244,649 次近期查看

## 48%

100% 在线

### 您将学到的内容有

• Implement mathematical concepts using real-world data

• Derive PCA from a projection perspective

• Understand how orthogonal projections work

• Master PCA

## 您将获得的技能

Dimensionality ReductionPython ProgrammingLinear Algebra

100% 在线

1

## Statistics of Datasets

8 个视频 （总计 27 分钟）, 6 个阅读材料, 4 个测验
8 个视频
Welcome to module 141
Mean of a dataset4分钟
Variance of one-dimensional datasets4分钟
Variance of higher-dimensional datasets5分钟
Effect on the mean4分钟
Effect on the (co)variance3分钟
See you next module!27
6 个阅读材料
About Imperial College & the team5分钟
How to be successful in this course5分钟
Set up Jupyter notebook environment offline10分钟
Symmetric, positive definite matrices10分钟
3 个练习
Mean of datasets15分钟
Variance of 1D datasets15分钟
Covariance matrix of a two-dimensional dataset15分钟
2

## Inner Products

8 个视频 （总计 36 分钟）, 1 个阅读材料, 5 个测验
8 个视频
Dot product4分钟
Inner product: definition5分钟
Inner product: length of vectors7分钟
Inner product: distances between vectors3分钟
Inner product: angles and orthogonality5分钟
Inner products of functions and random variables (optional)7分钟
1 个阅读材料
Basis vectors20分钟
4 个练习
Dot product10分钟
Properties of inner products20分钟
General inner products: lengths and distances20分钟
Angles between vectors using a non-standard inner product20分钟
3

## Orthogonal Projections

6 个视频 （总计 25 分钟）, 1 个阅读材料, 3 个测验
6 个视频
Projection onto 1D subspaces7分钟
Example: projection onto 1D subspaces3分钟
Projections onto higher-dimensional subspaces8分钟
Example: projection onto a 2D subspace3分钟
This was module 3!32
1 个阅读材料
Full derivation of the projection20分钟
2 个练习
Projection onto a 1-dimensional subspace25分钟
Project 3D data onto a 2D subspace40分钟
4

## Principal Component Analysis

10 个视频 （总计 52 分钟）, 5 个阅读材料, 2 个测验
10 个视频
Problem setting and PCA objective7分钟
Finding the coordinates of the projected data5分钟
Reformulation of the objective10分钟
Finding the basis vectors that span the principal subspace7分钟
Steps of PCA4分钟
PCA in high dimensions5分钟
Other interpretations of PCA (optional)7分钟
Summary of this module42
This was the course on PCA56
5 个阅读材料
Vector spaces20分钟
Orthogonal complements10分钟
Multivariate chain rule10分钟
Lagrange multipliers10分钟
Did you like the course? Let us know!10分钟
1 个练习
Chain rule practice20分钟

## 关于 数学在机器学习领域的应用 专项课程

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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• You will need good python knowledge to get through the course.

• This course is significantly harder and different in style: it uses more abstract concepts and requires much more programming experience than the other two courses. Therefore, when you complete the full specialization, you will be equipped with a much more diverse set of skills.

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