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Register a new userTowards Clustering-friendly Representations: Subspace Clustering via Graph Filtering
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Added by
Zhao Kang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However, this simple assumption does not always hold since the raw data might not be separable into subspaces. To recover the ``clustering-friendly representation and facilitate the subsequent clustering, we propose a graph filtering approach by which a smooth representation is achieved. Specifically, it injects graph similarity into data features by applying a low-pass filter to extract useful data representations for clustering. Extensive experiments on image and document clustering datasets demonstrate that our method improves upon state-of-the-art subspace clustering techniques. Especially, its comparable performance with deep learning methods emphasizes the effectiveness of the simple graph filtering scheme for many real-world applications. An ablation study shows that graph filtering can remove noise, preserve structure in the image, and increase the separability of classes.
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In recent years, multi-view subspace clustering has achieved impressive performance due to the exploitation of complementary imformation across multiple views. However, multi-view data can be very complicated and are not easy to cluster in real-world applications. Most existing methods operate on raw data and may not obtain the optimal solution. In this work, we propose a novel multi-view clustering method named smoothed multi-view subspace clustering (SMVSC) by employing a novel technique, i.e., graph filtering, to obtain a smooth representation for each view, in which similar data points have similar feature values. Specifically, it retains the graph geometric features through applying a low-pass filter. Consequently, it produces a ``clustering-friendly representation and greatly facilitates the downstream clustering task. Extensive experiments on benchmark datasets validate the superiority of our approach. Analysis shows that graph filtering increases the separability of classes.
Auto-Encoder (AE)-based deep subspace clustering (DSC) methods have achieved impressive performance due to the powerful representation extracted using deep neural networks while prioritizing categorical separability. However, self-reconstruction loss of an AE ignores rich useful relation information and might lead to indiscriminative representation, which inevitably degrades the clustering performance. It is also challenging to learn high-level similarity without feeding semantic labels. Another unsolved problem facing DSC is the huge memory cost due to $ntimes n$ similarity matrix, which is incurred by the self-expression layer between an encoder and decoder. To tackle these problems, we use pairwise similarity to weigh the reconstruction loss to capture local structure information, while a similarity is learned by the self-expression layer. Pseudo-graphs and pseudo-labels, which allow benefiting from uncertain knowledge acquired during network training, are further employed to supervise similarity learning. Joint learning and iterative training facilitate to obtain an overall optimal solution. Extensive experiments on benchmark datasets demonstrate the superiority of our approach. By combining with the $k$-nearest neighbors algorithm, we further show that our method can address the large-scale and out-of-sample problems.
Hyperspectral image (HSI) clustering is a challenging task due to the high complexity of HSI data. Subspace clustering has been proven to be powerful for exploiting the intrinsic relationship between data points. Despite the impressive performance in the HSI clustering, traditional subspace clustering methods often ignore the inherent structural information among data. In this paper, we revisit the subspace clustering with graph convolution and present a novel subspace clustering framework called Graph Convolutional Subspace Clustering (GCSC) for robust HSI clustering. Specifically, the framework recasts the self-expressiveness property of the data into the non-Euclidean domain, which results in a more robust graph embedding dictionary. We show that traditional subspace clustering models are the special forms of our framework with the Euclidean data. Basing on the framework, we further propose two novel subspace clustering models by using the Frobenius norm, namely Efficient GCSC (EGCSC) and Efficient Kernel GCSC (EKGCSC). Both models have a globally optimal closed-form solution, which makes them easier to implement, train, and apply in practice. Extensive experiments on three popular HSI datasets demonstrate that EGCSC and EKGCSC can achieve state-of-the-art clustering performance and dramatically outperforms many existing methods with significant margins.
Many state-of-the-art subspace clustering methods follow a two-step process by first constructing an affinity matrix between data points and then applying spectral clustering to this affinity. Most of the research into these methods focuses on the first step of generating the affinity, which often exploits the self-expressive property of linear subspaces, with little consideration typically given to the spectral clustering step that produces the final clustering. Moreover, existing methods often obtain the final affinity that is used in the spectral clustering step by applying ad-hoc or arbitrarily chosen postprocessing steps to the affinity generated by a self-expressive clustering formulation, which can have a significant impact on the overall clustering performance. In this work, we unify these two steps by learning both a self-expressive representation of the data and an affinity matrix that is well-normalized for spectral clustering. In our proposed models, we constrain the affinity matrix to be doubly stochastic, which results in a principled method for affinity matrix normalization while also exploiting known benefits of doubly stochastic normalization in spectral clustering. We develop a general framework and derive two models: one that jointly learns the self-expressive representation along with the doubly stochastic affinity, and one that sequentially solves for one then the other. Furthermore, we leverage sparsity in the problem to develop a fast active-set method for the sequential solver that enables efficient computation on large datasets. Experiments show that our method achieves state-of-the-art subspace clustering performance on many common datasets in computer vision.
Deep Subspace Clustering Networks (DSC) provide an efficient solution to the problem of unsupervised subspace clustering by using an undercomplete deep auto-encoder with a fully-connected layer to exploit the self expressiveness property. This method uses undercomplete representations of the input data which makes it not so robust and more dependent on pre-training. To overcome this, we propose a simple yet efficient alternative method - Overcomplete Deep Subspace Clustering Networks (ODSC) where we use overcomplete representations for subspace clustering. In our proposed method, we fuse the features from both undercomplete and overcomplete auto-encoder networks before passing them through the self-expressive layer thus enabling us to extract a more meaningful and robust representation of the input data for clustering. Experimental results on four benchmark datasets show the effectiveness of the proposed method over DSC and other clustering methods in terms of clustering error. Our method is also not as dependent as DSC is on where pre-training should be stopped to get the best performance and is also more robust to noise. Code - href{https://github.com/jeya-maria-jose/Overcomplete-Deep-Subspace-Clustering}{https://github.com/jeya-maria-jose/Overcomplete-Deep-Subspace-Clustering
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