課程配合網站：https://sites.google.com/a/math.ntu.edu.tw/t-2016s-data/


This course will cover the following topics.

(I) Singular value decomposition (SVD) and principal component analysis (PCA)
- Fundamentals and computations of SVD
- Fundamentals and computations of PCA
- Proper orthogonal modes and robust PCA
- Random sampling and random projections
- Randomized algorithms for low-rank matrix approximation
- Application in oscillating mass and dimensionality reduction
- Hands-on experiments and implementations in MATLAB

(II) Extended SVD and PCA
- Sparse SVD and sparse PCA
- Nonnegative SVD and nonnegative PCA
- Tensor decomposition, high order SVD, multilinear PCA, and nonnegative tensor decomposition
- Multilinear algebra
- Application in Cryo electron microscopy images
- Hands-on experiments and implementations in MATLAB

(III) Independent Component Analysis (ICA)
- Introduction to ICA
- Principal component analysis (whitening) as the preprocessing
- ICA via optimization approaches
- ICA by maximization of nongaussianity
- ICA by maximum likelihood estimation
- ICA by minimization of mutual information
- Applications in blind source separation for audio signals and images
- Hands-on experiments and implementations in MATLAB

(IV) Image Processing and Analysis
- Basic concepts of images
- Linear filtering for image denoising
- Diffusion and image processing
- Image recognition via machine learning
- SVD and linear discrimination analysis
- Application in real images
- Hands-on experiments and implementation in MATLAB

(V) Visualization and Exploratory Data Analysis (EDA)
- Interactive graphics and EDA
- General introduction to statistical graphics and matrix visualization
- Visualization for continuous and binary data
- Visualization for categorical data
- Visualization for data with cartography links
- Covariate-adjusted data visualization and visualization for other types of data and modeling
- Visualization for symbolic data and for big data