CS 357 - Fall 2020

CS 357 - Fall 2020

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Bisection Method - fixed typo 1 of 30

duration 18 minutes 52 seconds

Bisection Method - fixed typo

Bisection Method - fixed typo

From Mariana Silva 11/30/2020

2,480 plays 0
The bisection method to solve 1d nonlinear equation
PCA: Tumor dataset example 2 of 30

duration 38 minutes 14 seconds

PCA: Tumor dataset example

PCA: Tumor dataset example

From Mariana Silva 11/16/2020

2,855 plays 0
Using the same dataset from the MP (cancer data) to perform PCA
PCA Intro 3 of 30

duration 7 minutes 26 seconds

PCA Intro

PCA Intro

From Mariana Silva 11/16/2020

2,160 plays 0
Introducing PCA with simple dataset
SVD - IPython Notebook 4 of 30

duration 42 minutes 43 seconds

SVD - IPython Notebook

SVD - IPython Notebook

From Mariana Silva 11/12/2020

84 plays 0
Sync lecture from Spring 2020 solving an IPython notebook
SVD - Linear System Equations 5 of 30

duration 3 minutes 30 seconds

SVD - Linear System Equations

SVD - Linear System Equations

From Mariana Silva 11/12/2020

1,377 plays 0
Using SVD to solve linear system of equations
SVD - Image Compression 6 of 30

duration 8 minutes 48 seconds

SVD - Image Compression

SVD - Image Compression

From Mariana Silva 11/12/2020

2,142 plays 0
Low rank approximation and application to image compression
SVD - Condition Number 7 of 30

duration 1 minute 41 seconds

SVD - Condition Number

SVD - Condition Number

From Mariana Silva 11/12/2020

1,357 plays 0
Understanding condition number from SVD
SVD - Norms 8 of 30

duration 8 minutes 14 seconds

SVD - Norms

SVD - Norms

From Mariana Silva 11/12/2020

1,548 plays 0
Induced matrix norm when p = 2
SVD - Pseudo-Inverse 9 of 30

duration 3 minutes 48 seconds

SVD - Pseudo-Inverse

SVD - Pseudo-Inverse

From Mariana Silva 11/12/2020

2,119 plays 0
How we compute the pseudo-inverse of a matrix given the SVD
SVD - Matrix Rank 10 of 30

duration 8 minutes 9 seconds

SVD - Matrix Rank

SVD - Matrix Rank

From Mariana Silva 11/12/2020

1,831 plays 0
How we can get the rank of a matrix given the SVD
Linear Least Squares: solving IPython notebook 11 of 30

duration 39 minutes 53 seconds

Linear Least Squares: solving IPython notebook

Linear Least Squares: solving IPython notebook

From Mariana Silva 11/10/2020

105 plays 0
Sync lecture from Spring 2020
Linear Least Squares: example 12 of 30

duration 10 minutes 32 seconds

Linear Least Squares: example

Linear Least Squares: example

From Mariana Silva 11/10/2020

2,097 plays 0
Another way to compute the residual.
Linear Least Squares + SVD: 2-Cost 13 of 30

duration 7 minutes 51 seconds

Linear Least Squares + SVD: 2-Cost

Linear Least Squares + SVD: 2-Cost

From Mariana Silva 11/10/2020

2,003 plays 0
Summary of LLS with SVD and a cost analysis
Linear Least Squares + SVD: 1-Intro 14 of 30

duration 20 minutes 7 seconds

Linear Least Squares + SVD: 1-Intro

Linear Least Squares + SVD: 1-Intro

From Mariana Silva 11/10/2020

2,995 plays 0
Solving the linear least-squares problem using the SVD.
SVD - 5: Computational cost 15 of 30

duration 2 minutes 43 seconds

SVD - 5: Computational cost

SVD - 5: Computational cost

From Mariana Silva 11/1/2020

1,528 plays 0
What is the overall cost of SVD?
SVD - 4: Singular values 16 of 30

duration 3 minutes 49 seconds

SVD - 4: Singular values

SVD - 4: Singular values

From Mariana Silva 11/1/2020

1,762 plays 0
What do you know about the singular values?
SVD - 3: Solution from Eigenpairs 17 of 30

