# Kernel based analysis of massive data

arXiv: https://arxiv.org/abs/2003.13226 · HTML: https://mlsanity.com/paper/2003.13226/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2020.

## Built on by (most cited first, 11 of 11)

- [Local approximation of operators](https://mlsanity.com/paper/2202.06392/) (2022)
- [Approximation Rates for Shallow ReLUk Neural Networks on Sobolev Spaces via the Radon Transform](https://mlsanity.com/paper/2408.10996/) (2024)
- [Tractability of approximation by general shallow networks](https://mlsanity.com/paper/2308.03230/) (2023)
- [Learning on manifolds without manifold learning](https://mlsanity.com/paper/2402.12687/) (2024)
- [A manifold learning approach for gesture recognition from micro-Doppler radar measurements](https://mlsanity.com/paper/2110.01670/) (2021)
- [Encoding of data sets and algorithms](https://mlsanity.com/paper/2303.00984/) (2023)
- [Approximation by non-symmetric networks for cross-domain learning](https://mlsanity.com/paper/2305.03890/) (2023)
- [Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View](https://mlsanity.com/paper/2608.01357/) (2026)
- [Local transfer learning from one data space to another](https://mlsanity.com/paper/2302.00160/) (2023)
- [A signal separation view of classification](https://mlsanity.com/paper/2509.24140/) (2025)
- [Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples](https://mlsanity.com/paper/2608.06687/) (2026)

## Abstract (arXiv)

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.