Learning a Self-Expressive Network for Subspace Clustering
Learning a Self-Expressive Network for Subspace Clustering
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DOI：
10.1109/cvpr46437.2021.01221
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
Shangzhi Zhang;Chong You;R. Vidal;Chun-Guang Li
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文献类型：
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作者：
Shangzhi Zhang;Chong You;R. Vidal;Chun-Guang Li
最先进的子空间聚类方法基于自表达模型，该模型将每个数据点表示为其他数据点的线性组合。然而，这些方法是为有限样本数据集设计的，并且缺乏推广到样本外数据的能力。此外，由于自表达系数的数量与数据点的数量成二次方增长，因此它们处理大规模数据集的能力通常是有限的。在本文中，我们提出了一种新的子空间聚类框架，称为自表达网络（SENet），它采用了一个适当设计的神经网络来学习数据的自表达表示。我们表明，我们的SENet不仅可以学习具有所需属性的自表达系数的训练数据，但也处理样本外的数据。此外，我们还证明了SENet也可以用于对大规模数据集进行子空间聚类。在人工数据和真实的世界基准数据上进行的大量实验验证了所提方法的有效性。特别是，SENet在MNIST、Fashion MNIST和Extended MNIST上具有极强的竞争力，在CIFAR-10上具有最先进的性能。
State-of-the-art subspace clustering methods are based on the self-expressive model, which represents each data point as a linear combination of other data points. However, such methods are designed for a finite sample dataset and lack the ability to generalize to out-of-sample data. Moreover, since the number of self-expressive coefficients grows quadratically with the number of data points, their ability to handle large-scale datasets is often limited. In this paper, we propose a novel framework for subspace clustering, termed Self-Expressive Network (SENet), which employs a properly designed neural network to learn a self-expressive representation of the data. We show that our SENet can not only learn the self-expressive coefficients with desired properties on the training data, but also handle out-of-sample data. Besides, we show that SENet can also be leveraged to perform subspace clustering on large-scale datasets. Extensive experiments conducted on synthetic data and real world benchmark data validate the effectiveness of the proposed method. In particular, SENet yields highly competitive performance on MNIST, Fashion MNIST and Extended MNIST and state-of-the-art performance on CIFAR-10.