Back to Mathematics for Machine Learning: PCA

4.0

stars

1,378 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 Yuanfang

•Sep 07, 2019

A little more challenging than the other 2 courses in this series. The programming examples on K nearest neighbors, eigenvector fitting of facial data, and the PCA implementation are neat and rewarding. Can't help but feel there's still a great deal of math details that is only briefly mentioned - oh well there's always the free textbook to reference. Overall highly recommended.

By Gergo G

•May 15, 2019

This course is really challenging. A strong mathematical background is necessary or it needs to be developed during the lectures and self-study. The professor's explanations are clear, and still lead to complex ideas which is great. Programming assignments are also difficult, however they serve as a superb opportunity to develop your skills in Python.

By Anastasios P

•Dec 26, 2019

Challenging course, a lot harder than the two previous in the specialisation. Having said that, I really enjoyed it for the insights that it gave and for actually making me learn some Python as well. With this course you need to go search and fin the necessary functions and usage to complete the assignments. The best course in the series I believe.

By Idris R

•Nov 02, 2019

Great, challenging course. The instructor will expect much of you as the material is not spoon fed. At times this is frustrating but yet that's the best way to build your own intuition. This is a *hard* course and I imagine most of machine learning is like this. Fun, rewarding, and challenging. You'll flex your math and programming muscles.

By Ratnakar

•Jul 13, 2018

This is by far the best course I have taken. The Instructor is exceptional in setting the stage to understand the complex topic by letting us know the motivation of every concept, making us understand the fundamentals right, deep diving into the core of the topic and them nicely summarizing the topic along with the applications.

By David

•May 29, 2019

This was indeed a very challenging course. It was also very rewarding, and I felt that the instruction was great and relevant to the assigned tasks. The first two courses in the specialization were very high quality, and in my opinion this one lives up to the expectations that they set.

By FRANCK R S

•Jul 07, 2018

Very interesting and challenging subject: PSA, this MOOC together with the other 2 Mathematics for Machine Learning are one of the most useful I have ever made, actually they helped a lot in my other Machine learning and Deep learning studies! I highly recommend this fascinating MOOC

By mohit t

•May 13, 2018

Perfect course. It takes up more time and effort than the other two courses in the specialization. But what you learn by the end of it is totally worth the effort. Note that this is an Intermediate course compared to the other two which are beginner. So the extra rigor is expected.

By Oj S

•Jan 13, 2020

The introduction to PCA and steepest descent algorithms which might be a century old but still act the fundamentals of many state of art equations. So, you will learn the basics that how they function, and the real mathematics you need to know for ML using this course.

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 Ramon M T

•Oct 23, 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 Xavier B S

•Apr 05, 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

•Jul 06, 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 22, 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 03, 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 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 Aleksey A

•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 Q

•Feb 21, 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 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

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