Two-Stage Bagging Pruning for Reducing the Ensemble Size and Improving the Classification Performance

Ensemble methods, such as the traditional bagging algorithm, can usually improve the performance of a single classifier. However, they usually require large storage space as well as relatively time-consuming predictions. Many approaches were developed to reduce the ensemble size and improve the classification performance by pruning the traditional bagging algorithms. In this article, we proposed a two-stage strategy to prune the traditional bagging algorithm by combining two simple approaches: accuracy-based pruning (AP) and distance-based pruning (DP). These two methods, as well as their two combinations, “AP+DP” and “DP+AP” as the two-stage pruning strategy, were all examined. Comparing with the single pruning methods, we found that the two-stage pruning methods can furthermore reduce the ensemble size and improve the classification. “AP+DP” method generally performs better than the “DP+AP” method when using four base classifiers: decision tree, Gaussian naive Bayes, K-nearest neighbor, and logistic regression. Moreover, as compared to the traditional bagging, the two-stage method “AP+DP” improved the classification accuracy by 0.88%, 4.06%, 1.26%, and 0.96%, respectively, averaged over 28 datasets under the four base classifiers. It was also observed that “AP+DP” outperformed other three existing algorithms Brag, Nice, and TB assessed on 8 common datasets. In summary, the proposed two-stage pruning methods are simple and promising approaches, which can both reduce the ensemble size and improve the classification accuracy

Characteristic length of a Holographic Superconductor with dd-wave gap

After the discovery of the $s$-wave and $p$-wave holographic superconductors, holographic models of $d$-wave superconductor have also been constructed recently. We study analytically the perturbation of the dual gravity theory to calculate the superconducting coherence length $\xi$ of the $d$-wave holographic superconductor near the superconducting phase transition point. The superconducting coherence length $\xi$ divergents as $(1-T/T_c)^{-1/2}$ near the critical temperature $T_c$. We also obtain the magnetic penetration depth $\lambda\propto(T_c-T)^{-1/2}$ by adding a small external homogeneous magnetic field. The results agree with the $s$-wave and $p$-wave models, which are also the same as the Ginzburg-Landau theory.Comment: last version, 10 pages, accepted by PR

Proton Mass Decomposition from the QCD Energy Momentum Tensor

We report results on the proton mass decomposition and also on related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of $N_f = 2+1$ DWF configurations with three lattice spacings and three volumes, and several pion masses including the physical pion mass. With fully non-perturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 33(4)(4)\% and 37(5)(4)\% respectively in the $\overline{MS}$ scheme at $\mu = 2$ GeV. A quarter of the trace anomaly gives a 23(1)(1)\% contribution to the proton mass based on the sum rule, given 9(2)(1)\% contribution from the $u, d,$ and $s$ quark scalar condensates. The $u,d,s$ and glue momentum fractions in the $\overline{MS}$ scheme are in good agreement with global analyses at $\mu = 2$ GeV.Comment: 10 pages, 6 figure