Randomized approximate class-specific kernel spectral regression analysis for large-scale face verification

Kernel methods are known to be effective analyse complex objects by implicitly embedding them into some feature space. The approximate class-specific kernel spectral regression (ACS-KSR) method is a powerful tool for face verification. This consists of two steps: an eigenanalysis step and step, however, it may suffer from heavily computational overhead in practice, especially large-sample data sets. In this paper, we propose randomized algorithms based on the ACS-KSR method. main contribution our work four-fold. First, point out that formula utilized mathematically incomplete, give correction it. Moreover, consider how efficiently solve ratio-trace problem trace-ratio involved Second, well matrix approximately low-rank, best knowledge, there few theoretical results can provide simple feasible strategies determine numerical rank without forming explicitly. To fill-in gap, focus commonly used Gaussian practical strategy determining matrix. Third, numerically low-rank property matrix, modified Nyström with fixed-rank establish probabilistic error bound approximation. Fourth, although proposed reduce cost original method, required form store reduced unfavorable extremely settle problem, block Kaczmarz multiple right-hand sides, which no need compute convergence established. Comprehensive experiments real-world sets performed show effectiveness efficiency methods.