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 ).
New diagonal bundle method for clustering problems in large data sets
- Authors: Karmitsa, Napsu , Bagirov, Adil , Taheri, Sona
- Date: 2017
- Type: Text , Journal article
- Relation: European Journal of Operational Research Vol. 263, no. 2 (2017), p. 367-379
- Relation: http://purl.org/au-research/grants/arc/DP140103213
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- Description: Clustering is one of the most important tasks in data mining. Recent developments in computer hardware allow us to store in random access memory (RAM) and repeatedly read data sets with hundreds of thousands and even millions of data points. This makes it possible to use conventional clustering algorithms in such data sets. However, these algorithms may need prohibitively large computational time and fail to produce accurate solutions. Therefore, it is important to develop clustering algorithms which are accurate and can provide real time clustering in large data sets. This paper introduces one of them. Using nonsmooth optimization formulation of the clustering problem the objective function is represented as a difference of two convex (DC) functions. Then a new diagonal bundle algorithm that explicitly uses this structure is designed and combined with an incremental approach to solve this problem. The method is evaluated using real world data sets with both large number of attributes and large number of data points. The proposed method is compared with two other clustering algorithms using numerical results. © 2017 Elsevier B.V.