Dimensionality-reduced subspace clustering

Heckel, Reinhard; Tschannen, Michael; Bölcskei, Helmut

doi:10.1093/imaiai/iaw021

Cited by 30 publications

(34 citation statements)

References 35 publications

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“…Remark 8. One can sketch data more aggressively if the subspaces are not similar to each other [70]. This is also captured in Corollary 3 as follows.…”

Section: B Sketching Algorithms For Subspace Clusteringmentioning

confidence: 96%

Hypergraph Spectral Clustering in the Weighted Stochastic Block Model

Ahn

Lee

Suh

2018

IEEE J. Sel. Top. Signal Process.

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Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there are many other applications in which only multi-way similarity measures are available. This motivates us to explore the multi-way measurement setting. In this work, we develop two algorithms intended for such setting: Hypergraph Spectral Clustering (HSC) and Hypergraph Spectral Clustering with Local Refinement (HSCLR). Our main contribution lies in performance analysis of the poly-time algorithms under a random hypergraph model, which we name the weighted stochastic block model, in which objects and multi-way measures are modeled as nodes and weights of hyperedges, respectively. Denoting by n the number of nodes, our analysis reveals the following: (1) HSC outputs a partition which is better than a random guess if the sum of edge weights (to be explained later) is Ω(n); (2) HSC outputs a partition which coincides with the hidden partition except for a vanishing fraction of nodes if the sum of edge weights is ω(n); and (3) HSCLR exactly recovers the hidden partition if the sum of edge weights is on the order of n log n. Our results improve upon the state of the arts recently established under the model and they firstly settle the order-wise optimal results for the binary edge weight case. Moreover, we show that our results lead to efficient sketching algorithms for subspace clustering, a computer vision application. Lastly, we show that HSCLR achieves the information-theoretic limits for a special yet practically relevant model, thereby showing no computational barrier for the case.

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“…Remark 8. One can sketch data more aggressively if the subspaces are not similar to each other [70]. This is also captured in Corollary 3 as follows.…”

Section: B Sketching Algorithms For Subspace Clusteringmentioning

confidence: 96%

Hypergraph Spectral Clustering in the Weighted Stochastic Block Model

Ahn

Lee

Suh

2018

IEEE J. Sel. Top. Signal Process.

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“…To follow the same path, we also perform PCA on the feature vectors. However, one can instead use randomized dimension reduction methods that are shown to be useful for achieving high accuracy in the SSC framework [28,29,30].…”

Section: Resultsmentioning

confidence: 99%

Large-Scale Sparse Subspace Clustering Using Landmarks

Pourkamali-Anaraki

2019

2019 IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)

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Subspace clustering methods based on expressing each data point as a linear combination of all other points in a dataset are popular unsupervised learning techniques. However, existing methods incur high computational complexity on large-scale datasets as they require solving an expensive optimization problem and performing spectral clustering on large affinity matrices. This paper presents an efficient approach to subspace clustering by selecting a small subset of the input data called landmarks. The resulting subspace clustering method in the reduced domain runs in linear time with respect to the size of the original data. Numerical experiments on synthetic and real data demonstrate the effectiveness of our method. * This paper is accepted for publication in 2019 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), Pittsburgh, PA, USA.

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“…The effect is that OSC tends to assign non-zero weights to the same points as SSC and additionally selects neighbors of these points in terms of Euclidean distance. All of the above methods, including OSC, can be carried out on dimensionality reduced data points, in the spirit of [19,9]. We compare the performance of these methods in Section 5.…”

Section: Relation To Prior Workmentioning

confidence: 99%

Scalable Sparse Subspace Clustering via Ordered Weighted l<inf>1</inf> Regression

Oswal

Nowak

2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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The main contribution of the paper is a new approach to subspace clustering that is significantly more computationally efficient and scalable than existing stateof-the-art methods. The central idea is to modify the regression technique in sparse subspace clustering (SSC) by replacing the 1 minimization with a generalization called Ordered Weighted 1 (OWL) minimization which performs simultaneous regression and clustering of correlated variables. Using random geometric graph theory, we prove that OWL regression selects more points within each subspace, resulting in better clustering results. This allows for accurate subspace clustering based on regression solutions for only a small subset of the total dataset, significantly reducing the computational complexity compared to SSC. In experiments, we find that our OWL approach can achieve a speedup of 20× to 30× for synthetic problems and 4× to 8× on real data problems.* 1 Urvashi Oswal is with the

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Dimensionality-reduced subspace clustering

Cited by 30 publications

References 35 publications

Hypergraph Spectral Clustering in the Weighted Stochastic Block Model

Hypergraph Spectral Clustering in the Weighted Stochastic Block Model

Large-Scale Sparse Subspace Clustering Using Landmarks

Scalable Sparse Subspace Clustering via Ordered Weighted l<inf>1</inf> Regression

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