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Spectral Clustering meets Graphical Models

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VMVW01 - Variational methods, new optimisation techniques and new fast numerical algorithms

Co-authors: Dmitri Marin (UWO), Meng Tang (UWO), Ismail Ben Ayed (ETS, Montreal)

This talk discusses two seemingly unrelated data analysis methodologies: kernel clustering and graphical models. Clustering is widely used for general data where kernel methods are particularly popular due to their discriminating power. Graphical models such as Markov Random Fields (MRF) and related continuous geometric methods represent the state-of-the-art regularization methodology for image segmentation. While both clustering and regularization models are very widely used in machine learning and computer vision, they were not combined before due to significant differences in the corresponding optimization, e.g. spectral relaxation vs. combinatorial methods for submodular optimization and its approximations. This talk reviews the general properties of kernel clustering and graphical models, discusses their limitations (including newly discovered “density biases” in kernel methods), and proposes a general unified framework based on our new bound optimization algor ithm. In particular, we show that popular MRF potentials introduce principled geometric and contextual constraints into clustering, while standard kernel methodology allows graphical models to work with arbitrary high-dimensional features.

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