588 research outputs found
Consistency of Spectral Hypergraph Partitioning under Planted Partition Model
Hypergraph partitioning lies at the heart of a number of problems in machine
learning and network sciences. Many algorithms for hypergraph partitioning have
been proposed that extend standard approaches for graph partitioning to the
case of hypergraphs. However, theoretical aspects of such methods have seldom
received attention in the literature as compared to the extensive studies on
the guarantees of graph partitioning. For instance, consistency results of
spectral graph partitioning under the stochastic block model are well known. In
this paper, we present a planted partition model for sparse random non-uniform
hypergraphs that generalizes the stochastic block model. We derive an error
bound for a spectral hypergraph partitioning algorithm under this model using
matrix concentration inequalities. To the best of our knowledge, this is the
first consistency result related to partitioning non-uniform hypergraphs.Comment: 35 pages, 2 figures, 1 tabl
Learning Hypergraph-regularized Attribute Predictors
We present a novel attribute learning framework named Hypergraph-based
Attribute Predictor (HAP). In HAP, a hypergraph is leveraged to depict the
attribute relations in the data. Then the attribute prediction problem is
casted as a regularized hypergraph cut problem in which HAP jointly learns a
collection of attribute projections from the feature space to a hypergraph
embedding space aligned with the attribute space. The learned projections
directly act as attribute classifiers (linear and kernelized). This formulation
leads to a very efficient approach. By considering our model as a multi-graph
cut task, our framework can flexibly incorporate other available information,
in particular class label. We apply our approach to attribute prediction,
Zero-shot and -shot learning tasks. The results on AWA, USAA and CUB
databases demonstrate the value of our methods in comparison with the
state-of-the-art approaches.Comment: This is an attribute learning paper accepted by CVPR 201
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