A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted ℓ0-norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed to approximate the ℓ0-norm. The convergence of the global minimum points of the approximating problems towards global minimum points of the original problem is stated. The proposed method also exploits a suitable technique to choose the penalty parameter. Numerical results on synthetic and real data sets are finally provided, showing how some existing clustering methods can take advantages from the proposed filtering strategy.

Cristofari, A. (2017). Data filtering for cluster analysis by ℓ0-norm regularization. OPTIMIZATION LETTERS, 11(8), 1527-1546 [10.1007/s11590-017-1152-7].

Data filtering for cluster analysis by ℓ0-norm regularization

Andrea Cristofari
2017-01-01

Abstract

A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted ℓ0-norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed to approximate the ℓ0-norm. The convergence of the global minimum points of the approximating problems towards global minimum points of the original problem is stated. The proposed method also exploits a suitable technique to choose the penalty parameter. Numerical results on synthetic and real data sets are finally provided, showing how some existing clustering methods can take advantages from the proposed filtering strategy.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/09 - RICERCA OPERATIVA
English
Zero-norm approximation
Cluster analysis
Nonlinear optimization
https://link.springer.com/article/10.1007/s11590-017-1152-7
Cristofari, A. (2017). Data filtering for cluster analysis by ℓ0-norm regularization. OPTIMIZATION LETTERS, 11(8), 1527-1546 [10.1007/s11590-017-1152-7].
Cristofari, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/312406
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