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1198 lines
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1198 lines
36 KiB
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<title>7.4:动手实现k-均值 · GitBook</title>
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<li class="chapter " data-level="1.1" data-path="../">
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<a href="../">
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前言
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</a>
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</li>
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<li class="chapter " data-level="1.2" data-path="../Chapter1/">
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<a href="../Chapter1/">
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第一章 绪论
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.2.1" data-path="../Chapter1/为什么要数据挖掘.html">
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<a href="../Chapter1/为什么要数据挖掘.html">
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1.1:为什么要数据挖掘
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</a>
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</li>
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<li class="chapter " data-level="1.2.2" data-path="../Chapter1/什么是数据挖掘.html">
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<a href="../Chapter1/什么是数据挖掘.html">
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1.2: 什么是数据挖掘
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</a>
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</li>
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<li class="chapter " data-level="1.2.3" data-path="../Chapter1/数据挖掘主要任务.html">
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<a href="../Chapter1/数据挖掘主要任务.html">
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1.3:数据挖掘主要任务
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</a>
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</li>
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</ul>
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<li class="chapter " data-level="1.3" data-path="../Chapter2/">
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<a href="../Chapter2/">
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第二章 数据探索
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.3.1" data-path="../Chapter2/数据与属性.html">
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<a href="../Chapter2/数据与属性.html">
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2.1:数据与属性
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</a>
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</li>
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<li class="chapter " data-level="1.3.2" data-path="../Chapter2/数据的基本统计指标.html">
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<a href="../Chapter2/数据的基本统计指标.html">
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2.2:数据的基本统计指标
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</a>
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</li>
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<li class="chapter " data-level="1.3.3" data-path="../Chapter2/数据可视化.html">
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<a href="../Chapter2/数据可视化.html">
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2.3:数据可视化
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</a>
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</li>
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<li class="chapter " data-level="1.3.4" data-path="../Chapter2/相似性度量.html">
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<a href="../Chapter2/相似性度量.html">
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2.4:相似性度量
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="1.4" data-path="../Chapter3/">
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<a href="../Chapter3/">
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第三章 数据预处理
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.4.1" data-path="../Chapter3/为什么要数据预处理.html">
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<a href="../Chapter3/为什么要数据预处理.html">
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3.1:为什么要数据预处理
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</a>
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</li>
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<li class="chapter " data-level="1.4.2" data-path="../Chapter3/标准化.html">
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<a href="../Chapter3/标准化.html">
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3.2:标准化
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</a>
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</li>
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<li class="chapter " data-level="1.4.3" data-path="../Chapter3/非线性变换.html">
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<a href="../Chapter3/非线性变换.html">
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3.3:非线性变换
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</a>
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</li>
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<li class="chapter " data-level="1.4.4" data-path="../Chapter3/归一化.html">
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<a href="../Chapter3/归一化.html">
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3.4:归一化
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</a>
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</li>
