Tensor Dimensionality Reduction and Applications

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  • Tensor Dimensionality Reduction and Applications Book Detail

  • Author : Ruhui Jin
  • Release Date : 2022
  • Publisher :
  • Genre :
  • Pages : 0
  • ISBN 13 :
  • File Size : 32,32 MB

Tensor Dimensionality Reduction and Applications by Ruhui Jin PDF Summary

Book Description: Dimensionality reduction is a fundamental idea in data science and machine learning. Tensor is ubiquitous in modern data science due to its representation power for complex data settings. In this thesis, we study to efficiently reduce the size of tensor-structured data while preserving the essential information. We generalize classical reduction methods for vectors, matrices, such as random projections and low-rank decompositions, to be suitable for higher-order tensors. Numerical experiments show the proposed reduction algorithms result in significant storage savings and computation speed-ups. As a trade-off, from the theoretical perspective, the approximation errors between the original and reduced data are rigorously analyzed. Finally, these tensor dimension reduction techniques find usages in solving inverse problems, anomaly detection and financial portfolio allocation

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Due to advances in sensor, storage, and networking technologies, data is being generated on a daily basis at an ever-increasing pace in a wide range of applicat