Ruyun Chen

In this paper, through complex analysis, the convergence rate is given on a quadrature of a Fourier integral with symmetrical Jacobi weight. The interpolation nodes of this quadrature formula are expressed by the frequency, and the coefficients can be expressed by the Bessel function. When the frequency is close to 0, the nodes are close to those in the Gauss quadrature. When the frequency tends to infinity, the nodes tend symmetrically to the two ends of the integrand. The higher the frequency is, the higher the accuracy of this quadrature will be. Numerical examples are provided to illustrate the theoretical results.

Adaptive boost (AdaBoost) is a prominent example of an ensemble learning algorithm that combines weak classifiers into strong classifiers through weighted majority voting rules. AdaBoost’s weak classifier, with threshold classification, tries to find the best threshold in one of the data dimensions, dividing the data into two categories-1 and 1. However, in some cases, this Weak Learning algorithm is not accurate enough, showing poor generalization performance and a tendency to over-fit. To solve these challenges, we first propose a new Weak Learning algorithm that classifies examples based on multiple thresholds, rather than only one, to improve its accuracy. Second, in this paper, we make changes to the weight allocation scheme of the Weak Learning algorithm based on the AdaBoost algorithm to use potential values of other dimensions in the classification process, while the theoretical identification is provided to show its generality. Finally, comparative experiments between the two algorithms on 18 datasets on UCI show that our improved AdaBoost algorithm has a better generalization effect in the test set during the training iteration.