About this Course
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Intermediate Level

Approx. 18 hours to complete

Suggested: 4 weeks of study, 4-5 hours/week...

English

Subtitles: English

Skills you will gain

Python ProgrammingPrincipal Component Analysis (PCA)Projection MatrixMathematical Optimization
Learners taking this Course are
  • Machine Learning Engineers
  • Data Scientists
  • Biostatisticians
  • Scientists
  • Data Analysts

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 18 hours to complete

Suggested: 4 weeks of study, 4-5 hours/week...

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
5 hours to complete

Statistics of Datasets

8 videos (Total 27 min), 6 readings, 4 quizzes
8 videos
Welcome to module 141s
Mean of a dataset4m
Variance of one-dimensional datasets4m
Variance of higher-dimensional datasets5m
Effect on the mean4m
Effect on the (co)variance3m
See you next module!27s
6 readings
About Imperial College & the team5m
How to be successful in this course5m
Grading policy5m
Additional readings & helpful references5m
Set up Jupyter notebook environment offline10m
Symmetric, positive definite matrices10m
3 practice exercises
Mean of datasets15m
Variance of 1D datasets15m
Covariance matrix of a two-dimensional dataset15m
Week
2
4 hours to complete

Inner Products

8 videos (Total 36 min), 1 reading, 5 quizzes
8 videos
Dot product4m
Inner product: definition5m
Inner product: length of vectors7m
Inner product: distances between vectors3m
Inner product: angles and orthogonality5m
Inner products of functions and random variables (optional)7m
Heading for the next module!35s
1 reading
Basis vectors20m
4 practice exercises
Dot product10m
Properties of inner products20m
General inner products: lengths and distances20m
Angles between vectors using a non-standard inner product20m
Week
3
4 hours to complete

Orthogonal Projections

6 videos (Total 25 min), 1 reading, 3 quizzes
6 videos
Projection onto 1D subspaces7m
Example: projection onto 1D subspaces3m
Projections onto higher-dimensional subspaces8m
Example: projection onto a 2D subspace3m
This was module 3!32s
1 reading
Full derivation of the projection20m
2 practice exercises
Projection onto a 1-dimensional subspace25m
Project 3D data onto a 2D subspace40m
Week
4
5 hours to complete

Principal Component Analysis

10 videos (Total 52 min), 5 readings, 2 quizzes
10 videos
Problem setting and PCA objective7m
Finding the coordinates of the projected data5m
Reformulation of the objective10m
Finding the basis vectors that span the principal subspace7m
Steps of PCA4m
PCA in high dimensions5m
Other interpretations of PCA (optional)7m
Summary of this module42s
This was the course on PCA56s
5 readings
Vector spaces20m
Orthogonal complements10m
Multivariate chain rule10m
Lagrange multipliers10m
Did you like the course? Let us know!10m
1 practice exercise
Chain rule practice20m
4.0
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Top reviews from Mathematics for Machine Learning: PCA

By JSJul 17th 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.

By JVMay 1st 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!

Instructor

Avatar

Marc P. Deisenroth

Lecturer in Statistical Machine Learning
Department of Computing

About Imperial College London

Imperial College London is a world top ten university with an international reputation for excellence in science, engineering, medicine and business. located in the heart of London. Imperial is a multidisciplinary space for education, research, translation and commercialisation, harnessing science and innovation to tackle global challenges. Imperial students benefit from a world-leading, inclusive educational experience, rooted in the College’s world-leading research. Our online courses are designed to promote interactivity, learning and the development of core skills, through the use of cutting-edge digital technology....

About the Mathematics for Machine Learning Specialization

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science. In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require basic Python and numpy knowledge. At the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning....
Mathematics for Machine Learning

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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