Subspace Clustering

Clustering is one of the most commonly used data exploration tools, but data often hold interesting geometric structure for which generic clustering objectives are too coarse. Subspace clustering is a simple generalization that tries to fit each cluster with a low-dimensional subspace (ie, each cluster has a low-dimensional covariance structure). This is a very useful model for many problems in computer vision and computer network topology inference. Our group has developed state-of-the-art approaches for subspace clustering when the data matrix is incomplete and in the active clustering context.

Lipor, John, David Hong, Yan Shuo Tan, and Laura Balzano. 2021. “Subspace Clustering Using Ensembles of K-Subspaces.” Information and Inference: A Journal of the IMA 10 (1): 73–107. https://doi.org/10.1093/imaiai/iaaa031.
Lipor, John, and Laura Balzano. 2020. “Clustering Quality Metrics for Subspace Clustering.” Pattern Recognition, March, 107328. https://doi.org/10.1016/j.patcog.2020.107328.
Pimentel-Alarcón, D., G. Ongie, L. Balzano, R. Willett, and R. Nowak. 2017. “Low Algebraic Dimension Matrix Completion.” In 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 790–97. https://doi.org/10.1109/ALLERTON.2017.8262820.
Ongie, Greg, Rebecca Willett, Robert D. Nowak, and Laura Balzano. 2017. “Algebraic Variety Models for High-Rank Matrix Completion.” In PMLR, 2691–2700. http://proceedings.mlr.press/v70/ongie17a.html.
Lipor, John, and Laura Balzano. 2017. “Leveraging Union of Subspace Structure to Improve Constrained Clustering.” In PMLR, 2130–39. http://proceedings.mlr.press/v70/lipor17a.html.
Pimentel-Alarcón, D., L. Balzano, R. Marcia, R. Nowak, and R. Willett. 2017. “Mixture Regression as Subspace Clustering.” In 2017 International Conference on Sampling Theory and Applications (SampTA), 456–59. https://doi.org/10.1109/SAMPTA.2017.8024386.
Pimentel-Alarcón, D., L. Balzano, and R. Nowak. 2016. “Necessary and Sufficient Conditions for Sketched Subspace Clustering.” In 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 1335–43. https://doi.org/10.1109/ALLERTON.2016.7852389.
Pimentel-Alarcón, D., L. Balzano, R. Marcia, R. Nowak, and R. Willett. 2016. “Group-Sparse Subspace Clustering with Missing Data.” In 2016 IEEE Statistical Signal Processing Workshop (SSP), 1–5. https://doi.org/10.1109/SSP.2016.7551734.
Pimentel-Alarcón, D., L. Balzano, R. Marcia, R. Nowak, and R. Willett. 2016. “Group-Sparse Subspace Clustering with Missing Data.” In 2016 IEEE Statistical Signal Processing Workshop (SSP), 1–5. https://doi.org/10.1109/SSP.2016.7551734.
Lipor, J., and L. Balzano. 2015. “Margin-Based Active Subspace Clustering.” In 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 377–80. https://doi.org/10.1109/CAMSAP.2015.7383815.
Pimentel, D., R. Nowak, and L. Balzano. 2014. “On the Sample Complexity of Subspace Clustering with Missing Data.” In 2014 IEEE Workshop on Statistical Signal Processing (SSP), 280–83. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6884630.
Eriksson, Brian, Laura Balzano, and Robert Nowak. 2012. “High Rank Matrix Completion.” In Proc. of Intl. Conf. on Artificial Intell. and Stat. http://jmlr.csail.mit.edu/proceedings/papers/v22/eriksson12/eriksson12.pdf. 1
Balzano, Laura, Arthur Szlam, Benjamin Recht, and Robert Nowak. 2012. “K-Subspaces with Missing Data.” In Statistical Signal Processing Workshop (SSP), 2012 IEEE, 612–615. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6319774.