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## 44%

100% 在線

### 您將學到的內容有

• Implement mathematical concepts using real-world data

• Derive PCA from a projection perspective

• Understand how orthogonal projections work

• Master PCA

### 您將獲得的技能

Dimensionality ReductionPython ProgrammingLinear Algebra

100% 在線

1

## Statistics of Datasets

8 個視頻 （總計 27 分鐘）, 6 個閱讀材料, 4 個測驗
8 個視頻
Welcome to module 141
Mean of a dataset4分鐘
Variance of one-dimensional datasets4分鐘
Variance of higher-dimensional datasets5分鐘
Effect on the mean4分鐘
Effect on the (co)variance3分鐘
See you next module!27
6 個閱讀材料
About Imperial College & the team5分鐘
How to be successful in this course5分鐘
Set up Jupyter notebook environment offline10分鐘
Symmetric, positive definite matrices10分鐘
3 個練習
Mean of datasets15分鐘
Variance of 1D datasets15分鐘
Covariance matrix of a two-dimensional dataset20分鐘
2

## Inner Products

8 個視頻 （總計 36 分鐘）, 1 個閱讀材料, 5 個測驗
8 個視頻
Dot product4分鐘
Inner product: definition5分鐘
Inner product: length of vectors7分鐘
Inner product: distances between vectors3分鐘
Inner product: angles and orthogonality5分鐘
Inner products of functions and random variables (optional)7分鐘
1 個閱讀材料
Basis vectors20分鐘
4 個練習
Dot product30分鐘
Properties of inner products20分鐘
General inner products: lengths and distances30分鐘
Angles between vectors using a non-standard inner product30分鐘
3

## Orthogonal Projections

6 個視頻 （總計 25 分鐘）, 1 個閱讀材料, 3 個測驗
6 個視頻
Projection onto 1D subspaces7分鐘
Example: projection onto 1D subspaces3分鐘
Projections onto higher-dimensional subspaces8分鐘
Example: projection onto a 2D subspace3分鐘
This was module 3!32
1 個閱讀材料
Full derivation of the projection20分鐘
2 個練習
Projection onto a 1-dimensional subspace25分鐘
Project 3D data onto a 2D subspace1小時
4

## Principal Component Analysis

10 個視頻 （總計 52 分鐘）, 5 個閱讀材料, 2 個測驗
10 個視頻
Problem setting and PCA objective7分鐘
Finding the coordinates of the projected data5分鐘
Reformulation of the objective10分鐘
Finding the basis vectors that span the principal subspace7分鐘
Steps of PCA4分鐘
PCA in high dimensions5分鐘
Other interpretations of PCA (optional)7分鐘
Summary of this module42
This was the course on PCA56
5 個閱讀材料
Vector spaces20分鐘
Orthogonal complements20分鐘
Multivariate chain rule20分鐘
Lagrange multipliers20分鐘
Did you like the course? Let us know!10分鐘
1 個練習
Chain rule practice40分鐘