Machine Learning in 2D Compressed Sensing Datasets

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Keshvari, Fatemeh | 2022

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 55106 (05)
University: Sharif University of Technology
Department: Electrical Engineering
Advisor(s): Babaiezadeh, Massoud
Abstract:
Compressed Sensing (CS) technique refers to the digitalization process that efficiently reduces the number of measurements below the Nyquist rate while preserving signal structure. This technique was originally developed for the analysis of vector datasets. An x ∈R^n vector is transformed into an y ∈R^m vector so that n≪m. For a sufficient number of measurements, this transformation has been shown to preserve the signal structure. Therefore, the technique has been applied to machine learning applications.2D-CS was further developed for matrices (image datasets) so that they could be directly applied to matrices without flattening. X ∈R^(n×n) is transformed into Y ∈R^(m×m) via 2D-CD such n≪m. Learning under this transformation has not been extensively studied. We present this thesis as an attempt to demonstrate that learning can be accomplished under 2D-CS with a bit of error. The error band has been introduced for SVM in 1D-CS. This holds true here, but for a larger number of measurements. Additionally, a 2-dimensional version of SVM is proposed for learning 2D datasets in their base form.
Keywords:
Support Vector Machine (SVM) ; Compressive Sensing ; Machine Learning ; Nyquist Diagram ; Two Dimensional Learning