子空间聚类的非参数模型及变分贝叶斯学习

子空间聚类的目标是在不同的特征子集上对给定的一组数据归类.此非监督学习方法试图发现数据"在不同表达下的相似"模式,并且引起了相关领域大量的关注和研究.首先扩展Hoff提出的"均值与方差平移"模型为一个新的基于特征子集的非参数聚类模型,其优点是能应用变分贝叶斯方法学习模型参数.此模型结合Dirichlet过程混合模型和选择特征子集的非参数模型,能自动选择聚类个数和进行子空间聚类.然后给出基于马尔可夫链蒙特卡罗的参数后验推断算法.出于计算速度上的考虑,提出应用变分贝叶斯方法学习模型参数.在仿真数据上的实验结果及在人脸聚类问题上的应用均表明了此模型能同时选择相关特征和在这些特征上具有相似模式的数据点.在UCI"多特征数据库"上应用无需抽样的变分贝叶斯方法,其实验结果说明此方法能快速推断模型参数.

Nonparametric Model and Variational Bayesian Learning for Subspace Clustering

The goal of subspace clustering is to group a given set of data represented by different feature subsets. As an unsupervised learning method, subspace clustering tries to discover the patterns of "similarity examined under different presentations" and has received a great deal of interest and research in the related domains. Firstly the "mean and variance shift" model proposed by Hoff is extended to a new nonparametric model of subspace clustering based on subsets of features.The advantage of the model is that variational Bayesian method can be applied. The model based on the integration of a Dirichlet process mixture model and a nonparametric model of selecting subsets of features can automatically choose the number of clusters and perform subspace clustering. Then posterior inference of the model is done using Markov Chain Monte Carlo. Due to computational considerations the authors propose a variational Bayesian method to learn the parameters of the model. Experimental results using simulated data and the application to the problem of clustering face images illustrate the model can simultaneously selecting the relevant features and the data points that have similar pattern under these features. Experiments on the "multiple feature database" from the UCI repository show that variational Bayesian method without sampling can fleetly inference the parameters of the model.