A parallel hierarchical blocked adaptive cross approximation algorithm

Abstract

This paper presents a low-rank decomposition algorithm assuming any matrix element can be computed in O(1) time. The proposed algorithm first computes rank-revealing decompositions of sub-matrices with a blocked adaptive cross approximation (BACA) algorithm, and then applies a hierarchical merge operation via truncated singular value decompositions (H-BACA). The proposed algorithm significantly improves the convergence of the baseline ACA algorithm and achieves reduced computational complexity compared to the full decompositions such as rank-revealing QR. Numerical results demonstrate the efficiency, accuracy and parallel scalability of the proposed algorithm.

Detecting Label Noise via Leave-One-Out Cross-Validation

“…While we presented a preliminary analysis of the multiplicative update scheme's convergence behavior for a special case, future work is necessary for a thorough determination of the algorithm's region of convergence. There is also strong practical interest in the adaptation of the method to GPR extensions such as those based on non-Gaussian likelihoods and Nystr öm [36,37] or hierarchical low-rank approximations [38,39,40], as well as in Table 1: Label Noise -Rate/Level: the percentage of corrupted labels and the ratio between the noise and the standard deviation of the pristine labels; R 2 : the coefficient of determination between the inferred and actual label noise; AUC: area under the ROC curve of a 'noisy label' classifier that thresholds the learned σ i ; Precision at Recall Level: precision of the classifier at specified recall levels. Regression accuracy -plain/basic/full: Σ = 0, σI, diag (σ), respectively.…”

RBF approximation of three dimensional PDEs using Tensor Krylov subspace methods

“…At the third and the last step, the Adaptive Cross Approximation [45] is used for admissible interactions, completed by the standard full computation for close interactions. For the evaluation of the convergence of the ACA algorithm, we use the similar criterion in [45].…”

“…At the third and the last step, the Adaptive Cross Approximation [45] is used for admissible interactions, completed by the standard full computation for close interactions. For the evaluation of the convergence of the ACA algorithm, we use the similar criterion in [45]. The distances between each set of particles X I and Y J are evaluated from their projections on the axis defined by the two centres of each dataset.…”

Research on reducing fuzzy test sample set based on heuristic genetic algorithm

“…The approximation algorithm refers to the scenario or accuracy of using the relevant algorithm to solve some practical problems, and the solution given is the theoretical optimal solution. In the reduction of the sample set, the approximation algorithm refers to giving the smallest sample set of samples as accurately as possible, and obtaining high-quality samples is the only standard of the approximation algorithm (Liu et al, 2020).…”