418 research outputs found
Computing the Kullback-Leibler Divergence between two Weibull Distributions
We derive a closed form solution for the Kullback-Leibler divergence between
two Weibull distributions. These notes are meant as reference material and
intended to provide a guided tour towards a result that is often mentioned but
seldom made explicit in the literature
Efficient Information Theoretic Clustering on Discrete Lattices
We consider the problem of clustering data that reside on discrete, low
dimensional lattices. Canonical examples for this setting are found in image
segmentation and key point extraction. Our solution is based on a recent
approach to information theoretic clustering where clusters result from an
iterative procedure that minimizes a divergence measure. We replace costly
processing steps in the original algorithm by means of convolutions. These
allow for highly efficient implementations and thus significantly reduce
runtime. This paper therefore bridges a gap between machine learning and signal
processing.Comment: This paper has been presented at the workshop LWA 201
Maximum Entropy Models of Shortest Path and Outbreak Distributions in Networks
Properties of networks are often characterized in terms of features such as
node degree distributions, average path lengths, diameters, or clustering
coefficients. Here, we study shortest path length distributions. On the one
hand, average as well as maximum distances can be determined therefrom; on the
other hand, they are closely related to the dynamics of network spreading
processes. Because of the combinatorial nature of networks, we apply maximum
entropy arguments to derive a general, physically plausible model. In
particular, we establish the generalized Gamma distribution as a continuous
characterization of shortest path length histograms of networks or arbitrary
topology. Experimental evaluations corroborate our theoretical results
Propagation Kernels
We introduce propagation kernels, a general graph-kernel framework for
efficiently measuring the similarity of structured data. Propagation kernels
are based on monitoring how information spreads through a set of given graphs.
They leverage early-stage distributions from propagation schemes such as random
walks to capture structural information encoded in node labels, attributes, and
edge information. This has two benefits. First, off-the-shelf propagation
schemes can be used to naturally construct kernels for many graph types,
including labeled, partially labeled, unlabeled, directed, and attributed
graphs. Second, by leveraging existing efficient and informative propagation
schemes, propagation kernels can be considerably faster than state-of-the-art
approaches without sacrificing predictive performance. We will also show that
if the graphs at hand have a regular structure, for instance when modeling
image or video data, one can exploit this regularity to scale the kernel
computation to large databases of graphs with thousands of nodes. We support
our contributions by exhaustive experiments on a number of real-world graphs
from a variety of application domains
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