### Mathematical Biosciences and Engineering

2021, Issue 6: 7727-7742. doi: 10.3934/mbe.2021383
Research article Special Issues

# $\ell_{1}$-norm based safe semi-supervised learning

• Received: 04 June 2021 Accepted: 02 September 2021 Published: 07 September 2021
• In the past few years, Safe Semi-Supervised Learning (S3L) has received considerable attentions in machine learning field. Different researchers have proposed many S3L methods for safe exploitation of risky unlabeled samples which result in performance degradation of Semi-Supervised Learning (SSL). Nevertheless, there exist some shortcomings: (1) Risk degrees of the unlabeled samples are in advance defined by analyzing prediction differences between Supervised Learning (SL) and SSL; (2) Negative impacts of labeled samples on learning performance are not investigated. Therefore, it is essential to design a novel method to adaptively estimate importance and risk of both unlabeled and labeled samples. For this purpose, we present $\ell_{1}$-norm based S3L which can simultaneously reach the safe exploitation of the labeled and unlabeled samples in this paper. In order to solve the proposed ptimization problem, we utilize an effective iterative approach. In each iteration, one can adaptively estimate the weights of both labeled and unlabeled samples. The weights can reflect the importance or risk of the labeled and unlabeled samples. Hence, the negative effects of the labeled and unlabeled samples are expected to be reduced. Experimental performance on different datasets verifies that the proposed S3L method can obtain comparable performance with the existing SL, SSL and S3L methods and achieve the expected goal.

Citation: Haitao Gan, Zhi Yang, Ji Wang, Bing Li. $\ell_{1}$-norm based safe semi-supervised learning[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 7727-7742. doi: 10.3934/mbe.2021383

### Related Papers:

• In the past few years, Safe Semi-Supervised Learning (S3L) has received considerable attentions in machine learning field. Different researchers have proposed many S3L methods for safe exploitation of risky unlabeled samples which result in performance degradation of Semi-Supervised Learning (SSL). Nevertheless, there exist some shortcomings: (1) Risk degrees of the unlabeled samples are in advance defined by analyzing prediction differences between Supervised Learning (SL) and SSL; (2) Negative impacts of labeled samples on learning performance are not investigated. Therefore, it is essential to design a novel method to adaptively estimate importance and risk of both unlabeled and labeled samples. For this purpose, we present $\ell_{1}$-norm based S3L which can simultaneously reach the safe exploitation of the labeled and unlabeled samples in this paper. In order to solve the proposed ptimization problem, we utilize an effective iterative approach. In each iteration, one can adaptively estimate the weights of both labeled and unlabeled samples. The weights can reflect the importance or risk of the labeled and unlabeled samples. Hence, the negative effects of the labeled and unlabeled samples are expected to be reduced. Experimental performance on different datasets verifies that the proposed S3L method can obtain comparable performance with the existing SL, SSL and S3L methods and achieve the expected goal.

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• © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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