Ultrametric fitting by gradient descent
| Autor: | Giovanni Chierchia, Benjamin Perret |
|---|---|
| Přispěvatelé: | Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences Mathematical optimization Computer Science - Machine Learning Computer science Context (language use) Machine Learning (stat.ML) 0102 computer and information sciences 02 engineering and technology 01 natural sciences Regularization (mathematics) Machine Learning (cs.LG) [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] Statistics - Machine Learning 0202 electrical engineering electronic engineering information engineering Leverage (statistics) Ultrametric space ComputingMilieux_MISCELLANEOUS Statistical and Nonlinear Physics Function (mathematics) Hierarchical clustering 010201 computation theory & mathematics Graph (abstract data type) 020201 artificial intelligence & image processing [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Statistics Probability and Uncertainty Gradient descent |
| Zdroj: | Journal of Statistical Mechanics: Theory and Experiment Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2020, 2020 (12), pp.124004. ⟨10.1088/1742-5468/abc62d⟩ Advances in Neural Information Processing Systems 32 Advances in Neural Information Processing Systems 32, Dec 2019, Vancouver, Canada |
| ISSN: | 1742-5468 |
| DOI: | 10.1088/1742-5468/abc62d⟩ |
| Popis: | We study the problem of fitting an ultrametric distance to a dissimilarity graph in the context of hierarchical cluster analysis. Standard hierarchical clustering methods are specified procedurally, rather than in terms of the cost function to be optimized. We aim to overcome this limitation by presenting a general optimization framework for ultrametric fitting. Our approach consists of modeling the latter as a constrained optimization problem over the continuous space of ultrametrics. So doing, we can leverage the simple, yet effective, idea of replacing the ultrametric constraint with a min-max operation injected directly into the cost function. The proposed reformulation leads to an unconstrained optimization problem that can be efficiently solved by gradient descent methods. The flexibility of our framework allows us to investigate several cost functions, following the classic paradigm of combining a data fidelity term with a regularization. While we provide no theoretical guarantee to find the global optimum, the numerical results obtained over a number of synthetic and real datasets demonstrate the good performance of our approach with respect to state-of-the-art agglomerative algorithms. This makes us believe that the proposed framework sheds new light on the way to design a new generation of hierarchical clustering methods. Our code is made publicly available at \url{https://github.com/PerretB/ultrametric-fitting}. Comment: Accepted at NeurIPS 2019 |
| Databáze: | OpenAIRE |
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