Clusterwise support vector linear regression
- Authors: Joki, Kaisa , Bagirov, Adil , Karmitsa, Napsu , Mäkelä, Marko , Taheri, Sona
- Date: 2020
- Type: Text , Journal article
- Relation: European Journal of Operational Research Vol. 287, no. 1 (2020), p. 19-35
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- Description: In clusterwise linear regression (CLR), the aim is to simultaneously partition data into a given number of clusters and to find regression coefficients for each cluster. In this paper, we propose a novel approach to model and solve the CLR problem. The main idea is to utilize the support vector machine (SVM) approach to model the CLR problem by using the SVM for regression to approximate each cluster. This new formulation of the CLR problem is represented as an unconstrained nonsmooth optimization problem, where we minimize a difference of two convex (DC) functions. To solve this problem, a method based on the combination of the incremental algorithm and the double bundle method for DC optimization is designed. Numerical experiments are performed to validate the reliability of the new formulation for CLR and the efficiency of the proposed method. The results show that the SVM approach is suitable for solving CLR problems, especially, when there are outliers in data. © 2020 Elsevier B.V.
- Description: Funding details: Academy of Finland, 289500, 294002, 319274 Funding details: Turun Yliopisto Funding details: Australian Research Council, ARC, (Project no. DP190100580 ).
Aggregate subgradient method for nonsmooth DC optimization
- Authors: Bagirov, Adil , Taheri, Sona , Joki, Kaisa , Karmitsa, Napsu , Mäkelä, Marko
- Date: 2021
- Type: Text , Journal article
- Relation: Optimization Letters Vol. 15, no. 1 (2021), p. 83-96
- Relation: http://purl.org/au-research/grants/arc/DP190100580
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- Description: The aggregate subgradient method is developed for solving unconstrained nonsmooth difference of convex (DC) optimization problems. The proposed method shares some similarities with both the subgradient and the bundle methods. Aggregate subgradients are defined as a convex combination of subgradients computed at null steps between two serious steps. At each iteration search directions are found using only two subgradients: the aggregate subgradient and a subgradient computed at the current null step. It is proved that the proposed method converges to a critical point of the DC optimization problem and also that the number of null steps between two serious steps is finite. The new method is tested using some academic test problems and compared with several other nonsmooth DC optimization solvers. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Nonsmooth optimization-based hyperparameter-free neural networks for large-scale regression
- Authors: Karmitsa, Napsu , Taheri, Sona , Joki, Kaisa , Paasivirta, Pauliina , Defterdarovic, J. , Bagirov, Adil , Mäkelä, Marko
- Date: 2023
- Type: Text , Journal article
- Relation: Algorithms Vol. 16, no. 9 (2023), p.
- Relation: http://purl.org/au-research/grants/arc/DP190100580
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- Description: In this paper, a new nonsmooth optimization-based algorithm for solving large-scale regression problems is introduced. The regression problem is modeled as fully-connected feedforward neural networks with one hidden layer, piecewise linear activation, and the (Formula presented.) -loss functions. A modified version of the limited memory bundle method is applied to minimize this nonsmooth objective. In addition, a novel constructive approach for automated determination of the proper number of hidden nodes is developed. Finally, large real-world data sets are used to evaluate the proposed algorithm and to compare it with some state-of-the-art neural network algorithms for regression. The results demonstrate the superiority of the proposed algorithm as a predictive tool in most data sets used in numerical experiments. © 2023 by the authors.