Multi-Level Representation Learning for Deep Subspace Clustering

Kheirandishfard, Mohsen; Zohrizadeh, Fariba; Kamangar, Farhad

doi:10.1109/wacv45572.2020.9093277

Cited by 31 publications

(15 citation statements)

References 44 publications

(76 reference statements)

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“…In future work, we will extend our model to deep multi-view subspace clustering. We assume that there is consistent information among different views of multi-view data and that each view has view-specific information [21,24,45]. We impose a separation strategy on multi-view data, so that each view shares consistent structural information on the premise of maintaining its view-specific information.…”

Section: Discussionmentioning

confidence: 99%

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Deep Subspace Clustering with Block Diagonal Constraint

Liu

Sun

2020

Applied Sciences

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The deep subspace clustering method, which adopts deep neural networks to learn a representation matrix for subspace clustering, has shown good performance. However, this representation matrix ignores the structural constraint when it is applied to subspace clustering. It is known that samples from different classes can be taken as embedding in independent subspaces. Thus, the representation matrix should have a block diagonal structure. This paper presents the Deep Subspace Clustering with Block Diagonal Constraint (DSC-BDC), a model which constrains the representation matrix with block diagonal structure and gives a block diagonal regularizer for learning a suitable representation. Furthermore, to enhance the representation capacity, DSC-BDC reforms the block-diagonal structure constraint by performing a separation strategy on the representation matrix. Specifically, the separation strategy ensures that the most compact samples are selected to the represent data. An alternative optimization algorithm is designed for our model. Extensive experiments on four public and real-world databases demonstrate the effectiveness and superiority of our proposed model.

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Section: Discussionmentioning

confidence: 99%

“…According to Equation (2), the regularization term C κ means that the sum of k smallest eigenvalues of L C needs to be minimized, which is difficult to solve. However, according to the basic properties of the eigenvalues [20,45], the regularization term can be rewritten as:…”

Section: Model Optimizationmentioning

confidence: 99%

Deep Subspace Clustering with Block Diagonal Constraint

Liu

Sun

2020

Applied Sciences

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“…Our method differs significantly from [34] in that our proposed selfrepresentation model is designed to minimize the difference from the original data points by combining the self-expressive property of multiple subsets. Lastly, in this paper, we limit our discussion to the non-deep learning approaches that are more mathematically straightforward to explain and rely less on parameter tuning, and not to mention that deep learning approaches [35], [36] usually have high computational and memory complexity.…”

Section: Related Workmentioning

confidence: 99%

PMSSC: Parallelizable Multi-Subset based Self-Expressive Model for Subspace Clustering

Hotta¹,

Akashi²,

Tokai³

et al. 2021

Preprint

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Subspace clustering methods embrace a selfexpressive model that represents each data point as a linear combination of other data points in the dataset are powerful unsupervised learning techniques. However, when dealing with large-scale datasets, the representation of each data point by referring to all data points as a dictionary suffers from high computational complexity. To alleviate this issue, we introduce a parallelizable multi-subset based self-expressive model (PMS) which represents each data point by combing multiple subsets, with each consisting of only a small percentage of samples. The adoption of PMS in subspace clustering (PMSSC) leads to computational advantages because each optimization problem decomposed into each subset is small, and can be solved efficiently in parallel. Besides, PMSSC is able to combine multiple self-expressive coefficient vectors obtained from subsets, which contributes to the improvement of self-expressiveness. Extensive experiments on synthetic data and real-world datasets show the efficiency and effectiveness of our approach against competitive methods.

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“…The existing subspace clustering methods can be divided into five categories: statistical methods [2], iterative methods [3], algebraic algorithms [4], deep learning-base methods [5], [6] and spectral clustering-based methods [7]- [9]. Statistical methods require prior knowledge of the number and dimensions of subspaces.…”

Section: Introductionmentioning

confidence: 99%

Robust Multiview Subspace Clustering of Images via Tighter Rank Approximation

et al. 2021

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In this paper, we focus on the multi-view subspace clustering problem under the framework of third order tensor. Recently, tensor nuclear norm (TNN) has been widely used in the multi-view subspace clustering problem. It is known that TNN is a convex surrogate of the tensor rank. However, TNN is linearly proportional to the sum of the singular values. Thus solving the TNN minimization problem will overpenalize the large singular values and lead to a sub-optimal solution. To address this issue, in this paper, a novel tighter tensor log-determinant (TLD) regularizer is proposed to better approximate the tensor rank. Although the proposed method is non-convex, a closed-form solution has been deduced via solving the Euler-Lagrange equation. A corresponding algorithm associated with augmented Lagrangian multipliers is established and the constructed convergent sequence to the Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. Extensive experiments indicate that the proposed model achieves significant improvements compared to the state-of-the-art convex subspace clustering models.

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Multi-Level Representation Learning for Deep Subspace Clustering

Cited by 31 publications

References 44 publications

Deep Subspace Clustering with Block Diagonal Constraint

Deep Subspace Clustering with Block Diagonal Constraint

PMSSC: Parallelizable Multi-Subset based Self-Expressive Model for Subspace Clustering

Robust Multiview Subspace Clustering of Images via Tighter Rank Approximation

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