Deep Adversarial Inconsistent Cognitive Sampling for Multi-view Progressive Subspace Clustering

Deep multi-view clustering methods have achieved remarkable performance. However, all of them failed to consider the difficulty labels (uncertainty of ground-truth for training samples) over multi-view samples, which may result into a nonideal clustering network for getting stuck into poor local optima during training process; worse still, the difficulty labels from multi-view samples are always inconsistent, such fact makes it even more challenging to handle. In this paper, we propose a novel Deep Adversarial Inconsistent Cognitive Sampling (DAICS) method for multi-view progressive subspace clustering. A multiview binary classification (easy or difficult) loss and a feature similarity loss are proposed to jointly learn a binary classifier and a deep consistent feature embedding network, throughout an adversarial minimax game over difficulty labels of multiview consistent samples. We develop a multi-view cognitive sampling strategy to select the input samples from easy to difficult for multi-view clustering network training. However, the distributions of easy and difficult samples are mixed together, hence not trivial to achieve the goal. To resolve it, we define a sampling probability with theoretical guarantee. Based on that, a golden section mechanism is further designed to generate a sample set boundary to progressively select the samples with varied difficulty labels via a gate unit, which is utilized to jointly learn a multi-view common progressive subspace and clustering network for more efficient clustering. Experimental results on four real-world datasets demonstrate the superiority of DAICS over the state-of-the-art methods

A Critique of Self-Expressive Deep Subspace Clustering

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 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 that it can lead to a degenerate embedding of the data, which need not correspond to a union of subspaces at all and is poorly suited for clustering. We validate our theoretical results experimentally and also 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 deep subspace clustering model.Comment: Published as a conference paper at the International Conference on Learning Representations (ICLR) 202