Multilinear Subspace Learning Via Linear Tansforms and Grassmannian Manifold Analysis

Released on by Cagri Ozdemir
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  • Multilinear Subspace Learning Via Linear Tansforms and Grassmannian Manifold Analysis Book Detail

  • Author : Cagri Ozdemir
  • Release Date : 2023
  • Publisher :
  • Genre :
  • Pages : 0
  • ISBN 13 :
  • File Size : 76,76 MB
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Multilinear Subspace Learning Via Linear Tansforms and Grassmannian Manifold Analysis by Cagri Ozdemir PDF Summary

Book Description: Furthermore, in general, the number of observations is relatively small compared to the feature vector dimension potentially resulting in poor conditioning (referred to as the small sample size problem). Due to these issues, particularly when dealing with higher-order data with high dimensionality, there has been a growing interest in multilinear subspace learning (MSL) to maintain the natural representation of multidimensional arrays (commonly referred to as tensors). To best explore, analyze, and provide insights from such data, new mathematical tools are required in an effort to bridge the gap between traditional machine learning models and their multilinear counterparts. In this dissertation, we present new approaches and formulate mathematical theories to deal with such data using a multilinear (tensor-tensor) perspective. In particular, we provide insights into several different application areas within the machine learning community and illustrate how multilinear extensions can be achieved.

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