This paper focuses on the Matrix Factorization based Clustering (MFC) method which is one of the few closed form algorithms for the subspace clustering problem. Despite being simple, closed-form, and computation-efficient, MFC can outperform the other sophisticated subspace clustering methods in many challenging scenarios. We reveal the connection between MFC and the Innovation Pursuit (iPursuit) algorithm which was shown to be able to outperform the other spectral clustering based methods with a notable margin especially when the span of clusters are close. A novel theoretical study is presented which sheds light on the key performance factors of both algorithms (MFC/iPursuit) and it is shown that both algorithms can be robust to notable intersections between the span of clusters. Importantly, in contrast to the theoretical guarantees of other algorithms which emphasized on the distance between the subspaces as the key performance factor and without making the innovation assumption, it is shown that the performance of MFC/iPursuit mainly depends on the distance between the innovative components of the clusters.
翻译:本文侧重于基于子空间集群问题的少数封闭式算法之一的基于矩阵集束法(MFC)方法。MFC尽管是简单、封闭式和计算效率高的算法,但在许多具有挑战性的情况中,可以优于其他复杂的子空间聚集法。我们揭示了MFC与创新定位算法(iPursitut)之间的联系,该算法已证明能够优于其他基于光谱集集法的方法,其幅度显著,特别是在聚集范围接近时。我们介绍了新的理论研究,揭示了这两种算法(MFC/iPursiter)的关键性能要素,并表明这两种算法对于各组之间显著的交叉点是强大的。 重要的是,与其他算法的理论保证相比,强调子空间之间的距离是关键性能因素,而没有作出创新假设,显示MFC/iPursuit的性能主要取决于集群创新组成部分之间的距离。