VIDEODimensionality Reduction via SVD

Covers: theory of Singular Value Decomposition
Estimated time needed: 15 minutes
Questions this item adddesses:
  • How is the best rank r approximation of a matrix obtained using SVD?
  • What is the Eckart-Young-Mirsky Theorem?
How to use this item?

Watch the whole video at 1.25 speed.

  1. Expansion of SVD decomposition as the sum of rank one matrices.
  2. The best rank one, two, ... or r approximation (w.r.t. Frobenius norm (*)). Recall that
  1. Eckart-Young-Mirsky Theorem: Best rank r approximation of a matrix.
  • Definition (*): Given an mxn real matrix A, the Frobenius norm of A is defined as
Fail to play? Open the link directly: https://www.youtube.com/watch?v=xy3QyyhiuY4
Author(s) / creator(s) / reference(s)
Steve Brunton
Shortlist
publicShare

Singular Value Decomposition (SVD)

N. KalantarovaTotal time needed: ~2 hours
Learning Objectives
Learn the basics of SVD and its applications in dimensionality reduction
Potential Use Cases
Educational use. Gives basic introduction to SVD and some of its applications
Target Audience
INTERMEDIATEAnyone interested in SVD with basic linear algebra background.
Go through the following annotated items in order:
VIDEO 1. Overview of Singular Value Decomposition (SVD)
  • What is SVD?
  • What are the factors of SVD?
  • How are the factors of SVD related to the data matrix?
13 minutes
BOOK_CHAPTER 2. The theory of SVD
  • What is the relation between the SVD factors of a matrix and its four fundamental subspaces?
  • How is SVD computed?
  • How can SVD be used for image compression?
18 minutes
VIDEO 3. Dimensionality Reduction via SVD
  • How is the best rank r approximation of a matrix obtained using SVD?
  • What is the Eckart-Young-Mirsky Theorem?
15 minutes
VIDEO 4. Choosing the Optimal Rank for Truncating SVD
  • How to choose truncation value in SVD?
12 minutes
ARTICLE 5. (Optional) Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares
  • How to efficiently estimate missing entries of large matrices?
30 minutes

Concepts Convered

Stop searching alone.
Start building together.

Build applications based on AI Research, Engineering, and Product Development that people actually want to use
 

Adjust the levels below to see how we can help you.

Features just for you!

FreeApplied research live sessions
FreeAccess to community Slack workspace and social events
PaidFacilitate live discussion sessions
PaidGuided video creation experience to showcase your capstone project
FreeMLOps video live sessions
PaidHands-on MLOps video series
PaidAI products development video series
PaidGuided application building

What can I do here?

We believe in collaborative learning to make AI research more consumable and more accessible, while also helping developers implement and productionize their work.

Learn collaboratively &

plug into the network

Learn about the latest research in the field of your choice

Learn how to

Implement & deploy models

Learn how to

build products
To see further details of the above items, please sign up or sign in first.

Ready to get ahead?

Come with your ambitions, and let us super charge your efforts! Through personalized learning experiences, we will help you achieve your goals.

 

Find anything you like?

With an account, you can follow the topics you're interested in, and get notified about new content!

 

Our Users in Numbers!

Role

Highest Degree of Education

What That Degree Is In

Some of Our Stream Owners!

Interact with Our Experts!

testimonial icon
"I had a hard time keeping up with the latest in machine learning, let alone understanding and applying those concepts, until I found this community."

Emily W.

MSc Student

testimonial icon
"Unlike other workshops, this experience included designing more than just machine-learning models. Full end-to-end AI solutions including MLOps was a necessary part of the Capstone. It was incredible to be able to conceptualize, design and build an AI product which resulted in attracting real investors."

Edward J.

Product Manager

testimonial icon
"Best Environment to discuss theory and implementation of the latest in machine learning and to continuously learn."

Susan S.

Data Scientist

testimonial icon
"Hands-on and practical exposure to deep learning while working with experts from industry and brilliant members is something that I was missing before finding this platform."

Werner C.

Data Scientist

testimonial icon
"I had a hard time keeping up with the latest in machine learning, let alone understanding and applying those concepts, until I found this community."

Emily W.

MSc Student

testimonial icon
"Unlike other workshops, this experience included designing more than just machine-learning models. Full end-to-end AI solutions including MLOps was a necessary part of the Capstone. It was incredible to be able to conceptualize, design and build an AI product which resulted in attracting real investors."

Edward J.

Product Manager

testimonial icon
"Best Environment to discuss theory and implementation of the latest in machine learning and to continuously learn."

Susan S.

Data Scientist

testimonial icon
"Hands-on and practical exposure to deep learning while working with experts from industry and brilliant members is something that I was missing before finding this platform."

Werner C.

Data Scientist

testimonial icon
"I had a hard time keeping up with the latest in machine learning, let alone understanding and applying those concepts, until I found this community."

Emily W.

MSc Student

testimonial icon
"Unlike other workshops, this experience included designing more than just machine-learning models. Full end-to-end AI solutions including MLOps was a necessary part of the Capstone. It was incredible to be able to conceptualize, design and build an AI product which resulted in attracting real investors."

Edward J.

Product Manager