A probabilistic clustering method for data elements with normal distributed attributes

By considering uncertainty in the attributes common methods cannot be applicable in data clustering. In the recent years, many researches have been done by considering fuzzy concepts to interpolate the uncertainty. But when data elements attributes have probabilistic distributions, the uncertainty cannot be interpreted by fuzzy theory. In this article, a new concept for clustering of elements with predefined probabilistic distributions for their attributes has been proposed, so each observation will be as a member of a cluster with special probability. Two metaheuristic algorithms have been applied to deal with the problem. Squared Euclidean distance type has been considered to calculate the similarity of data elements to cluster centers. The sensitivity analysis shows that the proposed approach will converge to the classic approaches results when the variance of each point tends to be zero. Moreover, numerical analysis confirms that the proposed approach is efficient in clustering of probabilistic data.     

Comparison between method of moments and entropy regularization algorithm applied to parameter estimation for mixed-Weibull distribution

Mixed-Weibull distribution has been used to model a wide range of failure data sets, and in many practical situations the number of components in a mixture model is unknown. Thus, the parameter estimation of a mixed-Weibull distribution is considered and the important issue of how to determine the number of components is discussed. Two approaches are proposed to solve this problem. One is the method of moments and the other is a regularization type of fuzzy clustering algorithm. Finally, numerical examples and two real data sets are given to illustrate the features of the proposed approaches.     

A clustering approach to interpretable principal components

A new method for constructing interpretable principal components is proposed. The method first clusters the variables, and then interpretable (sparse) components are constructed from the correlation matrices of the clustered variables. For the first step of the method, a new weighted-variances method for clustering variables is proposed. It reflects the nature of the problem that the interpretable components should maximize the explained variance and thus provide sparse dimension reduction. An important feature of the new clustering procedure is that the optimal number of clusters (and components) can be determined in a non-subjective manner. The new method is illustrated using well-known simulated and real data sets. It clearly outperforms many existing methods for sparse principal component analysis in terms of both explained variance and sparseness.     

Vector quantization of amino acids: Analysis of the HIV V3 loop region

This paper is about techniques for clustering sequences such as nucleic or amino acids. Our application is to defining viral subtypes of HIV on the basis of similarities of V3 loop region amino acids of the envelope (env) gene. The techniques introduced here could apply with virtually no change to other HIV genes as well as to other problems and data not necessarily of viral origin. These algorithms as they apply to quantitative data have found much application in engineering contexts to compressing images and speech. They are called vector quantization and involve a mapping from a large number of possible inputs into a much smaller number of outputs. Many implementations, in particular those that go by the name generalized Lloyd or k-means, exist for choosing sets of possible outputs and mappings. With each there is an attempt to maximize similarities among inputs that map to any single output, or, alternatively, to minimize some measure of distortion between input and output. Here, two standard types of vector quantization are brought to bear upon the cited problem of clustering V3 loop amino acid sequences. Results of this clustering are compared to those of the well known UPGMA algorithms, the unweighted pair group method in which arithmetic averages are employed.     

Methods for eliciting aetiological clues from geographically clustered cases of disease, with application to leukaemia–lymphoma data

The nearest neighbour analysis method has been developed to determine whether a disease case may be regarded as being unusually close to other neighbouring cases of the same disease. Using this method, each disease case is classified as spatially 'clustered' or 'non-clustered'. The method is also used to provide a test for global clustering. 'Clusters' are constructed by amalgamating geographically neighbouring clustered cases into one contiguous 'cluster area'. This paper describes a method for studying differences between clustered and non-clustered cases, in terms of case 'attributes'. These attributes may be person related, such as age and sex, or area based, such as geographical isolation. The area-based variables are subject to geographical correlation. The comparison of clustered and non-clustered cases may reveal similarities or differences, which may, in turn, give clues to disease aetiology. A method for studying 'linkage' or similarities in attributes between cases that occur in the same clusters is also described. The methods are illustrated by application to incidence data for leukaemias and lymphomas.     

