43,369 research outputs found
Unsupervised Domain Adaptation using Regularized Hyper-graph Matching
Domain adaptation (DA) addresses the real-world image classification problem
of discrepancy between training (source) and testing (target) data
distributions. We propose an unsupervised DA method that considers the presence
of only unlabelled data in the target domain. Our approach centers on finding
matches between samples of the source and target domains. The matches are
obtained by treating the source and target domains as hyper-graphs and carrying
out a class-regularized hyper-graph matching using first-, second- and
third-order similarities between the graphs. We have also developed a
computationally efficient algorithm by initially selecting a subset of the
samples to construct a graph and then developing a customized optimization
routine for graph-matching based on Conditional Gradient and Alternating
Direction Multiplier Method. This allows the proposed method to be used widely.
We also performed a set of experiments on standard object recognition datasets
to validate the effectiveness of our framework over state-of-the-art
approaches.Comment: Final version appeared in IEEE International Conference on Image
Processing 201
A Decomposition Theorem for Maximum Weight Bipartite Matchings
Let G be a bipartite graph with positive integer weights on the edges and
without isolated nodes. Let n, N and W be the node count, the largest edge
weight and the total weight of G. Let k(x,y) be log(x)/log(x^2/y). We present a
new decomposition theorem for maximum weight bipartite matchings and use it to
design an O(sqrt(n)W/k(n,W/N))-time algorithm for computing a maximum weight
matching of G. This algorithm bridges a long-standing gap between the best
known time complexity of computing a maximum weight matching and that of
computing a maximum cardinality matching. Given G and a maximum weight matching
of G, we can further compute the weight of a maximum weight matching of G-{u}
for all nodes u in O(W) time.Comment: The journal version will appear in SIAM Journal on Computing. The
conference version appeared in ESA 199
Belief-Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions
We consider the general problem of finding the minimum weight \bm-matching
on arbitrary graphs. We prove that, whenever the linear programming (LP)
relaxation of the problem has no fractional solutions, then the belief
propagation (BP) algorithm converges to the correct solution. We also show that
when the LP relaxation has a fractional solution then the BP algorithm can be
used to solve the LP relaxation. Our proof is based on the notion of graph
covers and extends the analysis of (Bayati-Shah-Sharma 2005 and Huang-Jebara
2007}.
These results are notable in the following regards: (1) It is one of a very
small number of proofs showing correctness of BP without any constraint on the
graph structure. (2) Variants of the proof work for both synchronous and
asynchronous BP; it is the first proof of convergence and correctness of an
asynchronous BP algorithm for a combinatorial optimization problem.Comment: 28 pages, 2 figures. Submitted to SIAM journal on Discrete
Mathematics on March 19, 2009; accepted for publication (in revised form)
August 30, 2010; published electronically July 1, 201
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