Back to Mathematics for Machine Learning: PCA
Imperial College London

Mathematics for Machine Learning: PCA

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.

Status: Data Preprocessing
Status: Advanced Mathematics
IntermediateCourse21 hours

Featured reviews

CF

5.0Reviewed Jul 19, 2022

Really clear and well explained. The concepts are treated in detail enough to be applied. Very happy to have invested my time in this course. I strongly recomend it.

LI

4.0Reviewed Jun 27, 2020

Very challenging at times, but very good course none the less. Would recommend to any one who has a solid foundation of Linear Algebra (Course 1) and Multivariate Calculus (Course 2).

FK

4.0Reviewed May 27, 2020

Course content is interesting and well planned, Can be improved by making it Simpler for Students as it was more technical than the other 2 courses of the Specialization.

AP

4.0Reviewed Sep 8, 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.

JS

5.0Reviewed 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.

SS

4.0Reviewed May 5, 2021

Rather difficult course and will probably reqire to watch additional video-explanations on YouTube as well as studing math notation, etc. Otherwise, helpfull and comprehensive.

FB

5.0Reviewed 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!

SG

5.0Reviewed Sep 17, 2021

Very challenging course, requires intermediate knowledge of Python and the numpy library. PCA week 4 lab was truly a mind-blowing experience, taking over 5 hours to complete.

CH

5.0Reviewed Dec 27, 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.

MH

5.0Reviewed 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!!!!

HG

4.0Reviewed Jun 7, 2020

The course is generally good but the assignment setting definitely needs to be rectified. Thanks anyway for this course. An important element of machine learning.

TR

4.0Reviewed Sep 9, 2020

it's very fantastic course.i enjoyed a lot.i feel reading material should be increases in those courses,others things are perfectly ok.thanks for offering this courses.

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