A modified generalized lasso algorithm to detect local spatial clusters for count data

Detecting local spatial clusters for count data is an important task in spatial epidemiology. Two broad approaches—moving window and disease mapping methods—have been suggested in some of the literature to find clusters. However, the existing methods employ somewhat arbitrarily chosen tuning parameters, and the local clustering results are sensitive to the choices. In this paper, we propose a penalized likelihood method to overcome the limitations of existing local spatial clustering approaches for count data. We start with a Poisson regression model to accommodate any type of covariates, and formulate the clustering problem as a penalized likelihood estimation problem to find change points of intercepts in two-dimensional space. The cost of developing a new algorithm is minimized by modifying an existing least absolute shrinkage and selection operator algorithm. The computational details on the modifications are shown, and the proposed method is illustrated with Seoul tuberculosis data.     

基于聚类关联规则的缺失数据处理研究

 本文提出了基于聚类和关联规则的缺失数据处理新方法,通过聚类方法将含有缺失数据的数据集相近的记录归到一类,然后利用改进后的关联规则方法对各子数据集挖掘变量间的关联性,并利用这种关联性来填补缺失数据。通过实例分析,发现该方法对缺失数据处理,尤其是海量数据集具有较好的效果。     

Identification of target clusters by using the restricted normal mixture model

This paper addresses the problem of identifying groups that satisfy the specific conditions for the means of feature variables. In this study, we refer to the identified groups as “target clusters” (TCs). To identify TCs, we propose a method based on the normal mixture model (NMM) restricted by a linear combination of means. We provide an expectation–maximization (EM) algorithm to fit the restricted NMM by using the maximum-likelihood method. The convergence property of the EM algorithm and a reasonable set of initial estimates are presented. We demonstrate the method's usefulness and validity through a simulation study and two well-known data sets. The proposed method provides several types of useful clusters, which would be difficult to achieve with conventional clustering or exploratory data analysis methods based on the ordinary NMM. A simple comparison with another target clustering approach shows that the proposed method is promising in the identification.     

基于高斯谱聚类的风险商户聚类分析

随着电子支付的普及,市场涌现出越来越多的第三方支付平台,而当前关于第三方支付平台商户风险方面的研究相对较少。故本文提出基于高斯谱聚类的风险商户聚类方法,首先使用高斯混合模型构建交易-交易群体的双模网络;其次借助网络中信息传递的思想构建“商户-交易群体网络”的双模网络;再次使用双模网络聚类方法中的谱聚类方法同时对网络中的两类节点聚类,对商户节点聚类的结果可区分出不同风险级别的商户,对交易群体节点聚类的结果可以进一步描述风险商户的交易特征;最后本文分别在模拟数据和某第方支付平台的实际数据中验证了模型的有效性。实验结果表明,本文提出的方法不仅可以准确地区分出不同风险级别的商户群体,而且能总结归纳风险商户的交易特征,为风险商户的监管提供参考。     

Clustering for contingency tables: boxes and partitions

The correspondence analysis (CA) method appears to be an effective tool for analysis of interrelations between rows and columns in two-way contingency data. A discrete version of the method, box clustering, is developed in the paper using an approximation version of the CA model extended to the case when CA factor values are required to be Boolean. Several properties of the proposed SEFIT-BOX algorithm are proved to facilitate interpretation of its output. It is also shown that two known partitioning algorithms (applied within row or column sets only) could be considered as locally optimal algorithms for fitting the model, and extensions of these algorithms to a simultaneous row and column partitioning problem are proposed.     

