Séminaire du 24/03/2017, 14h00

vendredi 24 mars 2017, 14h00

Optimization on hierarchies of partitions

Conférencier : Ravi Kiran (CRIStAL)

The following talk will be split into three parts. They correspond to work that I have done during my PhD, and two post-docs.

In the first and principal part, we find the optimal cut in a hierarchy of partitions for a given energy by dynamic programming. Our approach formulates this particular dynamic program's sub-structure using the energetic lattice on the partitions. This approach allows us to characterize the possible energies that could be minimized, which must be h-increasing (which includes the classical additive energies). Further we characterize the braids to be the largest family of partitions which preserves the sub-structure. Applications to image segmentation illustrate the approach.

The second part of the talk will present the application of hyper-spectral imaging to the challenging problem of brain tumour detection in-vivo, in the lack of reliable ground truth. We explore the use of hierarchical clustering and hierarchical non-negative matrix factorization to the problem of hyper-spectral image segmentation. We further study the use of points in the image verified to be tumours by pathology as markers, to provide supervision for segmentation.

The third part will discuss the use of streaming principal subspace tracking on univariate time series for the purpose of unsupervised anomaly detection. This unsupervised approach also provides us a general way to identify the scale at which an anomaly appears. We discuss results on the Yahoo! and Numenta unsupervised anomaly evaluation benchmark-dataset.