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Robust Subspace Clustering via Thresholding [article]

Reinhard Heckel, Helmut Bölcskei
2015 arXiv   pre-print
We propose a simple low-complexity subspace clustering algorithm, which applies spectral clustering to an adjacency matrix obtained by thresholding the correlations between data points.  ...  A statistical performance analysis shows that the algorithm exhibits robustness to additive noise and succeeds even when the subspaces intersect.  ...  The resulting algorithm is termed thresholding-based subspace clustering (TSC).  ... 
arXiv:1307.4891v4 fatcat:zpvqqajshnbxvhq4nvrvqirsxa

Robust Subspace Recovery via Bi-Sparsity Pursuit [article]

Xiao Bian, Hamid Krim
2014 arXiv   pre-print
In this paper, we propose a bi-sparse model as a framework to analyze this problem and provide a novel algorithm to recover the union of subspaces in presence of sparse corruptions.  ...  Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces  ...  Our method, what we refer to as robust subspace recovery via bi-sparsity pursuit (RoSuRe), is based on linearized ADMM [10] .  ... 
arXiv:1403.8067v2 fatcat:zko7ckhw3rdbngpqo6pvzye73a

Sparse Subspace Clustering for Concept Discovery (SSCCD) [article]

Johanna Vielhaben, Stefan Blücher, Nils Strodthoff
2022 arXiv   pre-print
We novelly apply sparse subspace clustering to discover these concept subspaces.  ...  We empirically demonstrate the soundness of the proposed Sparse Subspace Clustering for Concept Discovery (SSCCD) method for a variety of different image classification tasks.  ...  via subspaces rather than cluster members.  ... 
arXiv:2203.06043v1 fatcat:yztxyaoxnnefdl74atrhfibgim

Constructing the L2-Graph for Robust Subspace Learning and Subspace Clustering

Xi Peng, Zhiding Yu, Zhang Yi, Huajin Tang
2017 IEEE Transactions on Cybernetics  
Under the framework of graph-based learning, the key to robust subspace clustering and subspace learning is to obtain a good similarity graph that eliminates the effects of errors and retains only connections  ...  The subspace clustering and subspace learning algorithms are developed upon L2-Graph.  ...  Algorithm 2 Robust Subspace Clustering with L2-Graph Input: A collection of data points X = {x i } n i=1 sampled from a union of linear subspaces {S i } c i=1 , the tradeoff parameter λ and thresholding  ... 
doi:10.1109/tcyb.2016.2536752 pmid:26992192 fatcat:ebinye2mz5cb5nvq55zd2lfoby

Mining Actionable Subspace Clusters in Sequential Data [chapter]

Kelvin Sim, Ardian Kristanto Poernomo, Vivekanand Gopalkrishnan
2010 Proceedings of the 2010 SIAM International Conference on Data Mining  
We conduct a wide range of experiments to demonstrate the actionability of the clusters and the robustness of our framework MASC.  ...  We propose to mine actionable subspace clusters from sequential data, which are subspaces with high and correlated utilities.  ...  However, setting the correct thresholds to obtain significant subspace clusters from real-world data is generally a guessing game, and these subspace clusters are usually sensitive to these thresholds,  ... 
doi:10.1137/1.9781611972801.39 dblp:conf/sdm/SimPG10 fatcat:yjy5qgv7fzgqfbvpbxeogdww5i

One-Step Robust Low-Rank Subspace Segmentation for Tumor Sample Clustering

Jian Liu, Yuhu Cheng, Xuesong Wang, Shuguang Ge, Wei Xiang
2021 Computational Intelligence and Neuroscience  
Low-rank subspace clustering is a popular algorithm in recent years. In this paper, we propose a novel one-step robust low-rank subspace segmentation method (ORLRS) for clustering the tumor sample.  ...  By imposing the discrete constraint on the low-rank matrix, without performing spectral clustering, ORLRS learns the cluster indicators of subspaces directly, i.e., performing the clustering task in one  ...  In this paper, we propose the one-step robust low-rank subspace clustering (ORLRS) method via discrete constraint and capped norm.  ... 
doi:10.1155/2021/9990297 pmid:34925501 pmcid:PMC8674076 fatcat:pyh73frin5erxearlbijzxmcqa

Subspace clustering with dense representations

Eva L. Dyer, Christoph Studer, Richard G. Baraniuk
2013 2013 IEEE International Conference on Acoustics, Speech and Signal Processing  
The resulting representations are then used as feature vectors to cluster the data in accordance with each signal's subspace membership.  ...  We demonstrate that the proposed least-squares approach leads to improved classification performance when compared to stateof-the-art subspace clustering methods on both synthetic and real-world experiments  ...  Algorithm 1 : 1 Dense subspace clustering (DSC) Input: Set of d vectors Y ∈ R n×d , number of subspace clusters p, and singular value threshold τ .  ... 
doi:10.1109/icassp.2013.6638260 dblp:conf/icassp/DyerSB13 fatcat:phjkepjbwrglnowgae3tlod7om

