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Principal Component Analysis
CS5240 Theoretical Foundations in Multimedia
Leow Wee Kheng
Department of Computer Science
School of Computing
National University of Singapore
4 days ago by hustwj
How Are Principal Component Analysis and Singular Value Decomposition Related?
Principal Component Analysis, or PCA, is a well-known and widely used technique applicable to a wide variety of applications such as dimensionality reduction, data compression, feature extraction, and visualization. The basic idea is to project a dataset from many correlated coordinates onto fewer uncorrelated coordinates called principal components while still retaining most of the variability present in the data.

Singular Value Decomposition, or SVD, is a computational method often employed to calculate principal components for a dataset. Using SVD to perform PCA is efficient and numerically robust. Moreover, the intimate relationship between them can guide our intuition about what PCA actually does and help us gain additional insights into this technique.

In this post, I will explicitly describe the mathematical relationship between SVD and PCA and highlight some benefits of doing so. If you have used these techniques in the past but aren’t sure how they work internally this article is for you. By the end you should have an understanding of the motivation for PCA and SVD, and hopefully a better intuition about how to effectively employ them.
pca  svd  math  linearalgebra 
14 days ago by euler
Statistics for Applications Chapter 9: Principal Component Analysis (PCA)
Prof. Philippe Rigollet

MIT Course Number
18.650 / 18.6501
15 days ago by hustwj
Lecture: Principal Componenet Analysis (PCA) - YouTube
Published on Feb 19, 2016

The SVD algorithm is used to produce the dominant correlated mode structures in a data matrix.
8 weeks ago by hustwj
Lecture: The Singular Value Decomposition (SVD) - YouTube
Published on Feb 19, 2016

Perhaps the most important concept in this course, an introduction to the SVD is given and its mathematical foundations.
8 weeks ago by hustwj
19. Principal Component Analysis - YouTube
MIT 18.650 Statistics for Applications, Fall 2016
View the complete course: http://ocw.mit.edu/18-650F16
Instructor: Philippe Rigollet

In this lecture, Prof. Rigollet reviewed linear algebra and talked about multivariate statistics.
8 weeks ago by hustwj
Dimensionality Reduction: Principal Components Analysis, Part 1 - YouTube
Data Science for Biologists
Dimensionality Reduction: Principal Components Analysis
Part 1

Course Website: data4bio.com

Nathan Kutz: faculty.washington.edu/kutz
Bing Brunton: faculty.washington.edu/bbrunton
Steve Brunton: faculty.washington.edu/sbrunton
8 weeks ago by hustwj

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