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<li class="chapter " data-level="1.4.5" data-path="../Chapter3/离散值编码.html">
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<a href="../Chapter3/离散值编码.html">
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3.5:离散值编码
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</a>
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</li>
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<li class="chapter " data-level="1.4.6" data-path="../Chapter3/生成多项式特征.html">
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<a href="../Chapter3/生成多项式特征.html">
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3.6:生成多项式特征
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</a>
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</li>
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<li class="chapter " data-level="1.4.7" data-path="../Chapter3/估算缺失值.html">
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<a href="../Chapter3/估算缺失值.html">
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3.7:估算缺失值
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="1.5" data-path="../Chapter4/">
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<a href="../Chapter4/">
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第四章 k-近邻
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.5.1" data-path="../Chapter4/k-近邻算法思想.html">
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<a href="../Chapter4/k-近邻算法思想.html">
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4.1:k-近邻算法思想
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</a>
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</li>
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<li class="chapter " data-level="1.5.2" data-path="../Chapter4/k-近邻算法原理.html">
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<a href="../Chapter4/k-近邻算法原理.html">
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4.2:k-近邻算法原理
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</a>
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</li>
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<li class="chapter " data-level="1.5.3" data-path="../Chapter4/k-近邻算法流程.html">
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<a href="../Chapter4/k-近邻算法流程.html">
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4.3:k-近邻算法流程
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</a>
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</li>
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<li class="chapter " data-level="1.5.4" data-path="../Chapter4/动手实现k-近邻.html">
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<a href="../Chapter4/动手实现k-近邻.html">
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4.4:动手实现k-近邻
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</a>
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</li>
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<li class="chapter " data-level="1.5.5" data-path="../Chapter4/实战案例.html">
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<a href="../Chapter4/实战案例.html">
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4.5:实战案例
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="1.6" data-path="../Chapter5/">
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<a href="../Chapter5/">
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第五章 线性回归
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.6.1" data-path="../Chapter5/线性回归算法思想.html">
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<a href="../Chapter5/线性回归算法思想.html">
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5.1:线性回归算法思想
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</a>
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</li>
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<li class="chapter " data-level="1.6.2" data-path="../Chapter5/线性回归算法原理.html">
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<a href="../Chapter5/线性回归算法原理.html">
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5.2:线性回归算法原理
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</a>
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</li>
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<li class="chapter " data-level="1.6.3" data-path="../Chapter5/线性回归算法流程.html">
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<a href="../Chapter5/线性回归算法流程.html">
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5.3:线性回归算法流程
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</a>
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</li>
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<li class="chapter " data-level="1.6.4" data-path="../Chapter5/动手实现线性回归.html">
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<a href="../Chapter5/动手实现线性回归.html">
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5.4:动手实现线性回归
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</a>
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</li>
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<li class="chapter " data-level="1.6.5" data-path="../Chapter5/实战案例.html">
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<a href="../Chapter5/实战案例.html">
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5.5:实战案例
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="1.7" data-path="../Chapter6/">
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<a href="../Chapter6/">
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第六章 决策树
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.7.1" data-path="../Chapter6/决策树算法思想.html">
