图书目录

          第  1 章  机器学习 ............................................................................................................ 1

              1.1  机器学习的分类 ........................................................................................................... 1

                   1.1.1 用监督学习预测未来 ........................................................................................ 2

                   1.1.2 用无监督学习发现隐藏结构 ............................................................................. 3

                   1.1.3 用强化学习解决交互问题 ................................................................................. 4

                   1.1.4 分类和回归术语 ................................................................................................ 4

              1.2  选择正确的算法 ........................................................................................................... 5

              1.3  常用的机器学习算法 .................................................................................................... 7

              1.4  机器学习的应用领域 .................................................................................................... 8

          第  2 章 MATLAB    软件 .............................................................................................................10

              2.1 MATLAB    数据类型 .................................................................................................... 10

                   2.1.1 矩阵 ................................................................................................................ 10

                   2.1.2 元胞数组 ......................................................................................................... 11

                   2.1.3 结构体 ............................................................................................................ 12

                   2.1.4 数据存储 ......................................................................................................... 14

                   2.1.5 tall 数组 .......................................................................................................... 17

                   2.1.6 稀疏矩阵 ......................................................................................................... 19

                   2.1.7 表与分类数组 ................................................................................................. 22

                   2.1.8 大型   MAT  文件 ............................................................................................... 25

              2.2 MATLAB    作图 ........................................................................................................... 27

                   2.2.1 二维线图 ......................................................................................................... 27

                   2.2.2 通用二维图形 ................................................................................................. 31

                   2.2.3 三维点或线图 ................................................................................................. 32

                   2.2.4 通用三维图形 ................................................................................................. 34

          第  3 章  数学基础知识 ..............................................................................................................36

              3.1  矩阵的微分 ................................................................................................................ 36

                   3.1.1 标量与矩阵求导通用的法则 ........................................................................... 36

                   3.1.2 矩阵和向量求导的通用法则 ........................................................................... 38

                   3.1.3 MATLAB    的实现 ............................................................................................ 39

              3.2  向量和矩阵积分 ......................................................................................................... 41

                   3.2.1 向量梯度 ......................................................................................................... 41

                   3.2.2 微分公式 ......................................................................................................... 41

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                   3.2.3 优化方法 ......................................................................................................... 42

                   3.2.4 拉格朗日乘子法 .............................................................................................. 42

                   3.2.5 向量矩阵积分实现 .......................................................................................... 42

              3.3  特征值分解和奇异值分解 .......................................................................................... 43

                   3.3.1 特征值分解 ..................................................................................................... 43

                   3.3.2 奇异值分解  .................................................................................................... 45

              3.4  最优化方法 ................................................................................................................ 47

                   3.4.1 无约束优化方法 .............................................................................................. 47

                   3.4.2 约束优化与      KKT  条件 .................................................................................... 53

                   3.4.3 二次规划 ......................................................................................................... 57

          第  4 章  线性回归分析 ..............................................................................................................60

              4.1  线性回归模型 ............................................................................................................. 60

                   4.1.1 线性模型 ......................................................................................................... 60

                   4.1.2 损失函数 ......................................................................................................... 60

                   4.1.3 随机梯度下降法 .............................................................................................. 61

                   4.1.4 线性回归简单实现 .......................................................................................... 61

              4.2  多元线性回归 ............................................................................................................. 63

              4.3  广义线性模型 ............................................................................................................. 68

                   4.3.1 广义线性模型介绍 .......................................................................................... 69

                   4.3.2 广义线性模型实现 .......................................................................................... 69

              4.4  多重共线性 ................................................................................................................ 75

                   4.4.1 什么是多重共线性 .......................................................................................... 75

                   4.4.2 多重共性后果 ................................................................................................. 76

                   4.4.3 多重共线性检验 .............................................................................................. 79

                   4.4.4 多重共线性回归实现 ...................................................................................... 79

              4.5  其他线性回归 ............................................................................................................. 80

                   4.5.1 岭回归 ............................................................................................................ 81

                   4.5.2 Lasso 回归 ...................................................................................................... 82

                   4.5.3 弹性网络 ......................................................................................................... 83

                   4.5.4 逐步回归 ......................................................................................................... 85

