## Matrix factorization Regularization

gahas
Posts: 2
Joined: Mon Jan 24, 2022 9:22 pm

### Matrix factorization Regularization Can anyone tell me where is the objective came from?
and on the model. why does it use W as the symbol of the factorized matrix, while W is used on the objective formula as weight?
Finally on the solution formula. What is the definition of I? on the video, the explanation of the solution formula is so minimum.
I cannot understand anything about the solution formula.

can somebody help me?
thank you so much.
lazyprogrammer
Posts: 127
Joined: Sat Jul 28, 2018 3:46 am

### Re: Matrix factorization Regularization

The main idea is that you are missing the "prerequisites". Helpful resources:

- read the course description (I hope you have done this!) where the prerequisites have been listed
- lecture "how to succeed in this course"
- FAQ lecture "machine learning and AI prerequisite roadmap"
- FAQ lecture "is this course for beginners or experts?"
- https://deeplearningcourses.com/course_order

What work did you do to ensure you met the prerequisites for this course?

Now to answer each question explicitly:

> Can anyone tell me where is the objective came from?

It's just the squared error loss with L2 regularization. We learned this in Linear Regression (see: prerequisite list).

> why does it use W as the symbol of the factorized matrix, while W is used on the objective formula as weight?

This is standard notation / convention for linear regression.

"W" and "w" are common symbols used for parameters in any kind of model.

Note that lowercase conventionally refers to a vector, while uppercase conventionally refers to a matrix.

You have to pay attention to context.

For example, "W" can be used in matrix factorization, "w" can be used in linear regression, "W" can be used for convolution, etc.

If you want to be involved in math or ML, you have to get used to the idea that the same letter can be used for multiple things.

For example, we could use "L" as loss, or "L" as likelihood, or "L" as the number of layers in a neural network.

It's simply a must to understand this, otherwise, you will get stuck often.

> Finally on the solution formula. What is the definition of I?

This is just convention in linear algebra to mean the identity matrix. Recall that basic matrix arithmetic and linear algebra are prerequisites for this course.

> on the video, the explanation of the solution formula is so minimum. I cannot understand anything about the solution formula.

That is what happens when you do not follow the prerequisites.

Unfortunately, there's no other way to say it.

Hopefully you found this helpful, let me know if not, or if you have any further questions.
gahas
Posts: 2
Joined: Mon Jan 24, 2022 9:22 pm

### Re: Matrix factorization Regularization

hai.. thank you for the answer.
where can I access this "prerequisites" list?
lazyprogrammer