# Incremental kernel PCA and the Nystr"om method

arXiv: https://arxiv.org/abs/1802.00043 · HTML: https://mlsanity.com/paper/1802.00043/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2018.

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

- [Bayesian Fusion of Active Contour Models and ConvNet Priors for Standing Dead Tree Segmentation](https://mlsanity.com/paper/2410.07421/) (2024)

## Abstract (arXiv)

Incremental versions of batch algorithms are often desired, for increased time efficiency in the streaming data setting, or increased memory efficiency in general. In this paper we present a novel algorithm for incremental kernel PCA, based on rank one updates to the eigendecomposition of the kernel matrix, which is more computationally efficient than comparable existing algorithms. We extend our algorithm to incremental calculation of the Nystr"om approximation to the kernel matrix, the first such algorithm proposed. Incremental calculation of the Nystr"om approximation leads to further gains in memory efficiency, and allows for empirical evaluation of when a subset of sufficient size has been obtained.