Parametric t-stochastic neighbor embedding with quantum neural network

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