Quantum Annealing for Robust Principal Component Analysis
This addresses the need for outlier-resistant dimensionality reduction in fields like fault detection and medical diagnostics, but it is incremental as it adapts an existing robust approach to quantum hardware.
The paper tackles the problem of making principal component analysis robust to outliers by optimizing over the L1-norm instead of the L2-norm, proposing QAPCA, a method using quantum annealing hardware, and finds that its reconstruction error is comparable to L1-BF on synthetic and real-world datasets.
Principal component analysis is commonly used for dimensionality reduction, feature extraction, denoising, and visualization. The most commonly used principal component analysis method is based upon optimization of the L2-norm, however, the L2-norm is known to exaggerate the contribution of errors and outliers. When optimizing over the L1-norm, the components generated are known to exhibit robustness or resistance to outliers in the data. The L1-norm components can be solved for with a binary optimization problem. Previously, L1-BF has been used to solve the binary optimization for multiple components simultaneously. In this paper we propose QAPCA, a new method for finding principal components using quantum annealing hardware which will optimize over the robust L1-norm. The conditions required for convergence of the annealing problem are discussed. The potential speedup when using quantum annealing is demonstrated through complexity analysis and experimental results. To showcase performance against classical principal component analysis techniques experiments upon synthetic Gaussian data, a fault detection scenario and breast cancer diagnostic data are studied. We find that the reconstruction error when using QAPCA is comparable to that when using L1-BF.