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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/linear-algebra-machine-learning
课程评论：没有评论
课程名称：机器学习的数学：线性代数 概述：本课程专注于线性代数，探讨其与向量和矩阵的关系。我们将学习向量和矩阵的概念及其操作，包括特征值和特征向量的复杂问题，以及如何利用这些知识解决实际问题。课程中，我们还将通过代码实现一些有趣的数据集应用，例如如何旋转人脸图像、提取特征向量，并了解PageRank算法的工作原理。课程后期会涉及短小的Python代码块和Jupyter笔记本，即使是没有编码经验的学员也能够轻松跟上。 通过本课程，您将对向量和矩阵有直观的理解，从而帮助您更好地解决线性代数问题，并将这些概念应用于机器学习领域。 课程大纲： 1. **线性代数与机器学习简介**：介绍线性代数在机器学习和数据科学中的相关性，重点发展数学直觉，不进行复杂的公式计算。 2. **向量作为空间中的物体**：学习向量的操作，如大小、夹角及向量投影，探讨基向量是否线性独立。 3. **矩阵在线性代数中的应用**：了解如何使用矩阵作为解决线性代数问题的工具，解决线性方程组，并讨论逆矩阵和行列式的直观理解。 4. **矩阵实现线性映射**：编写矩阵乘法和操作的代码，探讨如何通过矩阵在不同基下转化向量，并实现图像反射等应用。 5. **特征值和特征向量及其在数据问题中的应用**：学习特征向量和特征值的概念，应用于PageRank算法，并通过代码实现相关操作。 通过学习本课程，学员将掌握线性代数的基本概念，为进一步的机器学习应用打下坚实的基础。
Name:Introduction to Linear Algebra and to Mathematics for Machine Learning
Description:In this first module we look at how linear algebra is relevant to machine learning and data science. Then we'll wind up the module with an initial introduction to vectors. Throughout, we're focussing on developing your mathematical intuition, not of crunching through algebra or doing long pen-and-paper examples. For many of these operations, there are callable functions in Python that can do the adding up - the point is to appreciate what they do and how they work so that, when things go wrong or there are special cases, you can understand why and what to do.
Name:Vectors are objects that move around space
Description:In this module, we look at operations we can do with vectors - finding the modulus (size), angle between vectors (dot or inner product) and projections of one vector onto another. We can then examine how the entries describing a vector will depend on what vectors we use to define the axes - the basis. That will then let us determine whether a proposed set of basis vectors are what's called 'linearly independent.' This will complete our examination of vectors, allowing us to move on to matrices in module 3 and then start to solve linear algebra problems.
Name:Matrices in Linear Algebra: Objects that operate on Vectors
Description:Now that we've looked at vectors, we can turn to matrices. First we look at how to use matrices as tools to solve linear algebra problems, and as objects that transform vectors. Then we look at how to solve systems of linear equations using matrices, which will then take us on to look at inverse matrices and determinants, and to think about what the determinant really is, intuitively speaking. Finally, we'll look at cases of special matrices that mean that the determinant is zero or where the matrix isn't invertible - cases where algorithms that need to invert a matrix will fail.
Name:Matrices make linear mappings
Description:In Module 4, we continue our discussion of matrices; first we think about how to code up matrix multiplication and matrix operations using the Einstein Summation Convention, which is a widely used notation in more advanced linear algebra courses. Then, we look at how matrices can transform a description of a vector from one basis (set of axes) to another. This will allow us to, for example, figure out how to apply a reflection to an image and manipulate images. We'll also look at how to construct a convenient basis vector set in order to do such transformations. Then, we'll write some code to do these transformations and apply this work computationally.
Name:Eigenvalues and Eigenvectors: Application to Data Problems
Description:Eigenvectors are particular vectors that are unrotated by a transformation matrix, and eigenvalues are the amount by which the eigenvectors are stretched. These special 'eigen-things' are very useful in linear algebra and will let us examine Google's famous PageRank algorithm for presenting web search results. Then we'll apply this in code, which will wrap up the course.
In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works. Since we're aiming at data-driven applications, we'll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you'll write code blocks and encounter Jupyter notebooks in Python, but don't worry, these will be quite short, focussed on the concepts, and will guide you through if you’ve not coded before. At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these concepts to machine learning.