          第  5 章  逻辑回归分析 ..............................................................................................................91

              5.1  逻辑回归概述 ............................................................................................................. 91

              5.2  模型表达式 ................................................................................................................ 92

              5.3  损失函数 .................................................................................................................... 93

                   5.3.1 单个样本评估正确的概率 ............................................................................... 93

                   5.3.2 所有样本评估正确的概率 ............................................................................... 93

                   5.3.3 损失函数 ......................................................................................................... 93

              5.4  模型求解 .................................................................................................................... 94

              5.5  逻辑回归的应用 ......................................................................................................... 95

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          第  6 章  K- 均值聚类算法分析 ...............................................................................................102

              6.1  K- 均值聚类算法概述 ............................................................................................... 102

                   6.1.1 K- 均值聚类算法的思想................................................................................ 102

                   6.1.2 K- 均值聚类算法的三要素 ............................................................................ 103

                   6.1.3 K- 均值聚类算法的步骤................................................................................ 103

                   6.1.4 K- 均值聚类算法的优缺点 ............................................................................ 104

                   6.1.5 K- 均值聚类算法调优 ................................................................................... 105

              6.2  K- 均值聚类算法实现 ............................................................................................... 107

                   6.2.1 K- 均值聚类算法函数 ................................................................................... 107

                   6.2.2 K- 均值聚类基于颜色的分割 .........................................................................111

              6.3  K- 均值聚类改进算法 ............................................................................................... 114

                   6.3.1 K-means++  算法 ........................................................................................... 114

                   6.3.2 ISODATA   算法 ............................................................................................. 117

          第  7 章  决策树分析 ...............................................................................................................125

              7.1  决策树的简介 ........................................................................................................... 125

              7.2  决策树的原理 ........................................................................................................... 125

                   7.2.1 信息熵 .......................................................................................................... 127

                   7.2.2 信息增益 ....................................................................................................... 127

                   7.2.3 信息增益率 ................................................................................................... 127

                   7.2.4 基尼系数 ....................................................................................................... 128

              7.3 3 种算法的对比 ........................................................................................................ 129

              7.4  剪树处理 .................................................................................................................. 129

                   7.4.1 预剪枝 .......................................................................................................... 129

                   7.4.2 后剪枝 .......................................................................................................... 129

              7.5  决策树的特点 ........................................................................................................... 130

              7.6  分类树的函数 ........................................................................................................... 130

                   7.6.1 创建分类树 ................................................................................................... 130

                   7.6.2 改进分类树 ................................................................................................... 133

                   7.6.3 解释分类树 ................................................................................................... 134

                   7.6.4 交叉验证分类树 ............................................................................................ 136

                   7.6.5 测量性能 ....................................................................................................... 138

              7.7  决策树的应用 ........................................................................................................... 141

          第  8 章  主成分分析 ...............................................................................................................148

              8.1  降维方法 .................................................................................................................. 148

              8.2  进行   PCA 的原因 ..................................................................................................... 149

              8.3 PCA   数学原理 .......................................................................................................... 149

                   8.3.1 内积与投影 ................................................................................................... 149

                   8.3.2 基 .................................................................................................................. 150

                   8.3.3 基变换的矩阵表示 ........................................................................................ 151

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              8.4 PCA   涉及的主要问题 ............................................................................................... 152

              8.5 PCA   的优化目标 ...................................................................................................... 153

              8.6 PCA   的求解步骤 ...................................................................................................... 154

              8.7 PCA   的优缺点与应用场景 ....................................................................................... 154

                   8.7.1 PCA  方法的优点 ........................................................................................... 155

                   8.7.2 PCA  方法的缺点 ........................................................................................... 155

                   8.7.3 PCA  的应用场景 ........................................................................................... 155

              8.8 PCA   相关函数 .......................................................................................................... 156

              8.9  偏最小二乘回归和主成分回归 ................................................................................. 160

          第  9 章  支持向量机分析 ........................................................................................................167

              9.1  线性分类 .................................................................................................................. 167

                   9.1.1 逻辑回归 ....................................................................................................... 167

                   9.1.2 逻辑回归表述       SVM ...................................................................................... 168

