Back to Mathematics for Machine Learning: PCA

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2,836 ratings

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....

WS

Jul 6, 2021

Now i feel confident about pursuing machine learning courses in the future as I have learned most of the mathematics which will be helpful in building the base for machine learning, data science.

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.

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By Tarek L

•Sep 11, 2019

This is a difficult course, but it really gave me an appreciation of the mathematics behind machine learning. I encourage anyone doing this course to read Deisenroth's free book Mathematics for Machine Learning (mml-book.com) to better understand the notation and technique used to get to the proofs. If anything, the rigor of this course inspired me to further pursue learning in mathematics to strengthen my machine learning foundation.

By Ling J

•Apr 18, 2018

The whole content of this course is fantastic, not all details were covered in the video, but main ideas were expressed in a great way buy math formulations. Pay attention to those vectors and matrices, especially their dimensions, this will help you solve problem quickly. More important, matrix is just a way to express a bunch of similar things, knowing the meaning of those basis vectors is important.

By Sriram R

•Jun 18, 2019

This is one of toughest course in this specialization. Having said that, it was interesting to learn about the inner working of the PCA and is well taught. At times it was tough to follow and could have been better if there are some additional examples explained to reinforce the concept. Also week 4 is kind of rushed with little or no time to fully appreciate the beauty of PCA.

By Yuanfang F

•Sep 7, 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 Sertan A

•Dec 14, 2020

Actually I was not encouraged while I am taking the course since the quest for understanding such abstract concepts required me to spend a lot of outside research and reading. Course also requires a strong understanding of Python and Anaconda (for debugging purposes). I can not say that I understand everything regarding PCA, but it became a nice foundation to built upon.

By Marcelo R

•Jul 26, 2020

Unlike the other two modules, the course is quite challenging, some details are omitted in the explanation and one has to look for them in the forum or on the internet. Some notebooks for programming have problems and need to be downloaded and run virtually. Still, the content is exciting, thanks to the Imperial College London for the course and the opportunity.

By Renato

•May 3, 2020

This course is challenging, it requires a lot of participation in the forum plus an overlook on the internet to help you out understand a little more how the vector (eigenvectors) relate to the efficiency of PCA. It is pretty interesting to understand the algorithm itself and how it works. Be aware to review a lot and take your time to understand things.

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 2, 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 Xavier P

•Nov 9, 2020

Fantastic teacher !! He succeeds in finding the right balance between theory and concrete examples. All the concepts presented over the 4 weeks smoothly merge at the end of the course to give a good global picture of the PCA algorithm and its applications. As a sidenote, the Jupyter notebooks contain mistakes or can be quite confusing.

By Jaiber J

•May 1, 2020

A great course, worth the money. It was hard, as it should be. The explanations are concise, and the assignments take much more to complete, at times leaving us scratching the head. Anyway, I'm so glad to have completed, it has provided me such great insight about how mathematics powers the machine learning algorithms we use everyday.

By Ratnakar M

•Jul 12, 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 MUHAMMAD Z I F

•Mar 22, 2021

This course is amazing. But you if you guys maybe in the future to make some small example. I really dont get the concept when there is no example. I mean the example with a number in it or maybe i said the direct implementation. But all is great. Thanks you for teaching me this. I hope you guys well. thanks

By Geoffrey K

•Jun 5, 2020

This course is at a higher level than the first two in the specialisation, and the instructor focusses on the mathematics of matrices, while the assessments are programming. There are easier courses for just PCA (which I thought helped me). Looks like most learners find a way through, and its worth it.

By Fernando M

•Jun 30, 2020

It was a great course. Challenging at some points since I'm new in Python but it was worth the effort and I really learn a lot and now I comprehend the maths behind PCA algorithm. The point in which the relationship between eigenvalues of the covariance matrix is used in the PCA algorithm was amazing.

By Juan P M C

•Sep 19, 2020

Even though I had lots of problems with the last coding exercise, I still learned a lot from this course. I loved how the instructor went from the basics of statistical representation and started using all of these tools in order to show us how the PCA algorithm works and why is it effective.

By Adithya P

•Oct 1, 2020

Course 3 was quite challenging when compared to 1 and 2.

But, the instructor have explained the concept very well, the coding assignments were bit confusing and time killing.

Got to learn some important ML mathematics and the concept of projection, inner product and PCA were amazing.

Thank You

By surbhi

•Jun 17, 2020

Learning Mathematics in this way and in efficient manner from basics and very clearly is really nice. I am very thankful to this course , teachers, Imperial College London as well as team of Coursera for providing such a great platform to learn all these skills and enhance our knowledge.

By David L

•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 Traning_Chotot

•Jul 19, 2021

This is a good course coming with a very good book which you can use to reference later on even if you don't fully understand what or how PCA derives.

The exercise & lectures were interesting and guiding you enough to pass all tests. Take note and reference the book are keys to succeed.

By FRANCK R S

•Jul 7, 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 anurag

•Apr 18, 2020

Its a very informational and interesting course. I understood a lot about PCA in this amazing course.

It was a good addition to the previous two courses of the certification. I would like to get similar courses in statistics and probability useful in Machine learning.

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