Ruprecht-Karls-Universität Heidelberg




HCI Colloquia

56. Heidelberger Bildverarbeitungsforum

Schwerpunktthema: "Bildverarbeitungssoftware: Anforderungen, Qualitätskriterien und Standardbibliotheken"

Das 56. Heidelberger Bildverarbeitungsforum findet am Dienstag, 7. Oktober von 11 - 17.15 Uhr am HCI statt.
Das Programm kann direkt hier angesehen oder von der Webseite heruntergeladen werden.

Estimating Maximally Probable Constrained Relations by Mathematical Programming

Björn Andres, MPI für Informatik, Saarbrücken

21.10.2014, 16:15, big seminar room

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a linear order on a set). We contribute a family of probability measures on the set of all relations between two finite, non-empty sets, which offers a joint abstraction of multi-label classification, correlation clustering and ranking by linear ordering. Estimating (learning) a maximally probable measure, given (a training set of) related and unrelated pairs, is a convex optimization problem. Estimating (inferring) a maximally probable relation, given a measure, is a 01-linear program. It is solved in linear time for maps. It is NP-hard for equivalence relations and linear orders. Practical solutions for all three cases are shown in experiments with real data. Finally, estimating a maximally probable measure and relation jointly is posed as a mixed-integer nonlinear program. This formulation suggests a mathematical programming approach to semi-supervised learning.

Planar Correlation Clustering and Higher Order Potentials

Julian Yarkony (UC Santa Barbara)

16.07.2013, 16:15, big seminar room

In this talk we consider the problem of correlation clustering for image segmentation. We introduce the PlanarCC (Yarkony et al 2012) solver for planar correlation clustering. Next we introduce long range repulsive potentials to dual decomposition using PlanarCC (Andres, Yarkony et al 2013 submission). Finally we consider a large series of higher order potentials and prove why dual decomposition tends not to produce tight bounds easily. We apply this knowledge to analyzing Diverse M Best for planar correlation clustering (Yarkony et al 2013 submission).

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