09. Video: Singular Value Decomposition

Singular Value Decomposition

Let's do a quick check of understanding. If we let A be our user-item matrix, we can write the decomposition of that matrix in the following way.

A = U \Sigma V^T

Use the quizzes below to test your understanding of what these matrices represent, as well as the dimensions of these matrices.

QUIZ QUESTION::

Match each matrix to the appropriate statement about it.

ANSWER CHOICES:

U

Sigma

V

Statement	Matrix
A matrix that provides how users feel about latent features.
A matrix that provides weights in descending order with how much each latent feature matters towards reconstructing the original user-item matrix.
A matrix that provides how items (movies in this case) relate to each latent feature .

SOLUTION:

Statement	Matrix
A matrix that provides how users feel about latent features.	U
A matrix that provides weights in descending order with how much each latent feature matters towards reconstructing the original user-item matrix.	Sigma
A matrix that provides how items (movies in this case) relate to each latent feature .	V

QUIZ QUESTION::

Let k be the number of latent features used, n be the number of users, and m be the number of items. With this in mind, match each matrix to its corresponding dimensions. For the below, consider rows-columns as the structure.

ANSWER CHOICES:

m-k

k-m

n-k

k-by-n

k-k

n-by-m

Matrix	Dimensions
U
Sigma
V
V-transpose

SOLUTION:

Matrix	Dimensions
V	m-k
V-transpose	k-m
U	n-k
Sigma	k-k