Abstract
Adaptive Lasso preserves oracle properties comparing to classical Lasso. It performs as well as if the true underlying model is provided in advance. In order to let feature subset selected by Adaptive Lasso preserve more local information, which is discriminative and benefit for classification, Manifold-regularized Adaptive Lasso (MrALasso) is proposed for feature selection. Reconstructing response by linear sum of features is considered in manifold embedded in high-dimensional space. A similarity graph of data points is built. Connected points are restricted to stay together as close as possible so that the intrinsic geometry of the data and the local structure are preserved. An effective iterative algorithm, with detailed proof of convergence, is proposed to solve the optimization problem. Experimental results of feature selection on several classical gene datasets show the effectiveness and superiority of the proposed method.
B. Luo—This work was supported in part by National Natural Science Foundation of China under Grant 61472002, 61572030 and 61671018, and Collegiate Natural Science Fund of Anhui Province under Grant KJ2017A014.
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Chen, SB., Zhang, YM., Luo, B. (2018). Manifold-Regularized Adaptive Lasso. In: Ren, J., et al. Advances in Brain Inspired Cognitive Systems. BICS 2018. Lecture Notes in Computer Science(), vol 10989. Springer, Cham. https://doi.org/10.1007/978-3-030-00563-4_53
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