Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direc...Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direction method of multipliers and hierarchical alternating least squares method.When the given matrix is huge,the cost of computation and communication is too high.Therefore,ONMF becomes challenging in the large-scale setting.The random projection is an efficient method of dimensionality reduction.In this paper,we apply the random projection to ONMF and propose two randomized algorithms.Numerical experiments show that our proposed algorithms perform well on both simulated and real data.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
Non-negative matrix factorization(NMF)is a recently popularized technique for learning partsbased,linear representations of non-negative data.The traditional NMF is optimized under the Gaussian noise or Poisson noise ...Non-negative matrix factorization(NMF)is a recently popularized technique for learning partsbased,linear representations of non-negative data.The traditional NMF is optimized under the Gaussian noise or Poisson noise assumption,and hence not suitable if the data are grossly corrupted.To improve the robustness of NMF,a novel algorithm named robust nonnegative matrix factorization(RNMF)is proposed in this paper.We assume that some entries of the data matrix may be arbitrarily corrupted,but the corruption is sparse.RNMF decomposes the non-negative data matrix as the summation of one sparse error matrix and the product of two non-negative matrices.An efficient iterative approach is developed to solve the optimization problem of RNMF.We present experimental results on two face databases to verify the effectiveness of the proposed method.展开更多
基金the National Natural Science Foundation of China(No.11901359)Shandong Provincial Natural Science Foundation(No.ZR2019QA017)。
文摘Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direction method of multipliers and hierarchical alternating least squares method.When the given matrix is huge,the cost of computation and communication is too high.Therefore,ONMF becomes challenging in the large-scale setting.The random projection is an efficient method of dimensionality reduction.In this paper,we apply the random projection to ONMF and propose two randomized algorithms.Numerical experiments show that our proposed algorithms perform well on both simulated and real data.
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.
基金This work was supported by the Scholarship Award for Excellent Doctoral Student granted by Ministry of Education,and the National Natural Science Foundation of China(Grant No.60875044)。
文摘Non-negative matrix factorization(NMF)is a recently popularized technique for learning partsbased,linear representations of non-negative data.The traditional NMF is optimized under the Gaussian noise or Poisson noise assumption,and hence not suitable if the data are grossly corrupted.To improve the robustness of NMF,a novel algorithm named robust nonnegative matrix factorization(RNMF)is proposed in this paper.We assume that some entries of the data matrix may be arbitrarily corrupted,but the corruption is sparse.RNMF decomposes the non-negative data matrix as the summation of one sparse error matrix and the product of two non-negative matrices.An efficient iterative approach is developed to solve the optimization problem of RNMF.We present experimental results on two face databases to verify the effectiveness of the proposed method.
