This paper considers the problem of subspace clustering under noise. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabelled input data points, which are assumed to lie in a union of low-dimensional subspaces. We show that a modified version of SSC is provably effective in correctly identifying the underlying sub...

Biomedical experts are increasingly confronted with what is often called Big Data, an important subclass of high-dimensional data. High-dimensional data analysis can be helpful in finding relationships between records and dimensions. However, due to data complexity, experts are decreasingly capable of dealing with increasingly complex data. Mapping higher dimensional data to a smaller number of...

Durch Problemstellungen bei der Anwendung von traditionellen Clustering-Algorithmen auf hochdimensionalen Daten motiviert, wurde im Rahmen meiner Diplomarbeit ein neues algorithmisches Konzept zum effizienten Subspace Clustering entwickelt. Eine mögliche Anwendung dieses Konzeptes stellt die Analyse von CGH Daten dar. Durch Subspace Clustering ist es möglich, Gruppen von Patienten zu identifizi...

In this paper, we present an e↵ective tree based subspace clustering technique (TreeCLUS) for finding clusters in network intrusion data and for detecting known as well as unknown attacks without using any labelled tra c or signatures or training. To establish its e↵ectiveness in finding appropriate number of clusters, we perform a cluster stability analysis. We also introduce an e↵ective clust...

In this material, we provide the theoretical analyses to show that the trivial coefficients always correspond to the codes over errors. Lemmas 1–3 show that our errors-removing strategy will perform well when the lp-norm is enforced over the representation, where p = {1, 2,∞}. Let x 6= 0 be a data point in the union of subspaces SD that is spanned by D = [Dx D−x], where Dx and D−x consist of th...

Subspace clustering separates data points approximately lying on union of affine subspaces into several clusters. This paper presents a novel nonparametric Bayesian subspace clustering model that infers both the number of subspaces and the dimension of each subspace from the observed data. Though the posterior inference is hard, our model leads to a very efficient deterministic algorithm, DP-sp...

Subspace clustering refers to the problem of segmenting a set of data points approximately drawn from a union of multiple linear subspaces. Aiming at the subspace clustering problem, various subspace clustering algorithms have been proposed and low rank representation based subspace clustering is a very promising and efficient subspace clustering algorithm. Low rank representation method seeks ...

Data sources representing attribute information in combination with network information are widely available in today’s applications. To realize the full potential for knowledge extraction, mining techniques like clustering should consider both information types simultaneously. Recent clustering approaches combine subspace clustering with dense subgraph mining to identify groups of objects that...

Subspace clustering with missing data (SCMD) is a useful tool for analyzing incomplete datasets. Let d be the ambient dimension, and r the dimension of the subspaces. Existing theory shows that Nk = O(rd) columns per subspace are necessary for SCMD, andNk = O(min{d , d}) are sufficient. We close this gap, showing that Nk = O(rd) is also sufficient. To do this we derive deterministic sampling co...