# oASIS: Adaptive Column Sampling for Kernel Matrix Approximation

arXiv: https://arxiv.org/abs/1505.05208 · HTML: https://mlsanity.com/paper/1505.05208/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2015.

## Built on by (most cited first, 1 of 1)

- [Certified Approximation for Interpretable Representer Landmarks](https://mlsanity.com/paper/2609.38901/) (2026)

## Abstract (arXiv)

Kernel matrices (e.g. Gram or similarity matrices) are essential for many state-of-the-art approaches to classification, clustering, and dimensionality reduction. For large datasets, the cost of forming and factoring such kernel matrices becomes intractable. To address this challenge, we introduce a new adaptive sampling algorithm called Accelerated Sequential Incoherence Selection (oASIS) that samples columns without explicitly computing the entire kernel matrix. We provide conditions under which oASIS is guaranteed to exactly recover the kernel matrix with an optimal number of columns selected. Numerical experiments on both synthetic and real-world datasets demonstrate that oASIS achieves performance comparable to state-of-the-art adaptive sampling methods at a fraction of the computational cost. The low runtime complexity of oASIS and its low memory footprint enable the solution of large problems that are simply intractable using other adaptive methods.