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Physics Maths Engineering

Kernel-Based Analysis of Massive Data

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Hrushikesh N. Mhaskar

Hrushikesh N. Mhaskar


  Peer Reviewed

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© attribution CC-BY

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rating
559 Views

Added on

2024-10-26

Doi: http://dx.doi.org/10.3389/fams.2020.00030

Related Subjects
Physics
Math
Chemistry
Computer science
Engineering
Earth science
Biology

Abstract

Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity, divide-and-conquer, and distributed learning. In this paper, we develop a very general theory of approximation by networks, which we have called eignets, to achieve local, stratified approximation. The very massive nature of the data allows us to use these eignets to solve inverse problems, such as finding a good approximation to the probability law that governs the data and finding the local smoothness of the target function near different points in the domain. In fact, we develop a wavelet-like representation using our eignets. Our theory is applicable to approximation on a general locally compact metric measure space. Special examples include approximation by periodic basis functions on the torus, zonal function networks on a Euclidean sphere (including smooth ReLU networks), Gaussian networks, and approximation on manifolds. We construct pre-fabricated networks so that no data-based training is required for the approximation.

The article "Kernel-Based Analysis of Massive Data" by Hrushikesh N. Mhaskar, published in Frontiers in Applied Mathematics and Statistics in October 2020, addresses the challenges of analyzing large datasets using kernel-based methods.

Key Questions about 'Kernel-Based Analysis of Massive Data'

The article "Kernel-Based Analysis of Massive Data" by Hrushikesh N. Mhaskar, published in Frontiers in Applied Mathematics and Statistics in October 2020, addresses the challenges of analyzing large datasets using kernel-based methods.

1. How can kernel-based methods be applied to massive data analysis?

The study explores the use of kernel-based techniques to approximate functions within large datasets, aiming to enhance the efficiency and accuracy of data analysis processes.

2. What is the concept of 'eignets' in the context of data approximation?

The research introduces 'eignets' as a general theory of approximation by networks, designed to achieve local, stratified approximation of functions.

3. How do 'eignets' improve the approximation of functions in large datasets?

The article examines how 'eignets' facilitate more precise and localized approximations of functions within massive datasets, potentially leading to better performance in data analysis tasks.

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ARTICLE USAGE


Article usage: Oct-2024 to May-2025
Show by month Manuscript Video Summary
2025 May 122 122
2025 April 89 89
2025 March 68 68
2025 February 50 50
2025 January 105 105
2024 December 53 53
2024 November 56 56
2024 October 16 16
Total 559 559
Show by month Manuscript Video Summary
2025 May 122 122
2025 April 89 89
2025 March 68 68
2025 February 50 50
2025 January 105 105
2024 December 53 53
2024 November 56 56
2024 October 16 16
Total 559 559
Related Subjects
Physics
Math
Chemistry
Computer science
Engineering
Earth science
Biology
copyright icon

© attribution CC-BY

  • 0

rating
559 Views

Added on

2024-10-26

Doi: http://dx.doi.org/10.3389/fams.2020.00030

Related Subjects
Physics
Math
Chemistry
Computer science
Engineering
Earth science
Biology

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