Subspace clustering is a growing field of unsupervised learning that has gained much popularity in the computer vision community. Applications can be found in areas such as motion segmentation and face clustering. It assumes that data originate from a union of subspaces, and clusters the data depending on the corresponding subspace. In practice, it is reasonable to assume that a limited amount of labels can be obtained, potentially at a cost. Therefore, algorithms that can effectively and efficiently incorporate this information to improve the clustering model are desirable. In this paper, we propose an active learning framework for subspace clustering that sequentially queries informative points and updates the subspace model. The query stage of the proposed framework relies on results from the perturbation theory of principal component analysis, to identify influential and potentially misclassified points. A constrained subspace clustering algorithm is proposed that monotonically decreases the objective function subject to the constraints imposed by the labelled data. We show that our proposed framework is suitable for subspace clustering algorithms including iterative methods and spectral methods. Experiments on synthetic data sets, motion segmentation data sets, and Yale Faces data sets demonstrate the advantage of our proposed active strategy over state-of-the-art.
翻译:子空间集群是一个日益扩大的不受监督的学习领域,在计算机视觉界中已非常受欢迎。 应用程序可以在运动分割和面团组合等领域找到。 它假定数据来自子空间的组合,并根据相应的子空间对数据进行分组。 实际上,可以合理地假设可以以成本获得数量有限的标签,因此,最好能够有效和高效地纳入这一信息以改进集群模型的算法。 在本文件中,我们提议一个子空间集群的积极学习框架,以便按顺序查询信息点和更新子空间模型。 提议的框架的查询阶段依赖于主要组成部分分析的扰动理论的结果,以找出有影响力和潜在的分类点。 限制的子空间集群算法建议单方减少受有标签数据制约的目标功能。 我们表明,我们提议的框架适合于子空间组合算法,包括迭代方法和光谱方法。 合成数据集实验、运动分割数据集和耶鲁面数据集显示了我们拟议的积极战略对状态的优势。