2,326 research outputs found
Human Motion Capture Data Tailored Transform Coding
Human motion capture (mocap) is a widely used technique for digitalizing
human movements. With growing usage, compressing mocap data has received
increasing attention, since compact data size enables efficient storage and
transmission. Our analysis shows that mocap data have some unique
characteristics that distinguish themselves from images and videos. Therefore,
directly borrowing image or video compression techniques, such as discrete
cosine transform, does not work well. In this paper, we propose a novel
mocap-tailored transform coding algorithm that takes advantage of these
features. Our algorithm segments the input mocap sequences into clips, which
are represented in 2D matrices. Then it computes a set of data-dependent
orthogonal bases to transform the matrices to frequency domain, in which the
transform coefficients have significantly less dependency. Finally, the
compression is obtained by entropy coding of the quantized coefficients and the
bases. Our method has low computational cost and can be easily extended to
compress mocap databases. It also requires neither training nor complicated
parameter setting. Experimental results demonstrate that the proposed scheme
significantly outperforms state-of-the-art algorithms in terms of compression
performance and speed
Rate-distortion function of the stochastic block model
The stochastic block model (SBM) is extensively used to model networks in which users belong to certain communities. In recent years, the study of information-theoretic compression of such networks has gained attention, with works primarily focusing on lossless compression. In this work, we address the lossy compression of SBM graphs by characterizing the rate-distortion function under a Hamming distortion constraint. Specifically, we derive the conditional rate-distortion function of the SBM with community membership as side information to both the encoder and decoder. We approach this problem as the classical Wyner-Ziv lossy problem by minimising mutual information of the graph and its reconstruction conditioned on community labels. Lastly, we also derive the rate-distortion function of the Erdὄs-Rényl (ER) random graph model
Structural graph matching using the EM algorithm and singular value decomposition
This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding method
Community detection and stochastic block models: recent developments
The stochastic block model (SBM) is a random graph model with planted
clusters. It is widely employed as a canonical model to study clustering and
community detection, and provides generally a fertile ground to study the
statistical and computational tradeoffs that arise in network and data
sciences.
This note surveys the recent developments that establish the fundamental
limits for community detection in the SBM, both with respect to
information-theoretic and computational thresholds, and for various recovery
requirements such as exact, partial and weak recovery (a.k.a., detection). The
main results discussed are the phase transitions for exact recovery at the
Chernoff-Hellinger threshold, the phase transition for weak recovery at the
Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial
recovery, the learning of the SBM parameters and the gap between
information-theoretic and computational thresholds.
The note also covers some of the algorithms developed in the quest of
achieving the limits, in particular two-round algorithms via graph-splitting,
semi-definite programming, linearized belief propagation, classical and
nonbacktracking spectral methods. A few open problems are also discussed
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