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Computational Methods for Data Science

This repository contains lectures notes and the associated MATLAB code for the course "Computational Methods for Data Science". Lectures are primarily based upon chapters 13-20 of Data-driven modeling & scientific computations by J. Nathan Kutz. Special thanks to Craig Ginn for sharing his lecture notes that influenced those found in this repository.

Course Description

Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of statistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression.

Lecture Titles

Lecture 1: Basics of Fourier Series and the Fourier Transform

Lecture 2: Radar Detection and Filtering

Lecture 3: Radar Detection and Averaging

Lecture 4: Time-Frequency Analysis: Windowed Fourier Transforms

Lecture 5: Time-Frequency Analysis and Wavelets

Lecture 6: Multi-Resolution Analysis and the Wavelet Basis

Lecture 7: Spectrograms and the Gabor Transform in MATLAB

Lecture 8: Basic Concepts and Analysis of Images

Lecture 9: Linear Filtering for Image Denoising

Lecture 10: Diffusion and Image Processing

Lecture 11: The Singular Value Decomposition

Lecture 12: Principal Component Analysis Demonstrations

Lecture 13: Introduction to Principal Component Analysis

Lecture 14: Principal Component Analysis and Proper Orthogonal Decomposition

Lecture 15: Independent Component Analysis and Image Separation

Lecture 16: Image Separation and MATLAB

Lecture 17: Advanced Discussion of ICA

Lecture 18: Recognizing Dogs and Cats

Lecture 19: The SVD and Linear Disciminant Analysis

Lecture 20: Implementing Dog/Cat Recognition in MATLAB

Lecture 21: Beyond Least-Squares Fitting: The L1 Norm

Lecture 22: Signal Reconstruction and Circumventing Nyquist

Lecture 23: Data (Image) Reconstruction from Sparse Sampling

Lecture 24: Modal Expansion Techniques for PDEs

Lecture 25: PDE Dynamics in the Right (Best) Basis

Lecture 26: Theory of Dynamic Mode Decomposition (DMD)

Lecture 27: Dynamics of DMD Versus POD

Lecture 28: DMD and Delay Coordinates