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Functional Data Analysis
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Engineering
Instruction in: English
Course Code: 16645
Transcript Source: Partner Institution
Course Details: Level 400
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Introduction to Data Science
Probability and Data Analysis
Introduction to Statistical Modeling
Statistical Learning
Predictive Modeling
Bayesian Data Analysis
DESCRIPTION
1. Introduction to the functional data analysis.
2. Tools for exploring functional data:
a. Functional mean and variance.
b. Covariance and correlation functions.
c. Cross-covariance and cross-correlation functions.
3. From functional data to smooth functions:
a. Basis functions.
b. Smoothing functional data by least-squares.
c. Smoothing functional data with a roughness penalty.
4. Principal component analysis for functional data:
a. Defining functional PCA.
b. Visualizing the results.
c. Computational methods for functional PCA.
d. Regularized PCA.
5. Regression for functional data:
a. Functional linear models with scalar responses.
b. Functional linear models with functional responses.
6. Supervised classification for functional data:
a. k-nearest neighbors.
7. Unsupervised classification for functional data
1. k-means.
2. Tools for exploring functional data:
a. Functional mean and variance.
b. Covariance and correlation functions.
c. Cross-covariance and cross-correlation functions.
3. From functional data to smooth functions:
a. Basis functions.
b. Smoothing functional data by least-squares.
c. Smoothing functional data with a roughness penalty.
4. Principal component analysis for functional data:
a. Defining functional PCA.
b. Visualizing the results.
c. Computational methods for functional PCA.
d. Regularized PCA.
5. Regression for functional data:
a. Functional linear models with scalar responses.
b. Functional linear models with functional responses.
6. Supervised classification for functional data:
a. k-nearest neighbors.
7. Unsupervised classification for functional data
1. k-means.
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