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.
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 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