再论Stiefel流形上的矩阵分解聚类
Revisiting clustering as matrix factorisation on the Stiefel manifold
摘要：
本文研究了可能高维数据（例如图像，时间序列，基因表达数据和许多其他设置）的聚类，并将其重新表述为PAC-Bayesian框架中的低秩矩阵估计。我们的方法利用了著名的Burer-Monteiro因式分解策略从大规模优化，在低秩估计的背景下。此外，我们的Burer-Monteiro因子躺在Stiefel流形。我们提出了一个新的广义贝叶斯估计这个问题，并证明了新的预测范围的聚类。我们还设计了一个分量朗之万采样器的Stiefel流形上计算这个估计。
英文摘要：
This paper studies clustering for possibly high dimensional data (e.g. images, time series, gene expression data, and many other settings), and rephrase it as low rank matrix estimation in the PAC-Bayesian framework. Our approach leverages the well known Burer-Monteiro factorisation strategy from large scale optimisation, in the context of low rank estimation. Moreover, our Burer-Monteiro factors are shown to lie on a Stiefel manifold. We propose a new generalized Bayesian estimator for this problem and prove novel prediction bounds for clustering. We also devise a componentwise Langevin sampler on the Stiefel manifold to compute this estimator.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
