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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/pca-machine-learning
课程评论：没有评论
课程名称：机器学习的数学基础：主成分分析（PCA） 概述：本课程为中级水平，介绍了推导主成分分析（PCA）的数学基础，PCA是一种重要的降维技术。我们将讨论数据集的一些基本统计量，如均值和方差，以及使用内积计算向量之间的距离和角度，并推导数据在低维子空间上的正交投影。通过这些工具，我们将推导出PCA作为一种最小化数据点与其重构之间平均平方重构误差的方法。完成课程后，学员将熟悉重要的数学概念，并能独立实现PCA。如果您遇到困难，课程提供了一系列Jupyter笔记本，将帮助您探讨技术属性并指导您完成学习。如果您已经是专家，本课程也将为您复习一些知识。 课程内容要求： 1. 具备一定的抽象思维能力 2. 良好的线性代数背景（例如矩阵和向量代数、线性独立性、基） 3. 基本的多变量微积分知识（例如偏导数、基础优化） 4. 基本的Python编程和numpy知识 免责声明：本课程的抽象性和编程要求相对较高，尤其比本系列的其他两门课程更加困难。然而，这种抽象思维、代数运算和编程技能是理解和开发机器学习算法所必需的。 课程大纲： 1. 数据集统计：介绍如何使用基本统计量（如均值和方差）总结数据集（例如图像），并提供数学直觉和计算实践。 2. 内积：数据可视为向量，通过内积，我们可以讨论向量空间中的几何概念，如长度、距离和角度，帮助理解PCA。 3. 正交投影：将高维向量正交投影到低维子空间，理解这个几何过程对后续推导PCA的重要性。 4. 主成分分析：最终将结合前三部分的内容，从几何角度推导出PCA，完成显式推导和编程练习，使学员熟练掌握PCA的使用。 通过本课程，学员将获得扎实的数学基础和实践能力，更好地理解和应用机器学习中的降维技术。
Name:Statistics of Datasets
Description:Principal Component Analysis (PCA) is one of the most important dimensionality reduction algorithms in machine learning. In this course, we lay the mathematical foundations to derive and understand PCA from a geometric point of view. In this module, we learn how to summarize datasets (e.g., images) using basic statistics, such as the mean and the variance. We also look at properties of the mean and the variance when we shift or scale the original data set. We will provide mathematical intuition as well as the skills to derive the results. We will also implement our results in code (jupyter notebooks), which will allow us to practice our mathematical understand to compute averages of image data sets. Therefore, some python/numpy background will be necessary to get through this course. Note: If you have taken the other two courses of this specialization, this one will be harder (mostly because of the programming assignments). However, if you make it through the first week of this course, you will make it through the full course with high probability.
Name:Inner Products
Description:Data can be interpreted as vectors. Vectors allow us to talk about geometric concepts, such as lengths, distances and angles to characterize similarity between vectors. This will become important later in the course when we discuss PCA. In this module, we will introduce and practice the concept of an inner product. Inner products allow us to talk about geometric concepts in vector spaces. More specifically, we will start with the dot product (which we may still know from school) as a special case of an inner product, and then move toward a more general concept of an inner product, which play an integral part in some areas of machine learning, such as kernel machines (this includes support vector machines and Gaussian processes). We have a lot of exercises in this module to practice and understand the concept of inner products.
Name:Orthogonal Projections
Description:In this module, we will look at orthogonal projections of vectors, which live in a high-dimensional vector space, onto lower-dimensional subspaces. This will play an important role in the next module when we derive PCA. We will start off with a geometric motivation of what an orthogonal projection is and work our way through the corresponding derivation. We will end up with a single equation that allows us to project any vector onto a lower-dimensional subspace. However, we will also understand how this equation came about. As in the other modules, we will have both pen-and-paper practice and a small programming example with a jupyter notebook.
Name:Principal Component Analysis
Description:We can think of dimensionality reduction as a way of compressing data with some loss, similar to jpg or mp3. Principal Component Analysis (PCA) is one of the most fundamental dimensionality reduction techniques that are used in machine learning. In this module, we use the results from the first three modules of this course and derive PCA from a geometric point of view. Within this course, this module is the most challenging one, and we will go through an explicit derivation of PCA plus some coding exercises that will make us a proficient user of PCA.
This intermediate-level course introduces the mathematical foundations to derive Principal Component Analysis (PCA), a fundamental dimensionality reduction technique. We'll cover some basic statistics of data sets, such as mean values and variances, we'll compute distances and angles between vectors using inner products and derive orthogonal projections of data onto lower-dimensional subspaces. Using all these tools, we'll then derive PCA as a method that minimizes the average squared reconstruction error between data points and their reconstruction. At the end of this course, you'll be familiar with important mathematical concepts and you can implement PCA all by yourself. If you’re struggling, you'll find a set of jupyter notebooks that will allow you to explore properties of the techniques and walk you through what you need to do to get on track. If you are already an expert, this course may refresh some of your knowledge. The lectures, examples and exercises require: 1. Some ability of abstract thinking 2. Good background in linear algebra (e.g., matrix and vector algebra, linear independence, basis) 3. Basic background in multivariate calculus (e.g., partial derivatives, basic optimization) 4. Basic knowledge in python programming and numpy Disclaimer: This course is substantially more abstract and requires more programming than the other two courses of the specialization. However, this type of abstract thinking, algebraic manipulation and programming is necessary if you want to understand and develop machine learning algorithms.
