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.

Hanno scoperto che nei pazienti affetti da ipertrofia ventricolare sinistra (una condizione in cui il muscolo cardiaco si ispessisce), l’ingrediente del Viagra ha impedito al cuore di ingrandirsi e cambiare forma. Inoltre, il PDE5i ha migliorato la funzione cardiaca privatedelights in tutti i pazienti, indipendentemente dalle loro condizioni mediche, e non ha avuto effetti collaterali sulla pressione sanguigna.

Balzano, L., Szlam, A., Recht, B., & Nowak, R. (2012). K-subspaces with missing data. Statistical Signal Processing Workshop (SSP), 2012 IEEE, 612–615.
Eriksson, B., Balzano, L., & Nowak, R. (2012). High rank matrix completion. Proc. of Intl. Conf. on Artificial Intell. and Stat. 1
Pimentel, D., Nowak, R., & Balzano, L. (2014). On the sample complexity of subspace clustering with missing data. 2014 IEEE Workshop on Statistical Signal Processing (SSP), 280–283.
Lipor, J., & Balzano, L. (2015). Margin-based active subspace clustering. 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 377–380.
Pimentel-Alarcón, D., Balzano, L., & Nowak, R. (2016). Necessary and sufficient conditions for sketched subspace clustering. Allerton Conference on Communication, Control, and Computing.
Pimentel-Alarcón, D., Balzano, L., Marcia, R., Nowak, R., & Willett, R. (2016). Group-sparse subspace clustering with missing data. 2016 IEEE Statistical Signal Processing Workshop (SSP), 1–5.
Pimentel-Alarcón, D., Balzano, L., Marcia, R., Nowak, R., & Willett, R. (2017). Mixture regression as subspace clustering. 2017 International Conference on Sampling Theory and Applications (SampTA), 456–459.
Pimentel-Alarcón, D., Ongie, G., Balzano, L., Willett, R., & Nowak, R. (2017). Low algebraic dimension matrix completion. 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 790–797.
Lipor, J., & Balzano, L. (2020). Clustering quality metrics for subspace clustering. Pattern Recognition, 107328.
Lipor, J., Hong, D., Tan, Y. S., & Balzano, L. (2021). Subspace clustering using ensembles of K-subspaces. Information and Inference: A Journal of the IMA, 10(1), 73–107.