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Forward Basis Selection for Pursuing Sparse Representations over a Dictionary
Dec. 2013 (vol. 35 no. 12)
pp. 3025-3036
Xiao-Tong Yuan, Sch. of Inf. & Control, Nanjing Univ. of Inf. Sci. & Technol., Nanjing, China
Shuicheng Yan, Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore
The forward greedy selection algorithm of Frank and Wolfe has recently been applied with success to coordinate-wise sparse learning problems, characterized by a tradeoff between sparsity and accuracy. In this paper, we generalize this method to the setup of pursuing sparse representations over a prefixed dictionary. Our proposed algorithm iteratively selects an atom from the dictionary and minimizes the objective function over the linear combinations of all the selected atoms. The rate of convergence of this greedy selection procedure is analyzed. Furthermore, we extend the algorithm to the setup of learning nonnegative and convex sparse representation over a dictionary. Applications of the proposed algorithms to sparse precision matrix estimation and low-rank subspace segmentation are investigated with efficiency and effectiveness validated on benchmark datasets.
Index Terms:
matrix algebra,convex programming,data analysis,greedy algorithms,image representation,image segmentation,iterative methods,learning (artificial intelligence),forward basis selection,subspace segmentation,high-dimensional data analysis,low-rank subspace segmentation,sparse precision matrix estimation,convex sparse representation setup,learning nonnegative setup,objective function minimization,pursuing sparse representations,coordinate-wise sparse learning problems,forward greedy selection algorithm,prefixed dictionary,Greedy algorithms,Sparse matrices,Gaussian processes,Dictionaries,subspace segmentation,Greedy selection,sparse representation,optimization,Gaussian graphical models
Citation:
Xiao-Tong Yuan, Shuicheng Yan, "Forward Basis Selection for Pursuing Sparse Representations over a Dictionary," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 12, pp. 3025-3036, Dec. 2013, doi:10.1109/TPAMI.2013.85
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