Recent advances of subspace clustering have provided a new way of constructing affinity matrices for clustering. Unlike the kernel-based subspace clustering, which needs tedious tuning among infinitely many kernel candidates, the self-expressive models derived from linear subspace assumptions in modern subspace clustering methods are rigorously combined with sparse or low-rank optimization theory to yield an affinity matrix as a solution of an optimization problem. Despite this nice theoretical aspect, the affinity matrices of modern subspace clustering have quite different meanings from the traditional ones, and even though the affinity matrices are expected to have a rough block-diagonal structure, it is unclear whether these are good enough to apply spectral clustering. In fact, most of the subspace clustering methods perform some sort of affinity value rearrangement to apply spectral clustering, but its adequacy for the spectral clustering is not clear; even though the spectral clustering step can also have a critical impact on the overall performance. To resolve this issue, in this paper, we provide a nonparametric method to estimate the probabilistic cluster membership from these affinity matrices, which we can directly find the clusters from. The likelihood for an affinity matrix is defined nonparametrically based on histograms given the probabilistic membership, which is defined as a combination of probability simplices, and an additional prior probability is defined to regularize the membership as a Bernoulli distribution. Solving this maximum a posteriori problem replaces the spectral clustering procedure, and the final discrete cluster membership can be calculated by selecting the clusters with maximum probabilities. The proposed method provides state-of-the-art performance for well-known subspace clustering methods on popular benchmark databases.

中文翻译：

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子空间聚类概率隶属度的非参数估计


子空间聚类的最新进展提供了一种构建聚类亲和矩阵的新方法。与基于核的子空间聚类需要在无限多个候选核之间进行繁琐的调整不同，现代子空间聚类方法中从线性子空间假设导出的自表达模型与稀疏或低秩优化理论严格结合，产生亲和力矩阵：优化问题的解决方案。尽管有这个很好的理论方面，但现代子空间聚类的亲和力矩阵与传统子空间聚类的含义有很大不同，并且即使亲和力矩阵预计具有粗糙的块对角线结构，但尚不清楚它们是否足以应用谱聚类。事实上，大多数子空间聚类方法都执行某种亲和值重排来应用谱聚类，但其对于谱聚类的充分性尚不清楚；尽管谱聚类步骤也可能对整体性能产生关键影响。为了解决这个问题，在本文中，我们提供了一种非参数方法来根据这些亲和力矩阵估计概率聚类成员资格，我们可以直接从中找到聚类。亲和力矩阵的似然度是基于给定概率隶属度的直方图非参数定义的，概率隶属度被定义为概率单纯形的组合，并且定义附加先验概率以将隶属度正则化为伯努利分布。解决这个最大后验问题取代了谱聚类过程，并且可以通过选择具有最大概率的聚类来计算最终的离散聚类成员资格。 所提出的方法为流行基准数据库上的众所周知的子空间聚类方法提供了最先进的性能。