Auto-adaptive multi-scale Laplacian Pyramids for modeling non-uniform data
| Autor: | José R. Dorronsoro, Neta Rabin, Ángela Fernández, Dalia Fishelov |
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| Přispěvatelé: | UAM. Departamento de Ingeniería Informática, Aprendizaje Automático (ING EPS-001) |
| Rok vydání: | 2020 |
| Předmět: |
Clustering high-dimensional data
0209 industrial biotechnology Multi-scale interpolation Computer science Overfitting 02 engineering and technology Non-uniform data Cross-validation Kernel (linear algebra) 020901 industrial engineering & automation Artificial Intelligence 0202 electrical engineering electronic engineering information engineering Optimal stopping Electrical and Electronic Engineering Informática Kernel methods Laplacian Pyramids Function approximation Adaptive stopping Control and Systems Engineering Kernel (statistics) 020201 artificial intelligence & image processing Focus (optics) Laplace operator Algorithm Interpolation |
| Zdroj: | Biblos-e Archivo. Repositorio Institucional de la UAM Consejo Superior de Investigaciones Científicas (CSIC) |
| Popis: | Kernel-based techniques have become a common way for describing the local and global relationships of data samples that are generated in real-world processes. In this research, we focus on a multi-scale kernel based technique named Auto-adaptive Laplacian Pyramids (ALP). This method can be useful for function approximation and interpolation. ALP is an extension of the standard Laplacian Pyramids model that incorporates a modified Leave-One-Out Cross Validation procedure, which makes the method stable and automatic in terms of parameters selection without extra cost. This paper introduces a new algorithm that extends ALP to fit datasets that are non-uniformly distributed. In particular, the optimal stopping criterion will be point-dependent with respect to the local noise level and the sample rate. Experimental results over real datasets highlight the advantages of the proposed multi-scale technique for modeling and learning complex, high dimensional data They wish to thank Prof. Ronald R. Coifman for helpful remarks. They 525 also gratefully acknowledge the use of the facilities of Centro de Computación Científica (CCC) at Universidad Autónoma de Madrid. Funding: This work was supported by Spanish grants of the Ministerio de Ciencia, Innovación y Universidades [grant numbers: TIN2013-42351-P, TIN2015-70308-REDT, TIN2016-76406-P]; project CASI-CAM-CM supported by Madri+d 530 [grant number: S2013/ICE-2845]; project FACIL supported by Fundación BBVA (2016); and the UAM–ADIC Chair for Data Science and Machine Learning |
| Databáze: | OpenAIRE |
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