95,821 research outputs found
On Algorithms for and Computing with the Tensor Ring Decomposition
Tensor decompositions such as the canonical format and the tensor train
format have been widely utilized to reduce storage costs and operational
complexities for high-dimensional data, achieving linear scaling with the input
dimension instead of exponential scaling. In this paper, we investigate even
lower storage-cost representations in the tensor ring format, which is an
extension of the tensor train format with variable end-ranks. Firstly, we
introduce two algorithms for converting a tensor in full format to tensor ring
format with low storage cost. Secondly, we detail a rounding operation for
tensor rings and show how this requires new definitions of common linear
algebra operations in the format to obtain storage-cost savings. Lastly, we
introduce algorithms for transforming the graph structure of graph-based tensor
formats, with orders of magnitude lower complexity than existing literature.
The efficiency of all algorithms is demonstrated on a number of numerical
examples, and in certain cases, we demonstrate significantly higher compression
ratios when compared to previous approaches to using the tensor ring format.Comment: 24 pages, 3 figures, 6 tables, implementation of algorithms available
at https://github.com/oscarmickelin/tensor-ring-decompositio
The edge cloud: A holistic view of communication, computation and caching
The evolution of communication networks shows a clear shift of focus from
just improving the communications aspects to enabling new important services,
from Industry 4.0 to automated driving, virtual/augmented reality, Internet of
Things (IoT), and so on. This trend is evident in the roadmap planned for the
deployment of the fifth generation (5G) communication networks. This ambitious
goal requires a paradigm shift towards a vision that looks at communication,
computation and caching (3C) resources as three components of a single holistic
system. The further step is to bring these 3C resources closer to the mobile
user, at the edge of the network, to enable very low latency and high
reliability services. The scope of this chapter is to show that signal
processing techniques can play a key role in this new vision. In particular, we
motivate the joint optimization of 3C resources. Then we show how graph-based
representations can play a key role in building effective learning methods and
devising innovative resource allocation techniques.Comment: to appear in the book "Cooperative and Graph Signal Pocessing:
Principles and Applications", P. Djuric and C. Richard Eds., Academic Press,
Elsevier, 201
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