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<a href="../Chapter6/决策树算法思想.html">
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6.1:决策树算法思想
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</a>
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</li>
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<li class="chapter " data-level="1.7.2" data-path="../Chapter6/决策树算法原理.html">
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<a href="../Chapter6/决策树算法原理.html">
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6.2:决策树算法原理
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</a>
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</li>
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<li class="chapter " data-level="1.7.3" data-path="../Chapter6/决策树算法流程.html">
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<a href="../Chapter6/决策树算法流程.html">
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6.3:决策树算法流程
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</a>
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</li>
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<li class="chapter " data-level="1.7.4" data-path="../Chapter6/动手实现决策树.html">
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<a href="../Chapter6/动手实现决策树.html">
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6.4:动手实现决策树
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</a>
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</li>
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<li class="chapter " data-level="1.7.5" data-path="../Chapter6/实战案例.html">
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<a href="../Chapter6/实战案例.html">
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6.5:实战案例
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="1.8" data-path="./">
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<a href="./">
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第七章 k-均值
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.8.1" data-path="k-均值算法思想.html">
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<a href="k-均值算法思想.html">
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7.1:k-均值算法思想
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</a>
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</li>
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<li class="chapter " data-level="1.8.2" data-path="k-均值算法原理.html">
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<a href="k-均值算法原理.html">
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7.2:k-均值算法原理
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</a>
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</li>
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<li class="chapter " data-level="1.8.3" data-path="k-均值算法流程.html">
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<a href="k-均值算法流程.html">
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7.3:k-均值算法流程
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</a>
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</li>
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<li class="chapter active" data-level="1.8.4" data-path="动手实现k-均值.html">
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<a href="动手实现k-均值.html">
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7.4:动手实现k-均值
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</a>
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</li>
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<li class="chapter " data-level="1.8.5" data-path="实战案例.html">
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<a href="实战案例.html">
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7.5:实战案例
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="1.9" data-path="../Chapter8/">
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<a href="../Chapter8/">
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第八章 Apriori
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.9.1" data-path="../Chapter8/Apriori算法思想.html">
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<a href="../Chapter8/Apriori算法思想.html">
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8.1:Apriori算法思想
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</a>
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</li>
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<li class="chapter " data-level="1.9.2" data-path="../Chapter8/Apriori算法原理.html">
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<a href="../Chapter8/Apriori算法原理.html">
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8.2:Apriori算法原理
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</a>
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</li>
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<li class="chapter " data-level="1.9.3" data-path="../Chapter8/Apriori算法流程.html">
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<a href="../Chapter8/Apriori算法流程.html">
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8.3:Apriori算法流程
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</a>
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</li>
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<li class="chapter " data-level="1.9.4" data-path="../Chapter8/动手实现Apriori.html">
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<a href="../Chapter8/动手实现Apriori.html">
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8.4:动手实现Apriori
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</a>
