21,270 research outputs found
The Vertex Reinforced Jump Process and a Random Schr\"odinger operator on finite graphs
We introduce a new exponential family of probability distributions, which can
be viewed as a multivariate generalization of the Inverse Gaussian
distribution. Considered as the potential of a random Schr\"odinger operator,
this exponential family is related to the random field that gives the mixing
measure of the Vertex Reinforced Jump Process (VRJP), and hence to the mixing
measure of the Edge Reinforced Random Walk (ERRW), the so-called magic formula.
In particular, it yields by direct computation the value of the normalizing
constants of these mixing measures, which solves a question raised by Diaconis.
The results of this paper are instrumental in [Sabot-Zeng,2015], where several
properties of the VRJP and the ERRW are proved, in particular a functional
central limit theorem in transient regimes, and recurrence of the 2-dimensional
ERRW.Comment: 15 page
Hyperspectral image compression : adapting SPIHT and EZW to Anisotropic 3-D Wavelet Coding
Hyperspectral images present some specific characteristics that should be used by an efficient compression system. In compression, wavelets have shown a good adaptability to a wide range of data, while being of reasonable complexity. Some wavelet-based compression algorithms have been successfully used for some hyperspectral space missions. This paper focuses on the optimization of a full wavelet compression system for hyperspectral images. Each step of the compression algorithm is studied and optimized. First, an algorithm to find the optimal 3-D wavelet decomposition in a rate-distortion sense is defined. Then, it is shown that a specific fixed decomposition has almost the same performance, while being more useful in terms of complexity issues. It is shown that this decomposition significantly improves the classical isotropic decomposition. One of the most useful properties of this fixed decomposition is that it allows the use of zero tree algorithms. Various tree structures, creating a relationship between coefficients, are compared. Two efficient compression methods based on zerotree coding (EZW and SPIHT) are adapted on this near-optimal decomposition with the best tree structure found. Performances are compared with the adaptation of JPEG 2000 for hyperspectral images on six different areas presenting different statistical properties
Overlapping stochastic block models with application to the French political blogosphere
Complex systems in nature and in society are often represented as networks,
describing the rich set of interactions between objects of interest. Many
deterministic and probabilistic clustering methods have been developed to
analyze such structures. Given a network, almost all of them partition the
vertices into disjoint clusters, according to their connection profile.
However, recent studies have shown that these techniques were too restrictive
and that most of the existing networks contained overlapping clusters. To
tackle this issue, we present in this paper the Overlapping Stochastic Block
Model. Our approach allows the vertices to belong to multiple clusters, and, to
some extent, generalizes the well-known Stochastic Block Model [Nowicki and
Snijders (2001)]. We show that the model is generically identifiable within
classes of equivalence and we propose an approximate inference procedure, based
on global and local variational techniques. Using toy data sets as well as the
French Political Blogosphere network and the transcriptional network of
Saccharomyces cerevisiae, we compare our work with other approaches.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS382 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Adaptation of Zerotrees Using Signed Binary Digit Representations for 3D Image Coding
Zerotrees of wavelet coefficients have shown a good adaptability for the compression of three-dimensional images. EZW, the original algorithm using zerotree, shows good performance and was successfully adapted to 3D image compression. This paper focuses on the adaptation of EZW for the compression of hyperspectral images. The subordinate pass is suppressed to remove the necessity to keep the significant pixels in memory. To compensate the loss due to this removal, signed binary digit representations are used to increase the efficiency of zerotrees. Contextual arithmetic coding with very limited contexts is also used. Finally, we show that this simplified version of 3D-EZW performs almost as well as the original one
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