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A Bayesian Fisher-EM algorithm for discriminative Gaussian subspace clustering

机译：一种差别高斯子空间聚类贝叶斯渔业 - EM算法

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摘要

High-dimensional data clustering has become and remains a challenging task for modern statistics and machine learning, with a wide range of applications. We consider in this work the powerful discriminative latent mixture model, and we extend it to the Bayesian framework. Modeling data as a mixture of Gaussians in a low-dimensional discriminative subspace, a Gaussian prior distribution is introduced over the latent group means and a family of twelve submodels are derived considering different covariance structures. Model inference is done with a variational EM algorithm, while the discriminative subspace is estimated via a Fisher-step maximizing an unsupervised Fisher criterion. An empirical Bayes procedure is proposed for the estimation of the prior hyper-parameters, and an integrated classification likelihood criterion is derived for selecting both the number of clusters and the submodel. The performances of the resulting Bayesian Fisher-EM algorithm are investigated in two thorough simulated scenarios, regarding both dimensionality as well as noise and assessing its superiority with respect to state-of-the-art Gaussian subspace clustering models. In addition to standard real data benchmarks, an application to single image denoising is proposed, displaying relevant results. This work comes with a reference implementation for the software in the package accompanying the paper and available on CRAN.
机译：高维数据聚类已成为现代统计和机器学习的具有挑战性的任务，具有广泛的应用。我们考虑在这项工作中，强大的歧视性潜在混合模型，我们将其扩展到贝叶斯框架。将数据建模作为高斯判别子空间中高斯的混合物，在潜伏的群体手段上引入高斯先前分布，并且考虑不同的协方差结构，导出了12个子模型的系列。模型推断采用变分EM算法完成，而判别子空间通过渔民步骤估算，最大化无监督的Fisher标准。提出了一种经验贝叶斯程序，用于估计先前的超参数，导出集成的分类似然标准，用于选择簇数和子模型的数量。在两种彻底的模拟场景中研究了所得贝叶斯Fisher-EM算法的性能，关于维度以及噪声以及对最先进的高斯子空间聚类模型评估其优越性。除了标准的真实数据基准测试之外，还提出了一种在单个图像去噪的应用程序，显示相关结果。这项工作随附在纸纸上的包装中的软件参考实施，并在CRAN上提供。

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