February, 2022. arXiv:2202.04238 [quant-ph]

Paper abstract bibtex

Paper abstract bibtex

t-Stochastic Neighbor Embedding (t-SNE) is a non-parametric data visualization method in classical machine learning. It maps the data from the high-dimensional space into a low-dimensional space, especially a two-dimensional plane, while maintaining the relationship, or similarities, between the surrounding points. In t-SNE, the initial position of the low-dimensional data is randomly determined, and the visualization is achieved by moving the low-dimensional data to minimize a cost function. Its variant called parametric t-SNE uses neural networks for this mapping. In this paper, we propose to use quantum neural networks for parametric t-SNE to reflect the characteristics of high-dimensional quantum data on low-dimensional data. We use fidelity-based metrics instead of Euclidean distance in calculating high-dimensional data similarity. We visualize both classical (Iris dataset) and quantum (time-depending Hamiltonian dynamics) data for classification tasks. Since this method allows us to represent a quantum dataset in a higher dimensional Hilbert space by a quantum dataset in a lower dimension while keeping their similarity, the proposed method can also be used to compress quantum data for further quantum machine learning.

@misc{kawase_parametric_2022, title = {Parametric t-{Stochastic} {Neighbor} {Embedding} {With} {Quantum} {Neural} {Network}}, url = {http://arxiv.org/abs/2202.04238}, abstract = {t-Stochastic Neighbor Embedding (t-SNE) is a non-parametric data visualization method in classical machine learning. It maps the data from the high-dimensional space into a low-dimensional space, especially a two-dimensional plane, while maintaining the relationship, or similarities, between the surrounding points. In t-SNE, the initial position of the low-dimensional data is randomly determined, and the visualization is achieved by moving the low-dimensional data to minimize a cost function. Its variant called parametric t-SNE uses neural networks for this mapping. In this paper, we propose to use quantum neural networks for parametric t-SNE to reflect the characteristics of high-dimensional quantum data on low-dimensional data. We use fidelity-based metrics instead of Euclidean distance in calculating high-dimensional data similarity. We visualize both classical (Iris dataset) and quantum (time-depending Hamiltonian dynamics) data for classification tasks. Since this method allows us to represent a quantum dataset in a higher dimensional Hilbert space by a quantum dataset in a lower dimension while keeping their similarity, the proposed method can also be used to compress quantum data for further quantum machine learning.}, language = {en}, urldate = {2023-06-27}, publisher = {arXiv}, author = {Kawase, Yoshiaki and Mitarai, Kosuke and Fujii, Keisuke}, month = feb, year = {2022}, note = {arXiv:2202.04238 [quant-ph]}, keywords = {Quantum Physics, Computer Science - Machine Learning}, annote = {Comment: 9 pages, 7 figures}, file = {Kawase et al. - 2022 - Parametric t-Stochastic Neighbor Embedding With Qu.pdf:/Users/georgehuang/Zotero/storage/QZA7B2B2/Kawase et al. - 2022 - Parametric t-Stochastic Neighbor Embedding With Qu.pdf:application/pdf}, }

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