Back to Mathematics for Machine Learning: PCA

4.0

stars

1,379 ratings

•

305 reviews

This intermediate-level course introduces the mathematical foundations to derive Principal Component Analysis (PCA), a fundamental dimensionality reduction technique. We'll cover some basic statistics of data sets, such as mean values and variances, we'll compute distances and angles between vectors using inner products and derive orthogonal projections of data onto lower-dimensional subspaces. Using all these tools, we'll then derive PCA as a method that minimizes the average squared reconstruction error between data points and their reconstruction.
At the end of this course, you'll be familiar with important mathematical concepts and you can implement PCA all by yourself. If you’re struggling, you'll find a set of jupyter notebooks that will allow you to explore properties of the techniques and walk you through what you need to do to get on track. If you are already an expert, this course may refresh some of your knowledge.
The lectures, examples and exercises require:
1. Some ability of abstract thinking
2. Good background in linear algebra (e.g., matrix and vector algebra, linear independence, basis)
3. Basic background in multivariate calculus (e.g., partial derivatives, basic optimization)
4. Basic knowledge in python programming and numpy
Disclaimer: This course is substantially more abstract and requires more programming than the other two courses of the specialization. However, this type of abstract thinking, algebraic manipulation and programming is necessary if you want to understand and develop machine learning algorithms....

Jul 17, 2018

This is one hell of an inspiring course that demystified the difficult concepts and math behind PCA. Excellent instructors in imparting the these knowledge with easy-to-understand illustrations.

May 01, 2018

This course was definitely a bit more complex, not so much in assignments but in the core concepts handled, than the others in the specialisation. Overall, it was fun to do this course!

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By wonseok k

•Mar 03, 2020

hard but good course

By Keisuke F

•Sep 15, 2019

I had big fun of PCA

By Dominik B

•Feb 17, 2020

Great instructor!

By Sujeet B

•Jul 21, 2019

Tough, but great!

By Jitender S V

•Jul 25, 2018

AWESOME!!!!!!!!!!

By Shanxue J

•May 23, 2018

Truly exceptional

By Lintao D

•Sep 24, 2019

Very Good Course

By Shounak D

•Sep 15, 2018

Great course !

By Andrey

•Sep 17, 2018

Great course!

By Samresh

•Aug 10, 2019

Nice Course.

By David N

•Jul 24, 2019

Great course

By Artur

•Feb 29, 2020

good course

By Mohamed H

•Aug 10, 2019

fantastic

By Karthik

•May 03, 2018

RRhis cl

By Akash G

•Mar 20, 2019

awesome

By Bálint - H F

•Mar 20, 2019

Great !

By HARSH K D

•Jun 28, 2018

good

By Vassiliy T

•Jul 10, 2018

it is good, challenging course. i've learned a lot, but feel that i came away with quite patchy knowledge. This course is a big step up in complexity and delivery form the previous two courses. perhaps my expectations were not right to start with - one cannot learn this level of complexity so quickly. Admittedly there are many gaps between the lectures and course materials and what is asked in programming assignments. i ended up reading a lot online to fill in the gaps (i've learned a lot of python during the course, which is great!).nevertheless, after this course i feel equipped to continue with machine learning.

By Nikolay B

•Aug 03, 2019

Instructor gives the very dry but useful essence of the "philosophical" concepts of dot and generalized inner product, etc., - personally, liked that. Unfortunately, the offered problems are so far away from the delivered videos but the web search helps on getting the hints. This course makes you think - I learned a lot just by asking myself "what do they mean under this statement?", what they want in this task? Though I will appreciate if providers elaborate the material further and so instead of googling we spend our time watching - a single point access.

By Antonio C P

•Jan 24, 2020

It was a real tour de force on the mathematics, and I had some hard time following the ideas of the instructor many times. However, the topic was completely covered in a very systematic way, which is excellent in my opinion. My only suggestion is to focus more on what really matters: do we really have to spend such a long time discussing about different metrics for an inner product if in the end we only use the euclidean metric?

By Barnaby D

•Jan 03, 2020

Would give this course 5 stars if it was properly described so that expectation could match reality:

Give yourself plenty of time for this course - it will take quite a bit longer than described.

Make sure you are comfortable with Python and NumPy before you start (particularly the linear algebra functions).

It is very different (much less hand-holding) than the other courses in the specialization.

By Nelson F A

•Apr 25, 2019

This course brings together many of the concepts from the first two courses of the specialization. If you worked through them already, then this course is a must. There are some issues with the programming assignments and the lectures could do with some more practical examples. Be sure to check the discussions forums for help. For me they were essential to passing the course.

By Evgeny ( C

•Jul 25, 2018

It was a harder course where I spent double the time I have initially anticipated.

It is much harder than the two predecessor courses in specialization, and amount of direction when it comes to doing exercises is significantly smaller. More Python knowledge is required.

That said, I feel like I have finally understood the PCA and math behind it, which made it all worth it

By Mark S

•Jul 07, 2018

Loved the course, although I wish there was more ramp up to some of the complex scenarios (or anything simple but new). Very helpful forums/community. Requires a fair amount of external reading/referencing for some of the concepts which seem to be covered only at a high level in the lectures.I would love to see more courses on applied mathematics for machine learning.

By Jerome M

•Jul 26, 2018

The best of the 3 courses. This is a refresh course of course. A solid background in linear algebra is required in order to fully understand everything. I personnaly recommen the MIT course from Gilbert Strang before you try this one. The python exercises are very well designed and I can only be thankful to having shared this knowledge. Thank you Imperial College.

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