Convex Optimization
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Fast Optimization Methods for L1 Regularization: A Comparative Study and Two New Approaches
ECML '07 Proceedings of the 18th European conference on Machine Learning
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Efficient Online and Batch Learning Using Forward Backward Splitting
The Journal of Machine Learning Research
Bilevel visual words coding for image classification
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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L1-regularized least squares, with the ability of discovering sparse representations, is quite prevalent in the field of machine learning, statistics and signal processing. In this paper, we propose a novel algorithm called Dual Projected Newton Method (DPNM) to solve the l1-regularized least squares problem. In DPNM, we first derive a new dual problem as a box constrained quadratic programming. Then, a projected Newton method is utilized to solve the dual problem, achieving a quadratic convergence rate. Moreover, we propose to utilize some practical techniques, thus it greatly reduces the computational cost and makes DPNM more efficient. Experimental results on six real-world data sets indicate that DPNM is very efficient for solving the l1-regularized least squares problem, by comparing it with state of the art methods.