# A New Method for Performance Analysis in Nonlinear Dimensionality Reduction

arXiv: https://arxiv.org/abs/1711.06252 · HTML: https://mlsanity.com/paper/1711.06252/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2017.

## Built on by (most cited first, 3 of 3)

- [Enhancing cluster analysis via topological manifold learning](https://mlsanity.com/paper/2207.00510/) (2022)
- [Evaluating the Stability of Deep Learning Latent Feature Spaces](https://mlsanity.com/paper/2402.11404/) (2024)
- [REGAIN: REconciliation GAIN-driven Auxiliary Direction Learning](https://mlsanity.com/paper/2606.04380/) (2026)

## Abstract (arXiv)

In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor distributions in high dimensions. Some benchmark datasets are studied. We find that the local rank correlation closely corresponds to our visual interpretation of the quality of the output. In addition, we demonstrate that the local rank correlation is useful in estimating the intrinsic dimensionality of the original data, and in selecting a suitable value of tuning parameters used in some algorithms.