ECE 695E Data Analysis, Design of Experiment, ML Lecture 10: Principal Component Analysis

Table of Contents:
00:00 Lecture 10. Big Data Classification by Principal Component Analysis
01:11 copyright 2018
01:12 Course Outline
01:13 Big vs. small data
02:09 Small vs. big data
03:37 Where do data come from?
03:45 … driven by memory technology
04:41 "Big data" techniques apply to "little data" too
05:34 Our goal for the next few lectures …
07:38 Analysis of big data
09:35 Outline
09:38 Classification problem in big data
12:44 PCA helps classification
15:46 PCA Also help in data compression
17:07 Outline
17:07 Principle Component Analysis (PCA)
18:31 Basic Concept of PCA
21:19 PCA through Singular Value Decomposition
23:36 Reduce dimension by Singular Value Decomposition
23:42 Example 1: Rotation matrix
25:14 SVD rotates the axes optimally
28:10 SVD components allows reconstruction
30:24 Projection along PCs
32:03 Example 2: More general result
33:46 SVD approximates the exact result
34:55 (continued) Projection along PCs
36:18 Outline
36:24 Principle Component Analysis for classification
38:14 Image Transmission by Principle Component Analysis
38:41 MATLAB code (by Camsari)

This course will provide the conceptual foundation so that a student can use modern statistical concepts and tools to analyze data generated by experiments or numerical simulation. We will also discuss principles of design of experiments so that the data generated by experiments/simulation are statistically relevant and useful. We will conclude with a discussion of analytical tools for machine learning and principle component analysis. At the end of the course, a student will be able to use a broad range of tools embedded in MATLAB and Excel to analyze and interpret their data.

Topics Covered:
Review of Basic Statistical Concepts
Where do data come from: Big vs. Small Data
Collecting and Plotting Data: Principles of Robust Data Analysis
Physical vs. Empirical Distribution
Model Selection and Goodness of Fit
Scaling Theory of Design of Experiments
Statistical Theory of Design of Experiments
Machine Learning vs. Physics-based Machine Learning