Summary of Robust Estimation Of the Intrinsic Dimension Of Data Sets with Quantum Cognition Machine Learning, by Luca Candelori et al.
Robust estimation of the intrinsic dimension of data sets with quantum cognition machine learning
by 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
First submitted to arxiv on: 19 Sep 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Quantum Physics (quant-ph)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Our paper proposes a novel data representation method combining Quantum Cognition Machine Learning with manifold learning to estimate the intrinsic dimension of datasets. We represent each data point as a quantum state encoding both local properties and relations with the entire dataset, inspired by quantum geometry. A quantum metric is constructed from these states, exhibiting a spectral gap that corresponds to the intrinsic dimension. Our estimator detects this spectral gap, outperforming current state-of-the-art methods in synthetic benchmarks by being robust against Gaussian noise. We demonstrate our method’s applicability and robustness on real datasets like ISOMAP face database, MNIST, and Wisconsin Breast Cancer Dataset. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary We’ve developed a new way to understand the structure of big data sets. Our approach combines ideas from quantum physics and machine learning. Imagine each piece of data as a special kind of mathematical object called a “quantum state.” We use these states to create a map of the entire dataset, which helps us figure out how many important features or patterns are hiding inside it. This method is better than current approaches because it’s more accurate and can handle noisy data. We tested our approach on some real-world datasets and showed that it works well. |
Keywords
* Artificial intelligence * Machine learning * Manifold learning
