# Breaking the curse of dimensionality with Isolation Kernel

arXiv: https://arxiv.org/abs/2109.14198 · HTML: https://mlsanity.com/paper/2109.14198/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 54 references that are in the map.
- First posted on arXiv 29 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [Orthogonal Random Features](https://mlsanity.com/paper/1610.09072/) (2016)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [Optimal Learning Rates for Localized SVMs](https://mlsanity.com/paper/1507.06615/) (2015)
- [One-Class Support Measure Machines for Group Anomaly Detection](https://mlsanity.com/paper/1303.0309/) (2013)
- [Nearest-Neighbour-Induced Isolation Similarity and its Impact on Density-Based Clustering](https://mlsanity.com/paper/1907.00378/) (2019)
- [Improving the Effectiveness and Efficiency of Stochastic Neighbour Embedding with Isolation Kernel](https://mlsanity.com/paper/1906.09744/) (2019)
- [Isolation Kernel: The X Factor in Efficient and Effective Large Scale Online Kernel Learning](https://mlsanity.com/paper/1907.01104/) (2019)

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

- [Approximate Bayesian Computation Based on Maxima Weighted Isolation Kernel Mapping](https://mlsanity.com/paper/2201.12745/) (2022)

## Abstract (arXiv)

The curse of dimensionality has been studied in different aspects. However, breaking the curse has been elusive. We show for the first time that it is possible to break the curse using the recently introduced Isolation Kernel. We show that only Isolation Kernel performs consistently well in indexed search, spectral & density peaks clustering, SVM classification and t-SNE visualization in both low and high dimensions, compared with distance, Gaussian and linear kernels. This is also supported by our theoretical analyses that Isolation Kernel is the only kernel that has the provable ability to break the curse, compared with existing metric-based Lipschitz continuous kernels.