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Intermediate Level
Approx. 18 hours to complete
English

### What you will learn

• Implement mathematical concepts using real-world data

• Derive PCA from a projection perspective

• Understand how orthogonal projections work

• Master PCA

### Skills you will gain

Dimensionality ReductionPython ProgrammingLinear Algebra

## 47%

started a new career after completing these courses

## 44%

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.
Intermediate Level
Approx. 18 hours to complete
English

## Syllabus - What you will learn from this course

Content Rating81%(5,665 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 dataset20m
Week
2

## Week 2

5 hours to complete

## Inner Products

5 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 product30m
Properties of inner products20m
General inner products: lengths and distances30m
Angles between vectors using a non-standard inner product30m
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 subspace1h
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 complements20m
Multivariate chain rule20m
Lagrange multipliers20m
Did you like the course? Let us know!10m
1 practice exercise
Chain rule practice40m