正态混合模型的鲁棒聚类:一种伪β似然方法

IF 2 Q2 ECONOMICS Econometrics and Statistics Pub Date : 2023-11-01 DOI:10.1016/j.ecosta.2023.10.004
Soumya Chakraborty, Ayanendranath Basu, Abhik Ghosh
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引用次数: 3

摘要

与其他估计场景一样,在正常的混合设置中,基于似然的估计对于模型错误规范和异常值的存在是高度非鲁棒的(除了是一个不适定的优化问题)。针对该估计问题,提出了一种替代普通似然方法的鲁棒替代方法,该方法可以同时进行估计和数据聚类,并导致随后的异常检测。为了调用鲁棒性,在适当的约束条件下利用了基于密度功率散度最小化(或者,β-似然最大化)的方法。采用迭代重加权最小二乘方法来计算分量均值(或等价的聚类中心)和分量弥散矩阵的估计量,从而导致数据同时聚类。在统计和机器学习领域中,异常检测是一个非常重要的问题。通过不同设置下的仿真研究验证了该方法的有效性;与流行的现有方法(如k - mediids, TCLUST,修剪K-means和MCLUST)相比,它的性能具有竞争力或更好,特别是当混合成分(即簇)共享具有显著重叠的区域或外围簇存在较小但不可忽略的权重时(特别是在高维中)。用两个真实的数据集来说明新提出的方法与其他方法的性能以及在图像处理中的应用。该方法可以检测出错误分类率较低的聚类,并成功地指出这些数据集中的外围(异常)观测值。
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Robust Clustering with Normal Mixture Models: A Pseudo β-Likelihood Approach
As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust alternative to the ordinary likelihood approach for this estimation problem is proposed which performs simultaneous estimation and data clustering and leads to subsequent anomaly detection. To invoke robustness, the methodology based on the minimization of the density power divergence (or alternatively, the maximization of the β-likelihood) is utilized under suitable constraints. An iteratively reweighted least squares approach has been followed in order to compute the proposed estimators for the component means (or equivalently cluster centers) and component dispersion matrices which leads to simultaneous data clustering. Some exploratory techniques are also suggested for anomaly detection, a problem of great importance in the domain of statistics and machine learning. The proposed method is validated with simulation studies under different set-ups; it performs competitively or better compared to the popular existing methods like K-medoids, TCLUST, trimmed K-means and MCLUST, especially when the mixture components (i.e., the clusters) share regions with significant overlap or outlying clusters exist with small but non-negligible weights (particularly in higher dimensions). Two real datasets are also used to illustrate the performance of the newly proposed method in comparison with others along with an application in image processing. The proposed method detects the clusters with lower misclassification rates and successfully points out the outlying (anomalous) observations from these datasets.
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来源期刊
CiteScore
3.10
自引率
10.50%
发文量
84
期刊介绍: Econometrics and Statistics is the official journal of the networks Computational and Financial Econometrics and Computational and Methodological Statistics. It publishes research papers in all aspects of econometrics and statistics and comprises of the two sections Part A: Econometrics and Part B: Statistics.
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