基于超总体模型的设计效应分解

本文基于超总体模型研究抽样调查中设计效应的计算问题。首先以随机效应模型为基础，明确了简单随机、二阶段、不等概率和分层抽样对应的超总体模型，进而通过所给模型推导出分层、类集、加权单因素设计效应的计算公式和多因素组合的设计效应计算公式并给出了对应估计量，公式表明：多因素同时存在的组合设计效应等于对应单因素设计效应的乘积。最后，对设计效应的理论值、估计值和真实值之间的关系进行了蒙特卡洛仿真，并利用相对偏倚、相对均方误进行了评价。本文的研究，对复杂抽样设计中正确计算、使用设计效应具有指导意义。     

Studying Complexity of Model-based Clustering

Cluster analysis is a popular statistics and computer science technique commonly used in various areas of research. In this article, we investigate factors that can influence clustering performance in the model-based clustering framework. The four factors considered are the level of overlap, number of clusters, number of dimensions, and sample size. Through a comprehensive simulation study, we investigate model-based clustering in different settings. As a measure of clustering performance, we employ three popular classification indices capable of reflecting the degree of agreement in two partitioning vectors, thus making the comparison between the true and estimated classification vectors possible. In addition to studying clustering complexity, the performance of the three classification measures is evaluated.     

非线性面板数据聚类方法研究

对于一类变量非线性相关的面板数据,现有的基于线性算法的面板数据聚类方法并不能准确地度量样本间的相似性,且聚类结果的可解释性低。综合考虑变量非线性相关问题及聚类结果可解释性问题,提出一种非线性面板数据的聚类方法,通过非线性核主成分算法实现对样本相似性的测度,并基于混合高斯模型进行样本概率聚类,实证表明该方法的有效性及其对聚类结果的可解释性有所提高。     

Two-step estimation for inhomogeneous spatial point processes

Summary.  The paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second-order properties ( K -function). Regression parameters are estimated by using a Poisson likelihood score estimating function and in the second step minimum contrast estimation is applied for the residual clustering parameters. Asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rainforests.     

Back propagation neural networks and multiple regressions in the case of heteroskedasticity

This paper compares the performance between regression analysis and a clustering based neural network approach when the data deviates from the homoscedasticity assumption of regression. Heteroskedasticity is a problem that arises in linear regression due to the unequal error variances. One of the methods to deal heteroskedasticity in classical regression theory is weighted least-square regression (WLS). In order to deal the problem of heteroskedasticity, backpropagation neural network is applied. In this context, an algorithm is proposed which is based on robust estimates of location and dispersion matrix that helps in preserving the error assumption of the linear regression. Analysis is carried out with appropriate designs using simulated data and the results are presented.     

Clustering in weighted networks

In recent years, researchers have investigated a growing number of weighted networks where ties are differentiated according to their strength or capacity. Yet, most network measures do not take weights into consideration, and thus do not fully capture the richness of the information contained in the data. In this paper, we focus on a measure originally defined for unweighted networks: the global clustering coefficient. We propose a generalization of this coefficient that retains the information encoded in the weights of ties. We then undertake a comparative assessment by applying the standard and generalized coefficients to a number of network datasets.     

Modified genetic algorithm-based clustering for probability density functions

This article modifies two internal validity measures and applies them to evaluate the quality of clustering for probability density functions (pdfs). Based on these measures, we propose a new modified genetic algorithm called GA-CDF to establish the suitable clusters for pdfs. The proposed algorithm is tested by four numerical examples including two synthetic data sets and two real data sets. These examples illustrate the superiority of proposed algorithm over some existing algorithms in evaluating the internal or external validity measures. It demonstrates the feasibility and applicability of the GA-CDF for practical problems in data mining.     

Clustering transformed compositional data using K-means,with applications in gene expression and bicycle sharing system data

Although there is no shortage of clustering algorithms proposed in the literature, the question of the most relevant strategy for clustering compositional data (i.e. data whose rows belong to the simplex) remains largely unexplored in cases where the observed value is equal or close to zero for one or more samples. This work is motivated by the analysis of two applications, both focused on the categorization of compositional profiles: (1) identifying groups of co-expressed genes from high-throughput RNA sequencing data, in which a given gene may be completely silent in one or more experimental conditions; and (2) finding patterns in the usage of stations over the course of one week in the Velib' bicycle sharing system in Paris, France. For both of these applications, we make use of appropriately chosen data transformations, including the Centered Log Ratio and a novel extension called the Log Centered Log Ratio, in conjunction with the K-means algorithm. We use a non-asymptotic penalized criterion, whose penalty is calibrated with the slope heuristics, to select the number of clusters. Finally, we illustrate the performance of this clustering strategy, which is implemented in the Bioconductor package coseq, on both the gene expression and bicycle sharing system data.     

Novel quadratic programming approach for time series clustering with biomedical application

Fundamental problems in data mining mainly involve discrete decisions based on numerical analyses of data (e.g., class assignment, feature selection, data categorization, identifying outlier samples). These decision-making problems in data mining are combinatorial in nature and can naturally be formulated as discrete optimization problems. One of the most widely studied problems in data mining is clustering. In this paper, we propose a new optimization model for hierarchical clustering based on quadratic programming and later show that this model is compact and scalable. Application of this clustering technique in epilepsy, the second most common brain disorder, is a case point in this study. In our empirical study, we will apply the proposed clustering technique to treatment problems in epilepsy through the brain dynamics analysis of electroencephalogram (EEG) recordings. This study is a proof of concept of our hypothesis that epileptic brains tend to be more synchronized (clustered) during the period before a seizure than a normal period. The results of this study suggest that data mining research might be able to revolutionize current diagnosis and treatment of epilepsy as well as give a greater understanding of brain functions (and other complex systems) from a system perspective. This work was partially supported by the NSF grant CCF 0546574 and Rutgers Research Council grant-202018.