Model selection for probabilistic clustering using cross-validated likelihood

Cross-validated likelihood is investigated as a tool for automatically determining the appropriate number of components (given the data) in finite mixture modeling, particularly in the context of model-based probabilistic clustering. The conceptual framework for the cross-validation approach to model selection is straightforward in the sense that models are judged directly on their estimated out-of-sample predictive performance. The cross-validation approach, as well as penalized likelihood and McLachlan's bootstrap method, are applied to two data sets and the results from all three methods are in close agreement. The second data set involves a well-known clustering problem from the atmospheric science literature using historical records of upper atmosphere geopotential height in the Northern hemisphere. Cross-validated likelihood provides an interpretable and objective solution to the atmospheric clustering problem. The clusters found are in agreement with prior analyses of the same data based on non-probabilistic clustering techniques.     

Clustering of gamma-ray bursts through kernel principal component analysis

We consider the problem related to clustering of gamma-ray bursts (from “BATSE” catalogue) through kernel principal component analysis in which our proposed kernel outperforms results of other competent kernels in terms of clustering accuracy and we obtain three physically interpretable groups of gamma-ray bursts. The effectivity of the suggested kernel in combination with kernel principal component analysis in revealing natural clusters in noisy and nonlinear data while reducing the dimension of the data is also explored in two simulated data sets.     

An iterative algorithm for optimal variable weighting in K-means clustering

The K-means clustering method is a widely adopted clustering algorithm in data mining and pattern recognition, where the partitions are made by minimizing the total within group sum of squares based on a given set of variables. Weighted K-means clustering is an extension of the K-means method by assigning nonnegative weights to the set of variables. In this paper, we aim to obtain more meaningful and interpretable clusters by deriving the optimal variable weights for weighted K-means clustering. Specifically, we improve the weighted k-means clustering method by introducing a new algorithm to obtain the globally optimal variable weights based on the Karush-Kuhn-Tucker conditions. We present the mathematical formulation for the clustering problem, derive the structural properties of the optimal weights, and implement an recursive algorithm to calculate the optimal weights. Numerical examples on simulated and real data indicate that our method is superior in both clustering accuracy and computational efficiency.     

高维大数据基因网络中的社区发现——以NC方法为例

从大量基因中识别出致病基因是大数据下的一个十分重要的高维统计问题。基因间网络结构的存在使得对于致病基因的识别已从单个基因识别扩展到基因模块识别。从基因网络中挖掘出基因模块就是所谓的社区发现（或节点聚类）问题。绝大多数社区发现方法仅利用网络结构信息,而忽略节点本身的信息。Newman和Clauset于2016年提出了一个将二者有机结合的基于统计推断的社区发现方法（简称为NC方法）。本文以NC方法为案例,介绍统计方法在实际基因网络中的应用和取得的成果,并从统计学角度提出了改进措施。通过对NC方法的分析可以看出对于以基因网络为代表的非结构化数据,统计思想和原理在数据分析中仍然处于核心地位。而相应的统计方法则需要针对数据的特点及关心的问题进行相应的调整和优化。     

Dimension reduction for model-based clustering

We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and, depending on the estimated mixture model, on the variation on group covariances. The proposed method aims at reducing the dimensionality by identifying a set of linear combinations, ordered by importance as quantified by the associated eigenvalues, of the original features which capture most of the cluster structure contained in the data. Observations may then be projected onto such a reduced subspace, thus providing summary plots which help to visualize the clustering structure. These plots can be particularly appealing in the case of high-dimensional data and noisy structure. The new constructed variables capture most of the clustering information available in the data, and they can be further reduced to improve clustering performance. We illustrate the approach on both simulated and real data sets.     

Bayesian nonparametric clustering for large data sets

We propose two nonparametric Bayesian methods to cluster big data and apply them to cluster genes by patterns of gene–gene interaction. Both approaches define model-based clustering with nonparametric Bayesian priors and include an implementation that remains feasible for big data. The first method is based on a predictive recursion which requires a single cycle (or few cycles) of simple deterministic calculations for each observation under study. The second scheme is an exact method that divides the data into smaller subsamples and involves local partitions that can be determined in parallel. In a second step, the method requires only the sufficient statistics of each of these local clusters to derive global clusters. Under simulated and benchmark data sets the proposed methods compare favorably with other clustering algorithms, including k-means, DP-means, DBSCAN, SUGS, streaming variational Bayes and an EM algorithm. We apply the proposed approaches to cluster a large data set of gene–gene interactions extracted from the online search tool “Zodiac.”

