Quantum Laplacian Eigenmap
This work addresses a computational bottleneck in machine learning for researchers and practitioners dealing with high-dimensional data, though it is incremental as it adapts an existing quantum technique to a specific algorithm.
The authors tackled the computational inefficiency of classical Laplacian eigenmap algorithms for dimensionality reduction by proposing a quantum version that exponentially speeds up the process, achieving exponential speedup compared to polynomial-time classical methods.
Laplacian eigenmap algorithm is a typical nonlinear model for dimensionality reduction in classical machine learning. We propose an efficient quantum Laplacian eigenmap algorithm to exponentially speed up the original counterparts. In our work, we demonstrate that the Hermitian chain product proposed in quantum linear discriminant analysis (arXiv:1510.00113,2015) can be applied to implement quantum Laplacian eigenmap algorithm. While classical Laplacian eigenmap algorithm requires polynomial time to solve the eigenvector problem, our algorithm is able to exponentially speed up nonlinear dimensionality reduction.