Nonsmooth optimization-based model and algorithm for semisupervised clustering
- Authors: Bagirov, Adil , Taheri, Sona , Bai, Fusheng , Zheng, Fangying
- Date: 2023
- Type: Text , Journal article
- Relation: IEEE Transactions on Neural Networks and Learning Systems Vol. 34, no. 9 (2023), p. 5517-5530
- Relation: http://purl.org/au-research/grants/arc/DP190100580
- Full Text: false
- Reviewed:
- Description: Using a nonconvex nonsmooth optimization approach, we introduce a model for semisupervised clustering (SSC) with pairwise constraints. In this model, the objective function is represented as a sum of three terms: the first term reflects the clustering error for unlabeled data points, the second term expresses the error for data points with must-link (ML) constraints, and the third term represents the error for data points with cannot-link (CL) constraints. This function is nonconvex and nonsmooth. To find its optimal solutions, we introduce an adaptive SSC (A-SSC) algorithm. This algorithm is based on the combination of the nonsmooth optimization method and an incremental approach, which involves the auxiliary SSC problem. The algorithm constructs clusters incrementally starting from one cluster and gradually adding one cluster center at each iteration. The solutions to the auxiliary SSC problem are utilized as starting points for solving the nonconvex SSC problem. The discrete gradient method (DGM) of nonsmooth optimization is applied to solve the underlying nonsmooth optimization problems. This method does not require subgradient evaluations and uses only function values. The performance of the A-SSC algorithm is evaluated and compared with four benchmarking SSC algorithms on one synthetic and 12 real-world datasets. Results demonstrate that the proposed algorithm outperforms the other four algorithms in identifying compact and well-separated clusters while satisfying most constraints. © 2021 IEEE.
Robust piecewise linear L 1-regression via nonsmooth DC optimization
- Authors: Bagirov, Adil , Taheri, Sona , Karmitsa, Napsu , Sultanova, Nargiz , Asadi, Soodabeh
- Date: 2022
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 37, no. 4 (2022), p. 1289-1309
- Relation: http://purl.org/au-research/grants/arc/DP190100580
- Full Text: false
- Reviewed:
- Description: Piecewise linear (Formula presented.) -regression problem is formulated as an unconstrained difference of convex (DC) optimization problem and an algorithm for solving this problem is developed. Auxiliary problems are introduced to design an adaptive approach to generate a suitable piecewise linear regression model and starting points for solving the underlying DC optimization problems. The performance of the proposed algorithm as both approximation and prediction tool is evaluated using synthetic and real-world data sets containing outliers. It is also compared with mainstream machine learning regression algorithms using various performance measures. Results demonstrate that the new algorithm is robust to outliers and in general, provides better predictions than the other alternative regression algorithms for most data sets used in the numerical experiments. © 2020 Informa UK Limited, trading as Taylor & Francis Group.