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</li>
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<li class="chapter " data-level="1.9.5" data-path="../Chapter8/实战案例.html">
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<a href="../Chapter8/实战案例.html">
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8.5:实战案例
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="1.10" data-path="../Chapter9/">
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<a href="../Chapter9/">
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第九章 PageRank
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.10.1" data-path="../Chapter9/PageRank算法思想.html">
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<a href="../Chapter9/PageRank算法思想.html">
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9.1:PageRank算法思想
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</a>
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</li>
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<li class="chapter " data-level="1.10.2" data-path="../Chapter9/PageRank算法原理.html">
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<a href="../Chapter9/PageRank算法原理.html">
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9.2:PageRank算法原理
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</a>
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</li>
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<li class="chapter " data-level="1.10.3" data-path="../Chapter9/PageRank算法流程.html">
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<a href="../Chapter9/PageRank算法流程.html">
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9.3:PageRank算法流程
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</a>
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</li>
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<li class="chapter " data-level="1.10.4" data-path="../Chapter9/动手实现PageRank.html">
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<a href="../Chapter9/动手实现PageRank.html">
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9.4:动手实现PageRank
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</a>
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</li>
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<li class="chapter " data-level="1.10.5" data-path="../Chapter9/实战案例.html">
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<a href="../Chapter9/实战案例.html">
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9.5:实战案例
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="1.11" data-path="../Chapter10/">
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<a href="../Chapter10/">
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第十章 推荐系统
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</a>
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<ul class="articles">
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<li class="chapter " data-level="1.11.1" data-path="../Chapter10/推荐系统概述.html">
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<a href="../Chapter10/推荐系统概述.html">
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10.1:推荐系统概述
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</a>
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</li>
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<li class="chapter " data-level="1.11.2" data-path="../Chapter10/基于矩阵分解的协同过滤算法思想.html">
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<a href="../Chapter10/基于矩阵分解的协同过滤算法思想.html">
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10.2:基于矩阵分解的协同过滤算法思想
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</a>
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</li>
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<li class="chapter " data-level="1.11.3" data-path="../Chapter10/基于矩阵分解的协同过滤算法原理.html">
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<a href="../Chapter10/基于矩阵分解的协同过滤算法原理.html">
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10.3:基于矩阵分解的协同过滤算法原理
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</a>
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</li>
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<li class="chapter " data-level="1.11.4" data-path="../Chapter10/基于矩阵分解的协同过滤算法流程.html">
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<a href="../Chapter10/基于矩阵分解的协同过滤算法流程.html">
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10.4:基于矩阵分解的协同过滤算法流程
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</a>
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</li>
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<li class="chapter " data-level="1.11.5" data-path="../Chapter10/动手实现基于矩阵分解的协同过滤.html">
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<a href="../Chapter10/动手实现基于矩阵分解的协同过滤.html">
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10.5:动手实现基于矩阵分解的协同过滤
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</a>
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10.6:实战案例
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</a>
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<a href=".." >7.4:动手实现k-均值</a>
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<h1 id="74动手实现k-均值">7.4:动手实现k-均值</h1>
|
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<pre><code class="lang-python"><span class="hljs-comment">#encoding=utf8</span>
|
|
<span class="hljs-keyword">import</span> numpy <span class="hljs-keyword">as</span> np
|
|
|
|
<span class="hljs-comment"># 计算一个样本与数据集中所有样本的欧氏距离的平方</span>
|
|
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">euclidean_distance</span><span class="hljs-params">(one_sample, X)</span>:</span>
