Model-based clustering with envelopes
Model-based clustering with envelopes
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DOI：
10.1214/19-ejs1652
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发表时间：
2020-01
影响因子：
1.1
通讯作者：
Wenjing Wang;Xin Zhang;Qing Mai
中科院分区：
文献类型：
--
作者：
Wenjing Wang;Xin Zhang;Qing Mai
：聚类分析是多元统计和机器学习中重要的无监督学习技术。在本文中，我们提出了一组称为 CLEMM（包络混合模型聚类的缩写）的新混合模型，该模型基于广泛使用的高斯混合模型假设和包络方法的新兴研究领域。包络方法主要针对回归模型而制定，旨在同时降维和有效的参数估计，并包括用于分类和判别分析的包络判别子空间的最新公式。受分类中包络判别子空间追求的推动，我们考虑简约的概率混合模型，其中可以通过将数据投影到潜在的低维子空间来改进聚类分析。因此，所提出的 CLEMM 框架和相关的包络 EM 算法为无监督和半监督学习问题中的包络方法提供了基础。对模拟数据和两个基准数据集的数值研究表明，我们提出的方法相对于高斯混合模型、K 均值和层次聚类算法等经典方法有显着改进。 R 包可在 https://github.com/kusakehan/CLEMM 获取。
: Clustering analysis is an important unsupervised learning technique in multivariate statistics and machine learning. In this paper, we pro-pose a set of new mixture models called CLEMM (in short for Clustering with Envelope Mixture Models) that is based on the widely used Gaussian mixture model assumptions and the nascent research area of envelope methodology. Formulated mostly for regression models, envelope methodology aims for simultaneous dimension reduction and efficient parameter estimation, and includes a very recent formulation of envelope discriminant subspace for classification and discriminant analysis. Motivated by the envelope discriminant subspace pursuit in classification, we consider parsimonious probabilistic mixture models where the cluster analysis can be improved by projecting the data onto a latent lower-dimensional subspace. The proposed CLEMM framework and the associated envelope-EM algorithms thus provide foundations for envelope methods in unsupervised and semi-supervised learning problems. Numerical studies on simulated data and two benchmark data sets show significant improvement of our propose methods over the classical methods such as Gaussian mixture models, K-means and hierarchical clustering algorithms. An R package is available at https://github.com/kusakehan/CLEMM .