# Robust estimation of the intrinsic dimension of data sets with quantum cognition machine learning

**Authors:** Luca Candelori, Alexander G. Abanov, Jeffrey Berger, Cameron J. Hogan, Vahagn Kirakosyan, Kharen Musaelian, Ryan Samson, James E. T. Smith, Dario Villani, Martin T. Wells, Mengjia Xu  
**arXiv:** [2409.12805](https://arxiv.org/abs/2409.12805)  
**Date:** 2024-09-19  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2409.12805v1/

## Key points

- Introduction of a novel data representation method based on Quantum Cognition Machine Learning for manifold learning tasks
- Focus on estimating the intrinsic dimension of data sets by representing each data point as a quantum state
- Construction of a point cloud with a quantum metric revealing a spectral gap corresponding to the intrinsic dimension of the data
- Demonstration of robust estimates in the presence of point-wise Gaussian noise, contrasting current estimators that often overestimate due to noise artifacts
- Applicability tested on diverse datasets including ISOMAP face database, MNIST, and Wisconsin Breast Cancer Dataset
- Promising results in accurately estimating intrinsic dimensions while mitigating the impact of noise

## Summary

In this paper, Candelori et al. introduce a novel data representation method based on Quantum Cognition Machine Learning for manifold learning tasks. Their approach focuses on estimating the intrinsic dimension of data sets by representing each data point as a quantum state. This captures both its local properties and its relationship with the entire dataset. Drawing inspiration from quantum geometry, the researchers construct a point cloud equipped with a quantum metric that reveals a spectral gap corresponding to the intrinsic dimension of the data. This serves as the basis for their estimation method. Through experiments on synthetic manifold benchmarks, the team demonstrates that their estimates are robust in the presence of point-wise Gaussian noise. This contrasts with current estimators that often overestimate due to attributing "shadow dimensions" to noise artifacts. The robustness of their approach is particularly advantageous when working with real-world datasets affected by varying levels of noise. To validate their method's applicability, Candelori et al. test it on diverse datasets including the ISOMAP face database, MNIST, and the Wisconsin Breast Cancer Dataset. By leveraging principles from both quantum cognition and machine learning techniques, their approach showcases promising results in accurately estimating intrinsic dimensions while mitigating the impact of noise in practical scenarios.