This paper considers a problem of unsupervised spectral unmixing of hyperspectral data. Based on the Linear Mixing Model （ LMM）, a new method under the framework of nonnegative matrix fac- torization （NMF） is prop...This paper considers a problem of unsupervised spectral unmixing of hyperspectral data. Based on the Linear Mixing Model （ LMM）, a new method under the framework of nonnegative matrix fac- torization （NMF） is proposed, namely minimum distance constrained nonnegative matrix factoriza- tion （MDC-NMF）. In this paper, firstly, a new regularization term, called endmember distance （ED） is considered, which is defined as the sum of the squared Euclidean distances from each end- member to their geometric center. Compared with the simplex volume, ED has better optimization properties and is conceptually intuitive. Secondly, a projected gradient （PG） scheme is adopted, and by the virtue of ED, in this scheme the optimal step size along the feasible descent direction can be calculated easily at each iteration. Thirdly, a finite step （ no more than the number of endmem- bers） terminated algorithm is used to project a point on the canonical simplex, by which the abun- dance nonnegative constraint and abundance sum-to-one constraint can be accurately satisfied in a light amount of computation. The experimental results, based on a set of synthetic data and real da- ta, demonstrate that, in the same running time, MDC-NMF outperforms several other similar meth- ods proposed recently.展开更多
Hyperspectral imagery generally contains a very large amount of data due to hundreds of spectral bands.Band selection is often applied firstly to reduce computational cost and facilitate subsequent tasks such as land-...Hyperspectral imagery generally contains a very large amount of data due to hundreds of spectral bands.Band selection is often applied firstly to reduce computational cost and facilitate subsequent tasks such as land-cover classification and higher level image analysis.In this paper,we propose a new band selection algorithm using sparse nonnegative matrix factorization (sparse NMF).Though acting as a clustering method for band selection,sparse NMF need not consider the distance metric between different spectral bands,which is often the key step for most common clustering-based band selection methods.By imposing sparsity on the coefficient matrix,the bands' clustering assignments can be easily indicated through the largest entry in each column of the matrix.Experimental results showed that sparse NMF provides considerable insight into the clustering-based band selection problem and the selected bands are good for land-cover classification.展开更多
Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully...Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.展开更多
基金Supported by the National Natural Science Foundation of China （ No. 60872083 ） and the National High Technology Research and Development Program of China （No. 2007AA12Z149）.
文摘This paper considers a problem of unsupervised spectral unmixing of hyperspectral data. Based on the Linear Mixing Model （ LMM）, a new method under the framework of nonnegative matrix fac- torization （NMF） is proposed, namely minimum distance constrained nonnegative matrix factoriza- tion （MDC-NMF）. In this paper, firstly, a new regularization term, called endmember distance （ED） is considered, which is defined as the sum of the squared Euclidean distances from each end- member to their geometric center. Compared with the simplex volume, ED has better optimization properties and is conceptually intuitive. Secondly, a projected gradient （PG） scheme is adopted, and by the virtue of ED, in this scheme the optimal step size along the feasible descent direction can be calculated easily at each iteration. Thirdly, a finite step （ no more than the number of endmem- bers） terminated algorithm is used to project a point on the canonical simplex, by which the abun- dance nonnegative constraint and abundance sum-to-one constraint can be accurately satisfied in a light amount of computation. The experimental results, based on a set of synthetic data and real da- ta, demonstrate that, in the same running time, MDC-NMF outperforms several other similar meth- ods proposed recently.
基金Project (No.60872071) supported by the National Natural Science Foundation of China
文摘Hyperspectral imagery generally contains a very large amount of data due to hundreds of spectral bands.Band selection is often applied firstly to reduce computational cost and facilitate subsequent tasks such as land-cover classification and higher level image analysis.In this paper,we propose a new band selection algorithm using sparse nonnegative matrix factorization (sparse NMF).Though acting as a clustering method for band selection,sparse NMF need not consider the distance metric between different spectral bands,which is often the key step for most common clustering-based band selection methods.By imposing sparsity on the coefficient matrix,the bands' clustering assignments can be easily indicated through the largest entry in each column of the matrix.Experimental results showed that sparse NMF provides considerable insight into the clustering-based band selection problem and the selected bands are good for land-cover classification.
基金supported by the National Natural Science Foundation of China(Nos.11661141019 and 61621003)the National Ten Thousand Talent Program for Young Topnotch Talents+1 种基金Chinese Academy Science(CAS)Frontier Science Research Key Project for Top Young Scientist(No.QYZDB-SSW-SYS008)the Key Laboratory of Random Complex Structures and Data Science,CAS(No.2008DP173182).
文摘Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.
