A permutation test approach to the choice of size k for the nearest neighbors classifier

The k nearest neighbors (k-NN) classifier is one of the most popular methods for statistical pattern recognition and machine learning. In practice, the size k, the number of neighbors used for classification, is usually arbitrarily set to one or some other small numbers, or based on the cross-validation procedure. In this study, we propose a novel alternative approach to decide the size k. Based on a k-NN-based multivariate multi-sample test, we assign each k a permutation test based Z-score. The number of NN is set to the k with the highest Z-score. This approach is computationally efficient since we have derived the formulas for the mean and variance of the test statistic under permutation distribution for multiple sample groups. Several simulation and real-world data sets are analyzed to investigate the performance of our approach. The usefulness of our approach is demonstrated through the evaluation of prediction accuracies using Z-score as a criterion to select the size k. We also compare our approach to the widely used cross-validation approaches. The results show that the size k selected by our approach yields high prediction accuracies when informative features are used for classification, whereas the cross-validation approach may fail in some cases.     

两种地铁屏蔽门系统的适用性分析

介绍城市轨道交通中的两种屏蔽门系统,并对其适用性进行分析,提出半高式屏蔽门系统在我国北方地区城市轨道交通中比较适宜。     

德国选择党——疑欧势力的崛起与前景

德国选择党这支疑欧势力在现有的政党谱系中无法对号入座,却在德国政坛迅速崛起。本文分析该党目前的发展现状,从政党纲领、组织结构和政治动员等多方面探讨其成功原因,进而从政党生命周期理论出发,揭示这一新兴政党所处发展阶段及其对现有政党体制、尤其是右翼阵营的冲击,并研判该党的发展前景与制约因素。     

2-Edge connected dominating sets and 2-Connected dominating sets of a graph

A \(k\)-connected (resp. \(k\)-edge connected) dominating set \(D\) of a connected graph \(G\) is a subset of \(V(G)\) such that \(G[D]\) is \(k\)-connected (resp. \(k\)-edge connected) and each \(v\in V(G)\backslash D\) has at least one neighbor in \(D\). The \(k\) -connected domination number (resp. \(k\) -edge connected domination number) of a graph \(G\) is the minimum size of a \(k\)-connected (resp. \(k\)-edge connected) dominating set of \(G\), and denoted by \(\gamma _k(G)\) (resp. \(\gamma '_k(G)\)). In this paper, we investigate the relation of independence number and 2-connected (resp. 2-edge-connected) domination number, and prove that for a graph \(G\), if it is \(2\)-edge connected, then \(\gamma '_2(G)\le 4\alpha (G)-1\), and it is \(2\)-connected, then \(\gamma _2(G)\le 6\alpha (G)-3\), where \(\alpha (G)\) is the independent number of \(G\).     

Multi-neighborhood based iterated tabu search for routing and wavelength assignment problem

The routing and wavelength assignment problem (RWA) has shown to be NP-hard if the wavelength continuity constraint and the objective of minimizing the number of wavelengths are considered. This paper introduces a multi-neighborhood based iterated tabu search algorithm (MN-ITS), which consists of three neighborhoods with a unified incremental evaluation method, to solve the min-RWA problem. The proposed MN-ITS algorithm is tested on a set of widely studied real world instances as well as a set of challenging random ones in the literature. Comparison with other reference algorithms shows that the MN-ITS algorithm is able to improve five best upper bounds obtained by other competitive reference algorithms in the literature. This paper also presents an analysis to show the significance of the unified incremental evaluation technique and the combination of multiple neighborhoods.     

Bargaining within the Supply Chain and Its Implications in an Industry

Our main objective is to investigate the influence of the bargaining power within a chain on its industry. As a building block, we first discuss the implications of bargaining within a single chain by considering an asymmetric Nash bargaining over the wholesale price (BW). We show that both Manufacturer Stackelberg (MS) and vertical integration (VI) strategies are special cases of the BW contract. We then develop the Nash equilibrium in an industry with two supply chains that use BW. We identify the profit‐maximizing (coordinating) bargaining power within this industry. We show that when a chain is not monopolistic, VI does not coordinate the chain and that the MS contract, where the manufacturer has all the bargaining power, is coordinating when competition is intense. We find that the main determinant of the equilibrium in mature industries is to respond well to the actions of the competing chain rather than to directly maximize the profit of each chain. That is, the equilibrium does not necessarily maximize the profit of the entire industry. While a coordination of the industry could then increase the profitability of both chains, such a coordination is likely against antitrust law. Moreover, if one chain cannot change its actions, the other chain may unilaterally improve its profitability by deviating from the equilibrium. Our results lead to several predictions supported by empirical findings, such as that in competitive industries chains will work “close to” the MS contract.     

On the trimmed mean and minimax-variance L-estimation in Kolmogorov neighbourhoods

We consider the properties of the trimmed mean, as regards minimax-variance L-estimation of a location parameter in a Kolmogorov neighbourhood K() of the normal distribution: We first review some results on the search for an L-minimax estimator in this neighbourhood, i.e. a linear combination of order statistics whose maximum variance in K_t() is a minimum in the class of L-estimators. The natural candidate – the L-estimate which is efficient for that member of K_t,() with minimum Fisher information – is known not to be a saddlepoint solution to the minimax problem. We show here that it is not a solution at all. We do this by showing that a smaller maximum variance is attained by an appropriately trimmed mean. We argue that this trimmed mean, as well as being computationally simple – much simpler than the efficient L-estimate referred to above, and simpler than the minimax M- and R-estimators – is at least “nearly” minimax.     

Nd~(3+):YAG激光器提高输出和谱线调谐运转的实验研究

激光棒的热效应是影响固体激光器提高输出的重要因素。本文采取热补偿方式,首先测定其热焦距,确定补偿曲率,给出工艺方法,最后得到显著提高的输出,并选用实心F-P标准具和它们的组合调谐出荧光带中弱线的连续运转。     

非奇异H矩阵研究

给出了非奇异Ｈ矩阵的一个必要条件和一种简单实用的判定方法