. Experimental results with two EEG data sets in BCI competition, confirm the useful behavior of the proposed method.
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Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role to solve this problem. In this article, we present a comprehensive survey of the NMF-based methods proposed for hyperspectral unmixing. Taking the NMF model as a baseline, we show how to improve NMF by utilizing the main properties of HSIs (e.g., spectral, spatial, and structural information). We categorize three important development directions including constrained NMF, structured NMF, and generalized NMF. Furthermore, several experiments are conducted to illustrate the effectiveness of associated algorithms. Finally, we conclude the paper with possible future directions with the purposes of providing guidelines and inspiration to promote the development of hyperspectral unmixing.
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The effectiveness of non-negative matrix factorization (NMF) depends on a suitable choice of the number of bases, which is often difficult to decide in practice. This paper imposes sparseness on the factorization coefficients in order to determine the number of bases automatically during the decomposition process. The benefit of sparse promotion for NMF is demonstrated through application to sound source separation as well as acoustic-based human fall detection under strong interference.
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A novel approach using non-negative matrix factorization (NMF) for onset detection of musical notes from audio signals is presented. Unlike most commonly used conventional approaches, the proposed method exploits a new detection function constructed from the linear temporal bases that are obtained from a non-negative matrix decomposition of musical spectra. Both first-order difference and psychoacoustically motivated relative difference functions of the temporal profile are considered. As the approach works directly on input data, no prior knowledge or statistical information is thereby required. A practical issue of the choice of the factorization rank is also examined experimentally. Numerical examples are provided to show the performance of the proposed method.
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Hyperspectral image analysis has been an efficacious method utilized in remote sensing applications as it has the ability to discover richer information due to the presence of multiple spectral bands representing data, as opposed to the three bands in tri-color images. However, due to the dismal spatial resolution, a single pixel may comprise of a mixture of spectra belonging to multiple surface materials. Hyperspectral unmixing strives to extract the constituent spectra and their mixing percentages in each pixel. Independent Component Analysis (ICA) and Non-negative Matrix Factorization (NMF) are two prominent yet distinct methods used for hyperspectral unmixing. This paper proposes a novel method for hyperspectral unmixing, in which the fundamental notions of ICA are utilized to improve the accuracy of the standard NMF algorithm. This method was validated on standard and synthetic datasets and was observed to yield superior performance over the stand-alone implementations of ICA and NMF algorithms.
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Nonnegative Matrix Factorization (NMF) is a feature extraction method that has been also successfully applied to hyperspectral imaging. Several computational approaches have been proposed to improve NMF-based spectral unmixing. In this paper, we are concerned with several important issues related to the above application, i.e. which nonnegatively constrained algorithm is the most efficient for NMF-based hyperspectral unmixing, how to estimate the number of pure spectra, and how to accelerate the learning stage. The experiments demonstrate comparative studies, carried out for the hyperspectral images measured by the AVIRIS system.
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