Andrew Ng ML(1)——basic knowledge

introduction

• supervised learning(with labels)
  regressing
  classification

• unsupervised learning(no labels or same label)
  clustering

---

univariate (one variable) linear regressing (supervised learning)

• m: numbers of training examples
  x's: input variable/features
  y's: output variable/targets variable
  e.g.
  :single training example
  :training example

• regressing

Hypothesis:
Parameters:
cost function: (←this is a square error function，also the most commonly used one for regression problems)
goal:

simplify hypothesis as

each value of Theta1 corresponds a different hypothesis

hypothesis as

cost function(function J) when the hypothesis have two parameters Right:contour plot(等高线图) of cost function

---

"Batch"Gradient descent("Batch"梯度下降) with one variable

Batch:每一步梯度下降均用到了整个样本（中有对均方误差的累加）
have some functions
want min
outline:1.start with some (commonly they are all zeros) 2.keep changing to reduce until we hopefully end up at a mininum

Gradient descent algorithm (P.S. := 表示赋值， = 表示比较，需要同时更新两个parameters)
simplify hypothesis as 梯度下降公式中，导数项的含义 α的取值对梯度下降的影响（如果Θ已经取到局部最小值，由于导数项为0，解将一直保持在局部最小值）

simplify hypothesis as

cost function and Gradient descent algorithm when hypothesis have two parameters 导数项计算 将导数项代会上图中的梯度下降算法

最后，将梯度下降算法中得到的parameters代入，就能得到最优解线性拟合函数

---

---

Matrices and vectors（回顾）

• Vector: An n x 1 matrix (in this course)
  e.g. element,()

• matrices addition (略)

• scalar multiplication
  

• matrices multiplication

calculate all of predicted prices at the same time（单个假设函数）

Houses sizes:
2104
1416
1534
852

hypothesis:

(prediction = DataMatrix * parameters)

多个假设函数

多假设函数

• properties of matrices multiplication
  in general, expect
  

• matrices inverse (逆矩阵)

  if A is an m x m matrix, and if it has an inverse
  
  如果一个矩阵没有逆矩阵，贼该矩阵为奇异矩阵（singular）、退化矩阵（degenerate）
  如何手工求解逆矩阵？
  ，
  行列式:
  伴随矩阵：

  代入求解逆矩阵，但是一般用库求解

• matrix transpose(转置矩阵) 略

---