duration 10 minutes 30 seconds

SVD - 3: Solution from Eigenpairs

SVD - 3: Solution from Eigenpairs

From Mariana Silva 11/1/2020

2,406 plays 0
How we can obtain the SVD from the solution of an eigenvalue problem
SVD - 2: Reduced form 18 of 30

duration 10 minutes 21 seconds

SVD - 2: Reduced form

SVD - 2: Reduced form

From Mariana Silva 11/1/2020

2,152 plays 0
How can we write an SVD for over and under-determined systems?
Singular Value Decomposition (SVD) - 1: Intro 19 of 30

duration 3 minutes 4 seconds

Singular Value Decomposition (SVD) - 1: Intro

Singular Value Decomposition (SVD) - 1: Intro

From Mariana Silva 11/1/2020

2,318 plays 0
What is a singular value decomposition?
Linear Least Squares - 7: Computational Cost 20 of 30

duration 3 minutes 26 seconds

Linear Least Squares - 7: Computational Cost

Linear Least Squares - 7: Computational Cost

From Mariana Silva 10/31/2020

1,658 plays 0
What is the computational cost of solving the least squares problem using the normal equations?
Linear Least Squares - 6: Quadratic 21 of 30

duration 8 minutes 18 seconds

Linear Least Squares - 6: Quadratic

Linear Least Squares - 6: Quadratic

From Mariana Silva 10/31/2020

1,933 plays 0
Fitting data using quadratic curve
Linear Least Squares - 5: Example 22 of 30

duration 2 minutes 45 seconds

Linear Least Squares - 5: Example

Linear Least Squares - 5: Example

From Mariana Silva 10/31/2020

1,769 plays 0
How you can find the coefficient to fit points using a straight line
Linear Least Squares - 4: Graphical Interpretation 23 of 30

duration 4 minutes 10 seconds

Linear Least Squares - 4: Graphical Interpretation

Linear Least Squares - 4: Graphical Interpretation

From Mariana Silva 10/31/2020

1,903 plays 0
Another way to understand (and derive) the solution of a LLS problem
Linear Least Squares - 3: Uniqueness 24 of 30

duration 4 minutes 59 seconds

Linear Least Squares - 3: Uniqueness

Linear Least Squares - 3: Uniqueness

From Mariana Silva 10/31/2020

2,294 plays 0
When is the solution is unique and how do we know it is a solution?
Linear Least Squares - 2: Normal Equations 25 of 30

duration 7 minutes 46 seconds

Linear Least Squares - 2: Normal Equations

Linear Least Squares - 2: Normal Equations

From Mariana Silva 10/31/2020

3,080 plays 0
How can we solve a linear LS problem using Normal Equations
Linear Least Squares - 1: Intro 26 of 30

duration 8 minutes 21 seconds

Linear Least Squares - 1: Intro

Linear Least Squares - 1: Intro

From Mariana Silva 10/31/2020

2,894 plays 0
Introduction to Linear Least Squares
Interesting examples from an external website 27 of 30

duration 5 minutes 49 seconds

Interesting examples from an external website

Interesting examples from an external website

From Mariana Silva 10/29/2020

110 plays 0
Interactive tutorial
IPython notebook for ND optimization 28 of 30

duration 24 minutes 17 seconds

IPython notebook for ND optimization

IPython notebook for ND optimization

From Mariana Silva 10/29/2020

156 plays 0
Sync lecture (Spring 2020) going over the IPython notebook to show the ND Methods to solve unconstrained optimization problems
IPython notebook for 1D optimization 29 of 30

duration 26 minutes 3 seconds

IPython notebook for 1D optimization

IPython notebook for 1D optimization

From Mariana Silva 10/26/2020

94 plays 0
Sync lecture (Spring 2020) going over the IPython notebook to show the 1D Methods to solve unconstrained optimization problems
Constrained Optimization problem 30 of 30

duration 4 minutes 59 seconds

Constrained Optimization problem

Constrained Optimization problem

From Mariana Silva 10/24/2020

85 plays 0
Maximizing the area of a rectangle subject to a perimeter constraint.

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