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Bruni V, Cardinali ML, Vitulano D. A Short Review on Minimum Description Length: An Application to Dimension Reduction in PCA. ENTROPY 2022; 24:e24020269. [PMID: 35205563 PMCID: PMC8871178 DOI: 10.3390/e24020269] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Revised: 01/31/2022] [Accepted: 02/10/2022] [Indexed: 02/01/2023]
Abstract
The minimun description length (MDL) is a powerful criterion for model selection that is gaining increasing interest from both theorists and practicioners. It allows for automatic selection of the best model for representing data without having a priori information about them. It simply uses both data and model complexity, selecting the model that provides the least coding length among a predefined set of models. In this paper, we briefly review the basic ideas underlying the MDL criterion and its applications in different fields, with particular reference to the dimension reduction problem. As an example, the role of MDL in the selection of the best principal components in the well known PCA is investigated.
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Affiliation(s)
- Vittoria Bruni
- Department of Basic and Applied Sciences for Engineering, Sapienza Rome University, Via Antonio Scarpa 16, 00161 Rome, Italy; (V.B.); (M.L.C.)
- Istituto per le Applicazioni del Calcolo, Via dei Taurini 19, 00185 Rome, Italy
| | - Maria Lucia Cardinali
- Department of Basic and Applied Sciences for Engineering, Sapienza Rome University, Via Antonio Scarpa 16, 00161 Rome, Italy; (V.B.); (M.L.C.)
| | - Domenico Vitulano
- Department of Basic and Applied Sciences for Engineering, Sapienza Rome University, Via Antonio Scarpa 16, 00161 Rome, Italy; (V.B.); (M.L.C.)
- Istituto per le Applicazioni del Calcolo, Via dei Taurini 19, 00185 Rome, Italy
- Correspondence:
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