|
|
<span class="hljs-string">'''
|
|
input:
|
|
one_sample(ndarray):单个样本
|
|
X(ndarray):所有样本
|
|
output:
|
|
distances(ndarray):单个样本到所有样本的欧氏距离平方
|
|
'''</span>
|
|
one_sample = one_sample.reshape(<span class="hljs-number">1</span>, <span class="hljs-number">-1</span>)
|
|
distances = np.power(np.tile(one_sample, (X.shape[<span class="hljs-number">0</span>], <span class="hljs-number">1</span>)) - X, <span class="hljs-number">2</span>).sum(axis=<span class="hljs-number">1</span>)
|
|
<span class="hljs-keyword">return</span> distances
|
|
|
|
<span class="hljs-comment"># 从所有样本中随机选取k个样本作为初始的聚类中心</span>
|
|
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">init_random_centroids</span><span class="hljs-params">(k,X)</span>:</span>
|
|
<span class="hljs-string">'''
|
|
input:
|
|
k(int):聚类簇的个数
|
|
X(ndarray):所有样本
|
|
output:
|
|
centroids(ndarray):k个簇的聚类中心
|
|
'''</span>
|
|
n_samples, n_features = np.shape(X)
|
|
centroids = np.zeros((k, n_features))
|
|
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(k):
|
|
centroid = X[np.random.choice(range(n_samples))]
|
|
centroids[i] = centroid
|
|
<span class="hljs-keyword">return</span> centroids
|
|
|
|
<span class="hljs-comment"># 返回距离该样本最近的一个中心索引[0, k)</span>
|
|
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">_closest_centroid</span><span class="hljs-params">(sample, centroids)</span>:</span>
|
|
<span class="hljs-string">'''
|
|
input:
|
|
sample(ndarray):单个样本
|
|
centroids(ndarray):k个簇的聚类中心
|
|
output:
|
|
closest_i(int):最近中心的索引
|
|
'''</span>
|
|
distances = euclidean_distance(sample, centroids)
|
|
closest_i = np.argmin(distances)
|
|
<span class="hljs-keyword">return</span> closest_i
|
|
|
|
<span class="hljs-comment"># 将所有样本进行归类，归类规则就是将该样本归类到与其最近的中心</span>
|
|
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">create_clusters</span><span class="hljs-params">(k,centroids, X)</span>:</span>
|
|
<span class="hljs-string">'''
|
|
input:
|
|
k(int):聚类簇的个数
|
|
centroids(ndarray):k个簇的聚类中心
|
|
X(ndarray):所有样本
|
|
output:
|
|
clusters(list):列表中有k个元素，每个元素保存相同簇的样本的索引
|
|
'''</span>
|
|
clusters = [[] <span class="hljs-keyword">for</span> _ <span class="hljs-keyword">in</span> range(k)]
|
|
<span class="hljs-keyword">for</span> sample_i, sample <span class="hljs-keyword">in</span> enumerate(X):
|
|
centroid_i = _closest_centroid(sample, centroids)
|
|
clusters[centroid_i].append(sample_i)
|
|
<span class="hljs-keyword">return</span> clusters
|
|
|
|
<span class="hljs-comment"># 对中心进行更新</span>
|
|
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">update_centroids</span><span class="hljs-params">(k,clusters, X)</span>:</span>
|
|
<span class="hljs-string">'''
|
|
input:
|
|
k(int):聚类簇的个数
|
|
X(ndarray):所有样本
|
|
output:
|
|
centroids(ndarray):k个簇的聚类中心
|
|
'''</span>
|
|
n_features = np.shape(X)[<span class="hljs-number">1</span>]
|
|
centroids = np.zeros((k, n_features))
|
|
<span class="hljs-keyword">for</span> i, cluster <span class="hljs-keyword">in</span> enumerate(clusters):
|
|
centroid = np.mean(X[cluster], axis=<span class="hljs-number">0</span>)
|
|
centroids[i] = centroid
|
|
<span class="hljs-keyword">return</span> centroids
|
|
|
|
<span class="hljs-comment"># 将所有样本进行归类，其所在的类别的索引就是其类别标签</span>
|
|
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">get_cluster_labels</span><span class="hljs-params">(clusters, X)</span>:</span>
|
|
<span class="hljs-string">'''
|
|
input:
|
|
clusters(list):列表中有k个元素，每个元素保存相同簇的样本的索引
|
|
X(ndarray):所有样本
|
|
output:
|
|
y_pred(ndarray):所有样本的类别标签
|
|
'''</span>
|
|
y_pred = np.zeros(np.shape(X)[<span class="hljs-number">0</span>])
|
|
<span class="hljs-keyword">for</span> cluster_i, cluster <span class="hljs-keyword">in</span> enumerate(clusters):
|
|
<span class="hljs-keyword">for</span> sample_i <span class="hljs-keyword">in</span> cluster:
|
|
y_pred[sample_i] = cluster_i
|
|
<span class="hljs-keyword">return</span> y_pred
|
|
|
|
<span class="hljs-comment"># 对整个数据集X进行Kmeans聚类，返回其聚类的标签</span>
|
|
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">predict</span><span class="hljs-params">(k,X,max_iterations,varepsilon)</span>:</span>
|
|
<span class="hljs-string">'''
|
|
input:
|
|
k(int):聚类簇的个数
|
|
X(ndarray):所有样本
|
|
max_iterations(int):最大训练轮数
|
|
varepsilon(float):最小误差阈值
|
|
output:
|
|
y_pred(ndarray):所有样本的类别标签
|
|
'''</span>
|
|
<span class="hljs-comment"># 从所有样本中随机选取k样本作为初始的聚类中心</span>
|
|
centroids = init_random_centroids(k,X)
|
|
<span class="hljs-comment"># 迭代，直到算法收敛(上一次的聚类中心和这一次的聚类中心几乎重合)或者达到最大迭代次数</span>
|
|
<span class="hljs-keyword">for</span> _ <span class="hljs-keyword">in</span> range(max_iterations):
|
|
<span class="hljs-comment"># 将所有进行归类，归类规则就是将该样本归类到与其最近的中心</span>
|
|
clusters = create_clusters(k,centroids, X)
|
|
former_centroids = centroids
|
|
<span class="hljs-comment"># 计算新的聚类中心</span>
|
|
centroids = update_centroids(k,clusters, X)
|
|
<span class="hljs-comment"># 如果聚类中心几乎没有变化，说明算法已经收敛，退出迭代</span>
|
|
diff = centroids - former_centroids
|
|
<span class="hljs-keyword">if</span> diff.any() < varepsilon:
|
|
<span class="hljs-keyword">break</span>
|
|
y_pred = get_cluster_labels(clusters, X)
|
|
<span class="hljs-keyword">return</span> y_pred
|
|
</code></pre>
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<script src="../gitbook/gitbook-plugin-livereload/plugin.js"></script>
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</body>
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</html>
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