AMATH 482: Data Analysis and Signal Processing

• video lectures available at : https://faculty.washington.edu/kutz/KutzBook/KutzBook.html
• If you develop a new technique, show it works on a small system where you KNOW the truth.
• Machine learning is cool and all, but it should not be the first tool you go for. There are a lot simpler methods (SVD, Fourier Transform, etc) that might do the trick or make the problem easier.
• Solving a PDE? Convert it to an ODE and use ode45. Consider taking the Fourier transform to convert a spatial temporal signal to eliminate the spatial term.

Lecture Topics

Data Analysis

• Fourier Transforms
• Averaging and filtering in frequency domain
• Short-term transforms (Gabor Transforms)
• Wavelet Transforms (no smooth filters)

Image Processing

• Singular Value Decomposition (SVD)
• Principal Component Analysis (PCA)
• Low rank (dimension) approximations to data
• Dimensionality analysis of data

Classification & Clustering

Unsupervised Learning

• K-means
• Hierarchial Clustering
• Gaussian Mixture Models

Supervised Learning

• K-nearest Neighbors
• Linear Discriminant Analysis (pg 173 of pdf)
• Support Vector Machines (pg 179 of pdf)
• Classification & Regression Trees (pg 184 of pdf)

Dynamic Mode Decomposition

• http://dmdbook.com/
• Nonorthogonal Mode decomposition
• Extracting spatio-temporal properties

Compressive Sensing

• Sensing in large systems when you only have sparse measurements

Reduced Order Modeling

• Solving PDEs by reducing to ODEs
• Benefits of Fourier Transform in PDE --> ODE conversion

Homework Topics

HW 1

Using ultrasound data to track the location of a foreign object throughout a noisy medium. Techniques for handeling zero-mean frequency-based noise.

• Fourier Transforms
• Averaging in the Frequency Domain
• Filtering for Frequencies

HW 2

• Short-term fourier transforms (Gabor transforms)
• Spectrograms
• Music decomposition

HW 3

• Singular Value Decomposition (SVD)
• Dimensionality Analysis and Low-Rank (dimension) approximations of data
• Principal Component Analysis (PCA)

HW 4

• Data Preprocessing
• Classification and Clustering

HW 5

• Dynamic Mode decomposition
• Separating image foreground from background
• Extracting moving objects from video