A Critique of Self-Expressive Deep Subspace Clustering
A Critique of Self-Expressive Deep Subspace Clustering
复制标题
DOI：
--
复制
发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
B. Haeffele;Chong You;R. Vidal
中科院分区：
文献类型：
--
作者：
B. Haeffele;Chong You;R. Vidal
子空间聚类是一种无监督聚类技术，旨在将支持在线性子空间并集上的数据聚类，每个子空间定义一个维度低于环境空间的聚类。许多现有的关于这个问题的公式是基于利用线性子空间的自表达性质，其中子空间中的任何点都可以表示为子空间中其他点的线性组合。为了将这种方法扩展到支持非线性流形并集的数据，许多研究已经提出使用神经网络学习原始数据的适当核嵌入，该神经网络通过嵌入空间中数据上的自表达损失函数进行正则化，以鼓励在嵌入空间中数据上的线性子空间的并集。在这里，我们表明这种方法存在许多潜在的缺陷，这些缺陷在以前的工作中没有得到充分的解决。特别地，我们展示了模型公式通常在多种方式上是病态的，这可能导致数据的退化嵌入，这根本不需要对应于子空间的并集。我们通过实验验证了我们的理论结果，并重复了文献中报道的先前的实验，在这些实验中，我们得出结论，先前声称的性能优势的很大一部分可以归因于一个特别的后处理步骤，而不是聚类模型。
Subspace clustering is an unsupervised clustering technique designed to cluster data that is supported on a union of linear subspaces, with each subspace defining a cluster with dimension lower than the ambient space. Many existing formulations for this problem are based on exploiting the self-expressive property of linear subspaces, where any point within a subspace can be represented as linear combination of other points within the subspace. To extend this approach to data supported on a union of non-linear manifolds, numerous studies have proposed learning an appropriate kernel embedding of the original data using a neural network, which is regularized by a self-expressive loss function on the data in the embedded space to encourage a union of linear subspaces prior on the data in the embedded space. Here we show that there are a number of potential flaws with this approach which have not been adequately addressed in prior work. In particular, we show the model formulation is often ill-posed in multiple ways, which can lead to a degenerate embedding of the data, which need not correspond to a union of subspaces at all. We validate our theoretical results experimentally and additionally repeat prior experiments reported in the literature, where we conclude that a significant portion of the previously claimed performance benefits can be attributed to an ad-hoc post processing step rather than the clustering model.