118,745 recent views

## 50%

started a new career after completing these courses

## 48%

got a tangible career benefit from this course

#### Shareable Certificate

Earn a Certificate upon completion

#### 100% online

Start instantly and learn at your own schedule.

#### English

Subtitles: English

### Skills you will gain

Python ProgrammingPrincipal Component Analysis (PCA)Projection MatrixMathematical Optimization

## 50%

started a new career after completing these courses

## 48%

got a tangible career benefit from this course

#### Shareable Certificate

Earn a Certificate upon completion

#### 100% online

Start instantly and learn at your own schedule.

#### English

Subtitles: English

## Syllabus - What you will learn from this course

Content Rating79%(3,035 ratings)
Week
1

## Week 1

5 hours to complete

## Statistics of Datasets

5 hours to complete
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
About Imperial College & the team5m
How to be successful in this course5m
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

## Week 2

4 hours to complete

## Inner Products

4 hours to complete
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
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

## Week 3

4 hours to complete

## Orthogonal Projections

4 hours to complete
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
Full derivation of the projection20m
2 practice exercises
Projection onto a 1-dimensional subspace25m
Project 3D data onto a 2D subspace40m
Week
4

## Week 4

5 hours to complete

## Principal Component Analysis

5 hours to complete
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
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
308 Reviews

### 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!

## 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 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....