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Advances in Tensor Analysis with Applications in Text Mining

Sobhani, Elaheh | 2022

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  1. Type of Document: Ph.D. Dissertation
  2. Language: English
  3. Document No: 53771 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babaiezadeh, Masoud; Comon, Pierre; Jutten, Christian
  7. Abstract:
  8. Tensors or multi-way arrays are useful tools to identify unknown quantities thanks to the uniqueness of their decomposition. Tensor decompositions have been widely applied to obtain unknown components with physical meanings in many applications such as medical image and signal processing, hyperspectral images analysis, chemometrics, etc.In this thesis, we investigate the application of tensor decomposition for probability estimations, which are required for some targeted data/text mining tasks such as unsupervised clustering of data/documents. Besides criticizing the existing tensor decomposition algorithms for probability estimations, we propose to apply some proper constrained tensor decompositions, which result in more reliable and accurate estimations. Moreover, we introduce an algorithm for constrained tensor decomposition, called Simple Forward-Backward Splitting (SFBS), which is based on Proximal Minimization. SFBS performs better than state-of-the-art in decomposing noisy tensors while computationally less expensive.In addition, to evaluate the performance of tensor decomposition algorithms, we introduce an index that we name CorrIndex, which provides interpretable performance bounds, while keeping computational complexity to a reasonable level. Furthermore, we propose a method of moment estimation (standard averaging), which estimates the second and third order moments, with the same performance of state-of-the-art, but based on a much simpler concept, i.e. weighted averaging. Moreover, standard averaging performs better in small dimensions, and provides some advantages in terms of computational complexity.



  9. Keywords:
  10. Tensor Decomposition ; Performance Index ; Forward-Backward Splitting ; Text Mining ; Permutation and Scale Ambiguity ; Hidden/Latent Variable ; Unsupervised Clustering ; Third Order Moments

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