Sparse group lasso and high dimensional multinomial classification |
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| Affiliation: | 1. School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China;2. Key Laboratory of Marine Environmental Monitoring and Information Processing, Ministry of Industry and Information Technology, Harbin 150001, China;3. School of Information and Electronical Engineering, Harbin Institute of Technology (Weihai), Weihai 264209, China;1. Department of Mathematics, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran;2. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen East, Denmark |
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| Abstract: | The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is used to investigate the performance of the multinomial sparse group lasso classifier. On three different real data examples the multinomial group lasso clearly outperforms multinomial lasso in terms of achieved classification error rate and in terms of including fewer features for the classification. An implementation of the multinomial sparse group lasso algorithm is available in the R package msgl. Its performance scales well with the problem size as illustrated by one of the examples considered—a 50 class classification problem with 10 k features, which amounts to estimating 500 k parameters. |
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| Keywords: | Sparse group lasso Classification High dimensional data analysis Coordinate gradient descent Penalized loss |
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