DUSC: Dimensionality Unbiased Subspace Clustering

Ira Assent, Ralph Krieger, Emmanuel Müller, Thomas Seidl
2007 Seventh IEEE International Conference on Data Mining (ICDM 2007)  
For these applications, subspace clustering methods aim at detecting clusters in any subspace. Existing subspace clustering approaches fall prey to an effect we call dimensionality bias.  ...  for subspace clustering • definition of density based on statistical foundations • dimensionality unbiased subspace clustering model • powerful pruning properties  ...  Acknowledgments: This research was funded in part by the cluster of excellence on Ultra-high speed Mobile Information and Communication (UMIC) of the DFG (German Research Foundation grant EXC 89).  ... 
doi:10.1109/icdm.2007.49 dblp:conf/icdm/AssentKMS07 fatcat:xpcpscejrjbpzazkrgannqyl6q

Kernel Truncated Regression Representation for Robust Subspace Clustering [article]

Liangli Zhen, Dezhong Peng, Wei Wang, Xin Yao
2020 arXiv   pre-print
Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace.  ...  Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this assumption usually does not hold.  ...  KTRR for Robust Subspace Clustering In this section, we present the method to achieve subspace clustering by incorporating KTRR into the spectral clustering framework [31] .  ... 
arXiv:1705.05108v3 fatcat:obqzayltmbco3esxpx737syvg4

Flexible Fault Tolerant Subspace Clustering for Data with Missing Values

Stephan Gunnemann, Emmanuel Muller, Sebastian Raubach, Thomas Seidl
2011 2011 IEEE 11th International Conference on Data Mining  
We introduce a flexible notion of fault tolerance that adapts to the individual characteristics of subspace clusters and ensures a robust parameterization.  ...  Subspace clustering tackles the challenge of many attributes by cluster detection in any subspace projection of the data.  ...  With our variable thresholds we realize a flexible model that adapts to the individual cluster characteristics and that ensures a robust parameterization.  ... 
doi:10.1109/icdm.2011.70 dblp:conf/icdm/GunnemannMRS11 fatcat:lnmvpdht7rhldbepv3hhovh4fq

Kernel Truncated Regression Representation for Robust Subspace Clustering

Liangli Zhen, Dezhong Peng, Wei Wang, Xin Yao
2020 Information Sciences  
KTRR for Robust Subspace Clustering In this section, we present the method to achieve subspace clustering by incorporating KTRR into the spectral clustering framework [25] .  ...  We propose to remove these errors through hard thresholding on each column vector of the coefficient matrix C * via (17).  ... 
doi:10.1016/j.ins.2020.03.033 fatcat:m27dju426bdvblakjczmwqznvy

Quantum entanglement via two-qubit quantum Zeno dynamics

Xiang-Bin Wang, J. Q. You, Franco Nori
2008 Physical Review A. Atomic, Molecular, and Optical Physics  
If the rotation of each step is sufficiently small, the quantum Zeno effect will guarantee that the state is projected into the intended subspace after each measurement, and an almost-perfect cluster state  ...  We propose a method to generate large cluster states without using conditional (e.g., CNOT, C-phase) gates.  ...  We show that one can actually produce, almost deterministically, quantum entanglement, such as a cluster state via nondeterministic measurements, which we name "threshold measurements" or "J−measurements  ... 
doi:10.1103/physreva.77.062339 fatcat:p2nxtmfmnvaetcloooxkl5qhi4

Point cloud normal estimation via low-rank subspace clustering

Jie Zhang, Junjie Cao, Xiuping Liu, Jun Wang, Jian Liu, Xiquan Shi
2013 Computers & graphics  
In this paper, we present a robust normal estimation algorithm based on the low-rank subspace clustering technique.  ...  Then we segment the anisotropic neighborhood into several isotropic neighborhoods by low-rank subspace clustering with the guiding matrix, and identify a consistent subneighborhood for the current point  ...  The closed-form solutions of step 1 and step 4 can be solved via Soft Value Thresholding (SVT) operator [38] and the Lemma 3.2 in [13] , respectively.  ... 
doi:10.1016/j.cag.2013.05.008 fatcat:pox2qej5kfapdpgvtja7p6iao4

Multiple structure recovery via robust preference analysis

Luca Magri, Andrea Fusiello
2017 Image and Vision Computing  
First points are represented in the preference space, then Robust PCA (Principal Component Analysis) and Symmetric NMF (Non negative Matrix Factorization) are used to break the multi-model fitting problem  ...  of subspaces.  ...  Appendix A reviews some ideas, firstly emerged in the context of subspace clustering, that are extended to our general multi-model fitting problem.  ... 
doi:10.1016/j.imavis.2017.09.005 fatcat:ibck4muv2jagvbicz6njlsy76i

Improved Image Set Classification via Joint Sparse Approximated Nearest Subspaces

Shaokang Chen, Conrad Sanderson, Mehrtash T. Harandi, Brian C. Lovell
2013 2013 IEEE Conference on Computer Vision and Pattern Recognition  
We then extract local linear subspaces from a gallery image set via sparse representation.  ...  For each local linear subspace, we adaptively construct the corresponding closest subspace from the samples of a probe image set by joint sparse representation.  ...  In contrast, we propose to adaptively cluster the query image set via considering the clusters from a gallery image set.  ... 
doi:10.1109/cvpr.2013.65 dblp:conf/cvpr/ChenSHL13 fatcat:tkjau746sjfxze3g2tpuasukwq
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