     

大数据下张量充分降维方法及其应用研究

在大数据时代,金融学、基因组学和图像处理等领域产生了大量的张量数据。Zhong等(2015)提出了张量充分降维方法,并给出了处理二阶张量的序列迭代算法。鉴于高阶张量在实际生活中的广泛应用,本文将Zhong等(2015)的算法推广到高阶,以三阶张量为例,提出了两种不同的算法:结构转换算法和结构保持算法。两种算法都能够在不同程度上保持张量原有结构信息,同时有效降低变量维度和计算复杂度,避免协方差矩阵奇异的问题。将两种算法应用于人像彩图的分类识别,以二维和三维点图等形式直观展现了算法分类结果。将本文的结构保持算法与K-means聚类方法、t-SNE非线性降维方法、多维主成分分析、多维判别分析和张量切片逆回归共五种方法进行对比,结果表明本文所提方法在分类精度方面有明显优势,因此在图像识别及相关应用领域具有广阔的发展前景。     

稳健高效的高维成分数据近似零值插补方法及应用

随着计算机技术的迅猛发展,高维成分数据不断涌现并伴有大量近似零值和缺失,数据的高维特性不仅给传统统计方法带来了巨大的挑战,其厚尾特征、复杂的协方差结构也使得理论分析难上加难。于是如何对高维成分数据的近似零值进行稳健的插补,挖掘潜在的内蕴结构成为当今学者研究的焦点。对此,本文结合修正的EM算法,提出基于R型聚类的Lasso-分位回归插补法(SubLQR)对高维成分数据的近似零值问题予以解决。与现有高维近似零值插补方法相比,本文所提出的SubLQR具有如下优势。①稳健全面性:利用Lasso-分位回归方法,不仅可以有效地探测到响应变量的整个条件分布,还能提供更加真实的高维稀疏模式;②有效准确性:采用基于R型聚类的思想进行插补,可以降低计算复杂度,极大提高插补的精度。模拟研究证实,本文提出的SubLQR高效灵活准确,特别在零值、异常值较多的情形更具优势。最后将SubLQR方法应用于罕见病代谢组学研究中,进一步表明本文所提出的方法具有广泛的适用性。     

Bayesian Mixture Labeling and Clustering

Label switching is one of the fundamental issues for Bayesian mixture modeling. It occurs due to the nonidentifiability of the components under symmetric priors. Without solving the label switching, the ergodic averages of component specific quantities will be identical and thus useless for inference relating to individual components, such as the posterior means, predictive component densities, and marginal classification probabilities. The author establishes the equivalence between the labeling and clustering and proposes two simple clustering criteria to solve the label switching. The first method can be considered as an extension of K-means clustering. The second method is to find the labels by minimizing the volume of labeled samples and this method is invariant to the scale transformation of the parameters. Using a simulation example and the application of two real data sets, the author demonstrates the success of these new methods in dealing with the label switching problem.     

Regularized boxplot via convex clustering

A boxplot is a simple and effective exploratory data analysis tool for graphically summarizing a distribution of data. However, in cases where the quartiles in a boxplot are inaccurately estimated, these estimates can affect subsequent analyses. In this paper, we consider the problem of constructing boxplots in a bivariate setting with a categorical covariate with multiple subgroups, and assume that some of these boxplots can be clustered. We propose to use this grouping property to improve the estimation of the quartiles. We demonstrate that the proposed method more accurately estimates the quartiles compared to the usual boxplot. It is also shown that the proposed method identifies outliers effectively as a consequence of accurate quartiles, and possesses a clustering effect due to the group property. We then apply the proposed method to annual maximum precipitation data in South Korea and present its clustering results.