向量空间(Vector Spaces) 向量空间又称线性空间,是线性代数的中心内容和基本概念之一.在解析几何里引入向量的概念后,是许多问题的处理变得更为简洁和清晰,在此基础上的进一步抽象化,形成了与域相联系的向量空间概念.譬如,实系多项式的集合在定义适当的运算后构成向量空间,在代数上处理是方便的.单变元实函数的集合在定义适当的运算后,也构成向量空间,研究此类函数向量空间的数学分支称为泛函数 Example: R2(均为二维实向量) eg:…
Vector Space: R1, R2, R3,R4 , .... Each space Rn consists of a whole collection of vectors. R5 contains all column vectors with five components. This is called "5-dimensional space". The great thing about linear algebra is that it deals easily w…
首先从介绍了Large_margin Separating Hyperplane的概念. (在linear separable的前提下)找到largest-margin的分界面,即最胖的那条分界线.下面开始一步步说怎么找到largest-margin separating hyperplane. 接下来,林特意强调了变量表示符号的变化,原来的W0换成了b(这样的表示利于推导:觉得这种强调非常负责任,利于学生听懂,要不然符号换来换去的,谁知道你说的是啥) 既然目标是找larger-margin s…
Roadmap Course Introduction Large-Margin Separating Hyperplane Standard Large-Margin Problem Support Vector Machine Reasons behind Large-Margin Hyperplane Summary…
Roadmap Course Introduction Large-Margin Separating Hyperplane Standard Large-Margin Problem Support Vector Machine Reasons behind Large-Margin Hyperplane Summary…
Matrix and Determinant Let C be an M × N matrix with real-valued entries, i.e. C={cij}mxn Determinant is a value that can be computed from the elements of a square matrix. The determinant of a matrix A is denoted det(A), det A, or |A|. In the case of…
第一阶段技法: large margin (the relationship between large marin and regularization), hard-SVM,soft-SVM,dual problem(解对偶问题),kernel trick,kernel logistic regression, 主要思路是:(这里不区分线性与非线性,差别只是特征空间转换,X空间与Z空间的关系) 1. 从PLA出发,对于二维平面的二分类问题,PLA可能得出一堆能够正确分类的直线,但是哪一条直线…
Section 2.7     PA=LU and Section 3.1   Vector Spaces and Subspaces   Transpose(转置) example: 特殊情况,对称矩阵(symmetric matrices),例如: 思考:R^R(R的转置乘以R)有什么特殊的? 回答:always symmetric why?   Permutation(置换) P=execute row exchanges 之前A=LU是建立在no row exchanges 的基础上的,…
导语:其他集数可在[线性代数]标籤文章找到.线性子空间是一个大课题,这里先提供一个简单的入门,承接先前关于矩阵代数的讨论,期待与你的交流. Overview: Subspace definition In a vector space of Rn, sets of vectors spanning a volume EQUAL TO OR SMALLER THAN that of Rn form subspaces of that vector space of Rn. A subset H o…
Why are very few schools involved in deep learning research? Why are they still hooked on to Bayesian methods? First, this question assumes that every university should have a "deep learning" person.  Deep learning is mostly used in vision (and…