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Dictionary Learning for Sparse Representation based Classification

Mohseni Seh Deh, Saeed | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 55747 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babaiezadeh, Massoud
  7. Abstract:
  8. One of the problems in signal processing is supervised classification. In supervised classification, the goal is to learn the structures and patterns of a dataset using a set of labeled data called the training dataset to correctly classify data samples that are not used in the training data but follow the same pattern and structure. One approach to this problem that has recently received attention is neural networks. Although this approach has good performance in applications, in order to perform well, they require a large amount of data and many trainable parameters, which result in high computational complexity. Another approach to this problem is dictionary learning-based classification. In traditional dictionary learning, the goal is to learn overcomplete dictionaries based on the training dataset, which results in a sparse representation of the signal with a small reconstruction error. In this problem, the labels of the training dataset are not used during the training phase. However, in dictionary learning-based classification, the idea is to classify a data sample by the information in its representation over a learned dictionary, and the goal is to incorporate the information in the labels of the training dataset in the training phase to produce dictionaries with high classification rates. In this thesis, three methods for dictionary learning-based classification are presented. The first method is a fast and computationally inexpensive algorithm based on learning multiple undercomplete dictionaries (i.e. one for each class). A data sample is classified based on its representation error in each dictionary. The second method is a classification algorithm based on the energy content of different parts of the representation of a data sample over a learned dictionary. Finally, the third method introduces the idea of using an overcomplete dictionary as the first hidden layer of a neural network. The parameters in this method are optimized based on minimizing a unifying cost function for both reconstruction and classification losses. As the simulations show, our methods have higher classification accuracy than a number of successful methods in dictionary learning-based classification, and they are valuable candidates for supervised classification problems.
  9. Keywords:
  10. Sparse Representation ; Dictionary Learning ; Neural Networks ; Singular Value Decomposition (SVD) ; Overcomplete Dictionary ; Undercomplete Dictionary ; Supervised Classification

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