Given a graph between N high-dimensional nodes, can we faithfully visualize
it in just a few dimensions? We present an algorithm that improves the
state-of-the art in dimensionality reduction and visualization by extending
the Maximum Variance Unfolding method. Visualizations are shown for social
networks, species trees, image datasets and human activity.
If the connectivity between N nodes is unknown, can we link them to build a
graph? The space to explore is daunting with 2^(N^2) choices but two
interesting subfamilies are tractable: matchings and b-matchings. We place
distributions over these families and recover the optimal graph or perform
Bayesian inference over graphs efficiently using belief propagation
algorithms. Higher order distributions over matchings can also be handled
efficiently via fast Fourier algorithms. Applications are shown in
tracking, classification, and clustering.
Selected publications:
B. Shaw and T. Jebara. "Minimum Volume Embedding".
Artificial Intelligence and Statistics, AISTATS, March 2007.
B. Huang and T. Jebara. "Loopy Belief Propagation for Bipartite
Maximum Weight b-Matching". Artificial Intelligence and Statistics,
AISTATS, March 2007.
R. Kondor, A. Howard and T. Jebara. "Multi-Object Tracking with
Representations of the Symmetric Group". Artificial Intelligence and
Statistics, AISTATS, March 2007.
T. Jebara and V. Shchogolev. "B-Matching for Spectral Clustering" .
European Conference on Machine Learning, ECML, September 2006.
P. Shivaswamy and T. Jebara. "Permutation Invariant SVMs" .
International Conference on Machine Learning, ICML, June 2006.
