Back to Mathematics for Machine Learning: PCA

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2,544 ratings

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629 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....

JS

Jul 16, 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.

NS

Jun 18, 2020

Relatively tougher than previous two courses in the specialization. I'd suggest giving more time and being patient in pursuit of completing this course and understanding the concepts involved.

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By Anna U

•Jan 14, 2020

An excellently simple explanation of concepts of linear algebra and PCA. Applause for lector. I really liked this course and found it very useful for those newbies in machine learning like myself. I recommend this course to all my friends and others interested in.

By Umesh S

•Dec 26, 2020

Most challenging of all three courses but rewarding as well. Requires you have refreshed complex topics of Linear Algebra ( Khan academy and other you tube material are good starting point) . Looking forward to go even deeper in to this. Thanks Imperial !!!

By Ramon M T

•Oct 22, 2019

I liked the course quite a bit. I found it quite challenging (I had never seen any PCA) but it always kept me very interested. I had to use several sources to read a little more about PCA and to complete the last exercises, the forum is very helpful.

By Bingfeng H

•Aug 26, 2020

Very good course, although the programming assignments are challenging and some background knowlege in linear algebra and vector calculus required. You will need to do some independent research at times. But the instructions are clear and concise.

By Xavier B S

•Apr 5, 2018

Excellent course - challenging yet rewarding with good feedback from the teaching staff.

The video and the transparent white board are also great - look forward to seeing more MOOCs from Imperial as well as the release of the upcoming book

By Jafed E G

•Jul 6, 2019

I enjoy the lectures. The professor has a good speaking and teaching style which keeps me interested. Lots of concrete math examples which make it easier to understand. Very good slides which are well formulated and easy to understand

By chaomenghsuan

•Jul 18, 2018

This one is harder, I took longer time to figure out the assignments. Some of the concept that appeared in the assignments were not included in the lectures. I do hope that the assignments could have clearer instructions.

By Abhishek M

•Jun 21, 2019

Very nice course. It will be great to have a course on Statistics for Machine learning covering advanced concepts in probability theory. Thank you for offering such a great course. I have learnt a lot and enjoyed fully.

By María J S G

•Aug 29, 2019

Very good 3 courses for those of us who are beginners in Machine Learning and IA! However I miss a whole course, perhaps the first one of then four, teaching us what we need to know about python, numpy and plotting.

By Arnab M

•Jun 3, 2019

A great course. Learnt a lot, a lot of Linear Algebra, Projections/ Geometry/ all of these Mathematical ideas would help greatly in understanding of Machine Learning concepts and applying them to real world data!!..

By Dr. N D

•Aug 12, 2020

It was a very nice experience with this course. I learnt a lot of Python Coding. The coding exercise was really good. It was tough for me to code in Python. But I took time for it. thanks to the faculty members.

By AKSHAT M

•Aug 14, 2020

Really nice course and kudos to the instructor. Week 4 was a bit challenging, but still he made it quite easy for us to understand. Very happy to have gone through this course and completed the specialisation.

By Krishna K M

•Jun 24, 2019

I am not sure why the rating is so low for this course.

Personally, I found this course really insightful as the instructor explains what the different statistical measurements mean, and why are they useful.

By Akshat S

•Jul 24, 2019

I will present my self with some amazing songs!!

Excellent staircase to the heaven for learning PCA.

Breaking the habit of struggling with hardcore bookish mathematics.

Loose yourself in this adventure!!

By Jose A

•Jul 18, 2020

Well explained, some issues with assignments but some of them are to not just type and think a little.

May be one is a real mistake... hard time with it, but lot of learning too.

By prudgin g

•Feb 15, 2020

Challenging, but doable. Has some bugs in coding assignments, but clearing them out makes you understand things better. Get ready to spend extra time understanding the concepts.

By Christian H

•Dec 28, 2019

This course is well worth the time. I have a better understanding of one of the most foundational and biologically plausible machine learning algorithms used today! Love it.

By Tse-Yu L

•Mar 14, 2018

Practices and quiz are designed well while I will suggest to put more hints on programming parts, e.g., PCA. Overall, this series of course are pretty useful for beginner.

By Miguel A Q H

•Feb 20, 2020

This is the best course of the specialization, its very hard but it lets you to understand very important concepts of what means dimensionality reduccion.

Great Job!!!!

By Aymeric N

•Nov 25, 2018

This course demystifies the Principal Components Analysis through practical implementation. It gives me solid foundations for learning further data science techniques.

By XL T

•Apr 3, 2020

It is a bit difficult and jumpy. You will need some hard work to fill in the missing links of knowledge which not explicite on the lectrue. Overall, great experience.

By Fabrizio B

•Oct 31, 2020

Definitely the most challenging of the course making up this specialization. Finishing it with full scores is proportionally far more satisfying!!! Well done Marc!

By S J

•May 3, 2020

Your Teaching and Video quality is par excellence.....Thanks a lot for such amazing stuff...I am looking forward to joining more courses in the same line

By Christine D

•Apr 14, 2018

I found this course really excellent. Very clear explanations with very hepful illustrations.

I was looking for course on PCA, thank you for this one

By Ananta M

•Apr 20, 2020

Although the course was little out there and the instructor was trying his best to articulate a difficult topic, the overall experience is great.

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