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A novel heuristic algorithm to solve penalized regression-based clustering model

  • Shadi Hasanzadeh Tavakkoli
  • Yahya ForghaniEmail author
  • Reza Sheibani
Methodologies and Application
  • 5 Downloads

Abstract

Penalized regression-based clustering model (PRClust) is an extension of “sum-of-norms” clustering model. Three previously proposed heuristic algorithms for solving PRClust are: (1) DC-CD, which combines the difference of convex programming (DC) and a coordinate-wise descent algorithm (CD), (2) DC-ADMM, which combines DC with the alternating direction method of multipliers (ADMM), and (3) ALT, which uses alternate optimization. DC-CD uses \( p \times \left( {n \times \left( {n - 1} \right)} \right)/2 \) scalar slack variables to solve PRClust, where n is the number of data and p is the number of their features. In each iteration of DC-CD, these slack variables and cluster centers are updated using a second-order cone programming (SOCP). DC-ADMM uses \( p \times n \times \left( {n - 1} \right) \) scalar slack variables. In each iteration of DC-ADMM, these slack variables and cluster centers are updated with a standard ADMM. In this paper, first, PRClust is reformulated into an equivalent model. Then, a novel heuristic algorithm is proposed to solve the reformulated model. Our proposed algorithm needs only \( \left( {n \times \left( {n - 1} \right)} \right)/2 \) scalar slack variables which are much less than those of DC-CD and DC-ADMM, and updates them using a simple equation in each iteration of the algorithm. Therefore, updating slack variables in our proposed algorithm is less time-consuming than that of DC-CD and DC-ADMM. Our proposed algorithm updates only cluster centers using an unconstrained convex quadratic problem. Therefore, our proposed unconstrained convex quadratic problem is much smaller than the SOCP of DC-CD which is used to update both cluster centers and slack variables. Meanwhile, ALT updates cluster centers using a SOCP, while our proposed algorithm updates cluster centers using an unconstrained convex quadratic problem with the same number of variables. Solving an unconstrained convex quadratic problem is less time-consuming than a SOCP with the same number of variables. Our experimental results on 12 datasets confirm that the runtime of our proposed algorithm is better than that of DC-ADMM and DC-CD.

Keywords

“Sum-of-norms” (SON) clustering Penalized regression-based clustering (PRClust) DC-CD DC-ADMM 

Notes

Compliance with ethical standards

Conflict of interest

Zohreh Zendehdel declares that she has no conflict of interest. Yahya Forghani declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Islamic Azad UniversityMashhadIran

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