Back to Mathematics for Machine Learning: PCA

4.0

990 ratings

•

202 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 Liang S

•Jul 09, 2018

Teaching pacing is good, and clear in explanation. It will be good if there are some examples about how we should apply all these theories to some real problems.

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 Вернер А И

•Mar 18, 2018

Very tough course because of the programming assignments. Material was sometimes taught in a non-clear and deceiving way, e.g. covariance matrix of a dataset. Nevertheless, the course is good and covers lots of important details.

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.

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 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 Eddery L

•May 24, 2019

The instructor is great. HW setup sucks though.

By Andrew D

•Jun 02, 2019

Very difficult course, make sure to do the prereq courses first and understand everything from those courses.

By Giri G

•Jun 07, 2019

This was a very hard course for me. But I think the instructor has done the best possible he can with presenting and explaining the course

By Phạm N M H

•Jul 12, 2019

This maybe the most frustrating course and most advance compare to 2 other courses, you might confuse about the code in the assignment of this course. So, if you do have basic background about coding with numpy, matrices,etc..., I do recommend this course, if you qualify enough to fix the bugs of what the dev team left.

By Jiaxuan L

•Jul 15, 2019

Overall a good course. Very limited introduction to Python though.

By Kwak T h

•Jul 27, 2019

Good but slightly less deeper than the other two

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 Jessica P

•Aug 06, 2019

I agree with the others. Course didn't merge well with the 1st two which were perfect!

By Berkay E

•Aug 09, 2019

-Some of the contents are not clear.

+It gets great intuition for new learners in machine learning.

By João M G

•Aug 14, 2019

The course was great till the final week. The lectures did not explain very well the concepts and the assignment was poorly designed. It's a shame because I've loved the more rigorous way of this final course.

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 Abhishek P

•Sep 09, 2019

Course content tackles a difficult topic well. Only flaw is that programming assignments are poorly designed in some places and are quite difficult to pick up at times.

By Jordan V

•Aug 23, 2019

Course addresses important subject, but I worth like to have more in-depth explanation of the mathematics by the instructors and more examples.

By ranzhang

•Aug 29, 2019

I think it's really a hard lesson for me, but I've also learn a lot, thanks a lot for the teacher and coursera. Some Programming test take too long to execute, and there are some errors in it. just be careful

By Suyog P

•Sep 02, 2019

Finally understood basic intuition of PCA, never got perfect resource before. However, there was a sharp change in terms of course delivery than the previous two courses of this specialization. So, heads up.

By Xin W

•Sep 06, 2019

This course is full of mathematical derivation, so it is kind of boring.

By Manju S

•Jan 29, 2019

Good stuff:

Instructor has good knowledge of the subject. The course content structure is designed well.

Bad stuff:

Concepts could have been presented with more clarity. Programming assignments need more instructions and less assumption on what the students already know.

By Prashant D

•Feb 17, 2019

The lecturer is good and probably has a very good understanding of the mathematics. However if you are looking for a light and easy course, then this one is not for you. The mathematics is sometimes difficult to follow and although the lecturer patiently explains the derivation of the results, I had to go back and forth a number of times to understand what was happening.

By Malcolm M

•Mar 06, 2019

Far more challenging than the first two courses.