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## 48%

### 您將獲得的技能

Python ProgrammingPrincipal Component Analysis (PCA)Projection MatrixMathematical Optimization

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 dataset15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 product10分鐘
Properties of inner products20分鐘
General inner products: lengths and distances20分鐘
Angles between vectors using a non-standard inner product20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 subspace40分鐘
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 complements10分鐘
Multivariate chain rule10分鐘
Lagrange multipliers10分鐘
Did you like the course? Let us know!10分鐘
1 個練習
Chain rule practice20分鐘

## 關於 数学在机器学习领域的应用 專項課程

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....

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