# Nonparametric Basis Pursuit via Sparse Kernel-based Learning

arXiv: https://arxiv.org/abs/1302.5449 · HTML: https://mlsanity.com/paper/1302.5449/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2013.

## Built on by (most cited first, 6 of 6)

- [RadioDiff-3D: A 3D×3D Radio Map Dataset and Generative Diffusion Based Benchmark for 6G Environment-Aware Communication](https://mlsanity.com/paper/2507.12166/) (2025)
- [Distributed Online Learning with Multiple Kernels](https://mlsanity.com/paper/2102.12733/) (2021)
- [Multilinear Kernel Regression and Imputation via Manifold Learning](https://mlsanity.com/paper/2402.03648/) (2024)
- [Convolutional Filtering with RKHS Algebras](https://mlsanity.com/paper/2411.01341/) (2024)
- [MARS: Radio Map Super-resolution and Reconstruction Method under Sparse Channel Measurements](https://mlsanity.com/paper/2506.04682/) (2025)
- [Topology Identification and Inference over Graphs](https://mlsanity.com/paper/2512.10183/) (2025)

## Abstract (arXiv)

Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary advances in sparsity-aware modeling and processing, promotes the nonparametric basis pursuit advocated in this paper as the overarching framework for the confluence of kernel-based learning (KBL) approaches leveraging sparse linear regression, nuclear-norm regularization, and dictionary learning. The novel sparse KBL toolbox goes beyond translating sparse parametric approaches to their nonparametric counterparts, to incorporate new possibilities such as multi-kernel selection and matrix smoothing. The impact of sparse KBL to signal processing applications is illustrated through test cases from cognitive radio sensing, microarray data imputation, and network traffic prediction.