Bang-Shien Chen | Searcharxiv

arXiv2024

FracGM: A Fast Fractional Programming Technique for Geman-McClure Robust Estimator

Robust estimation is essential in computer vision, robotics, and navigation, aiming to minimize the impact of outlier measurements for improved accuracy. We present a fast algorithm for Geman-McClure robust estimation, FracGM, leveraging fractional programming techniques. This solver reformulates the original non-convex fractional problem to a convex dual problem and a linear equation system, iteratively solving them in an alternating optimization pattern. Compared to graduated non-convexity approaches, this strategy exhibits a faster convergence rate and better outlier rejection capability. In addition, the global optimality of the proposed solver can be guaranteed under given conditions. We demonstrate the proposed FracGM solver with Wahba's rotation problem and 3-D point-cloud registration along with relaxation pre-processing and projection post-processing. Compared to state-of-the-art algorithms, when the outlier rates increase from 20% to 80%, FracGM shows 53% and 88% lower rotation and translation increases. In real-world scenarios, FracGM achieves better results in 13 out of 18 outcomes, while having a 19.43% improvement in the computation time.

cs.CV↗

arXiv2022

Generating quantum feature maps for SVM classifier

We present and compare two methods of generating quantum feature maps for quantum-enhanced support vector machine, a classifier based on kernel method, by which we can access high dimensional Hilbert space efficiently. The first method is a genetic algorithm with multi-objective fitness function using penalty method, which incorporates maximizing the accuracy of classification and minimizing the gate cost of quantum feature map circuit. The second method uses variational quantum circuit, focusing on how to contruct the ansatz based on unitary matrix decomposition. Numerical results and comparisons are presented to demonstrate how the fitness fuction reduces gate cost while remaining high accuracy and conducting circuit through unitary matrix obtains even better performance. In particular, we propose some thoughts on reducing and optimizing the gate cost of a circuit while remaining perfect accuracy.

quant-ph↗