                   9.1.3 线性分类简单实例 ........................................................................................ 168

              9.2  硬间隔 ...................................................................................................................... 169

                   9.2.1 求解间隔 ....................................................................................................... 170

                   9.2.2 拉格朗日乘数法 ............................................................................................ 171

                   9.2.3 对偶问题 ....................................................................................................... 172

                   9.2.4 软间隔 .......................................................................................................... 173

                   9.2.5 核(Kernel)函数 ......................................................................................... 175

                   9.2.6 模型评估和超参数调优................................................................................. 176

              9.3  支持向量机的相关函数 ............................................................................................ 178

                   9.3.1 支持向量机回归函数 .................................................................................... 178

                   9.3.2 支持向量机分类函数 .................................................................................... 185

              9.4  用于二类分类的支持向量机 ..................................................................................... 192

                   9.4.1 用高斯核训练       SVM  分类器 .......................................................................... 192

                   9.4.2 使用自定义核函数训练            SVM  分类器 ............................................................ 195

                   9.4.3 绘制   SVM  分类模型的后验概率区域 ............................................................ 198

                   9.4.4 使用线性支持向量机分析图像 ..................................................................... 200

          第  10 章   朴素贝叶斯算法分析 ..............................................................................................203

              10.1  贝叶斯公式 ............................................................................................................ 203

              10.2  朴素贝叶斯算法的原理 .......................................................................................... 204

              10.3  朴素贝叶斯常用模型 .............................................................................................. 205

                   10.3.1 伯努利朴素贝叶斯模型 ............................................................................... 205

                   10.3.2 多项式朴素贝叶斯 ...................................................................................... 207

                   10.3.3 高斯朴素贝叶斯 .......................................................................................... 208

              10.4  拉普拉斯平滑 ......................................................................................................... 209

              10.5  朴素贝叶斯算法的优缺点 ...................................................................................... 210

              10.6  朴素贝叶斯算法的创建函数 ................................................................................... 210

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              10.7  朴素贝叶斯算法的实现 .......................................................................................... 212

                   10.7.1 逻辑回归模型的贝叶斯分析 ....................................................................... 212

                   10.7.2 判别分析、朴素贝叶斯分类器和决策树进行分类 ......................................      219

          第  11 章  随机森林算法分析 ..................................................................................................227

              11.1  集成学习 ................................................................................................................ 227

              11.2  集成学习的常见算法 .............................................................................................. 228

                   11.2.1 Bagging 算法 .............................................................................................. 228

                   11.2.2 Boosting 算法 .............................................................................................. 228

                   11.2.3 Stacking 算法 .............................................................................................. 229

              11.3  随机森林算法 ......................................................................................................... 230

                   11.3.1 随机森林算法简介 ...................................................................................... 231

                   11.3.2 随机森林算法原理 ...................................................................................... 231

                   11.3.3 随机森林算法优缺点 .................................................................................. 232

                   11.3.4 随机森林算法功能 ...................................................................................... 233

                   11.3.5 随机森林算法实现函数 ............................................................................... 233

                   11.3.6 随机森林算法的应用 .................................................................................. 244

          第  12 章   神经网络分析 .........................................................................................................249

              12.1  神经网络的概述 ..................................................................................................... 249

                   12.1.1 前馈神经网络 ............................................................................................. 249

                   12.1.2 前馈神经网络的应用 .................................................................................. 253

              12.2  卷积神经网络 ......................................................................................................... 258

                   12.2.1 用卷积代替全连接 ...................................................................................... 258

                   12.2.2 卷积层 ........................................................................................................ 259

                   12.2.3 汇聚层 ........................................................................................................ 259

                   12.2.4 全连接层 ..................................................................................................... 260

                   12.2.5 典型的卷积神经网络结构 ........................................................................... 260

                   12.2.6 几种典型的卷积神经网络 ........................................................................... 260

                   12.2.7 卷积神经网络实现 ...................................................................................... 263

              12.3  循环神经网络 ......................................................................................................... 267

                   12.3.1 循环神经网络概述 ...................................................................................... 267

                   12.3.2 循环神经网络的实现 .................................................................................. 272

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