Incremental DC optimization algorithm for large-scale clusterwise linear regression
- Authors: Bagirov, Adil , Taheri, Sona , Cimen, Emre
- Date: 2021
- Type: Text , Journal article
- Relation: Journal of Computational and Applied Mathematics Vol. 389, no. (2021), p. 1-17
- Relation: https://purl.org/au-research/grants/arc/DP190100580
- Full Text: false
- Reviewed:
- Description: The objective function in the nonsmooth optimization model of the clusterwise linear regression (CLR) problem with the squared regression error is represented as a difference of two convex functions. Then using the difference of convex algorithm (DCA) approach the CLR problem is replaced by the sequence of smooth unconstrained optimization subproblems. A new algorithm based on the DCA and the incremental approach is designed to solve the CLR problem. We apply the Quasi-Newton method to solve the subproblems. The proposed algorithm is evaluated using several synthetic and real-world data sets for regression and compared with other algorithms for CLR. Results demonstrate that the DCA based algorithm is efficient for solving CLR problems with the large number of data points and in particular, outperforms other algorithms when the number of input variables is small. © 2020 Elsevier B.V.
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
- Full Text: false
- Reviewed:
- 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.