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必须知道预测什么，即必须知道目标变量的分类信息。分类和回归属于监督学习。 @@ -43,7 +43,7 @@ * 想要完成何种任务，比如是预测明天下雨的概率还是对投票者按照兴趣分组；如果想要预测目标变量的值，则可以选择监督学习算法，否则可以选择无监督学习算法。 * 需要分析或收集的数据是什么 * 举例 -* ![选择算法图](./1.机器学习基础-选择算法.png) +* ![选择算法图](/images/1.MLFoundation/机器学习基础-选择算法.png) * 开发的步骤 * 1.收集数据 diff --git a/docs/11.使用Apriori算法进行关联分析.md b/docs/11.使用Apriori算法进行关联分析.md index 2dc4a838..04503a60 100644 --- a/docs/11.使用Apriori算法进行关联分析.md +++ b/docs/11.使用Apriori算法进行关联分析.md @@ -14,7 +14,7 @@ * 2.关联规则(association rules): 暗示两种物品之间可能存在很强的关系 * 总结：首先需要找到频繁项集，才能找到关联规则。 * 如下图： - * ![交易清单](./11.交易清单.png) + * ![交易清单](/images/11.Apriori/交易清单.png) * 支持度(support) * 数据集中包含该项集的记录所占的比例 * 例如上图中：{豆奶}的支持度=4/5， {豆奶，尿布}的支持度=3/5 @@ -36,10 +36,10 @@ * 如果某个项集是频繁的，那么它的所有子集也是频繁的，反之，一个项集是非频繁的，那么它的所有超集也是非频繁的。 * 例如： 我们假设知道{2, 3}是非频繁项，那么{0, 2, 3}, {1, 2, 3}, {0, 1, 2, 3}都是非频繁项。 * 如下图： - * ![非频繁项集](./11.非频繁项集.png) + * ![非频繁项集](/images/11.Apriori/非频繁项集.png) * 分级法： 频繁项集->关联规则 * 1.首先从一个频繁项集开始，接着创建一个规则列表，其中规则右部分只包含一个元素，然后对这个规则进行测试。 * 2.接下来合并所有剩余规则来创建一个新的规则列表，其中规则右部包含两个元素。 * 如下图： - * ![所有可能的项集组合](./11.所有可能的项集组合.png) + * ![所有可能的项集组合](/images/11.Apriori/所有可能的项集组合.png) * 最后： 每次增加频繁项集的大小，Apriori算法都会重新扫描整个数据集，是否有优化空间呢？ 下一章：FP-growth算法等着你的到来 diff --git a/docs/13.利用PCA来简化数据.md b/docs/13.利用PCA来简化数据.md index 143e2ac4..cfa3c031 100644 --- a/docs/13.利用PCA来简化数据.md +++ b/docs/13.利用PCA来简化数据.md @@ -1,6 +1,70 @@ - # 3) 利用PCA来简化数据 - -* 未完待续 +> 场景描述： + +* 我们正通过电视而非现场观看体育比赛，在电视的纯平显示器上有一个球。 +* 显示器大概包含了100万像素，而球则可能是由较少的像素组成，例如说一千个像素。 +* 人们实时的将显示器上的百万像素转换成为一个三维图像，该图像就给出运动场上球的位置。 +* 在这个过程中，人们已经将数据从一百万维降至了三维。这就被称为`降维(dimensionality reduction)` + +## 1 将维技术 + +> 数据显示并非大规模特征下的唯一难题，对数据进行简化还有如下一系列的原因： + +* 1) 使得数据集更容易使用 +* 2) 降低很多算法的计算开销 +* 3) 去除噪音 +* 4) 是的结果易懂 + +> 适用范围: + +* 在已标注与未标注的数据上都有降维技术。 +* 这里我们将主要关注未标注数据上的降维技术，将技术同样也可以应用于已标注的数据。 + +> 在以下3种降维技术中， PCA的应用目前最为广泛，因此本章主要关注PCA。 + +* 1) 主成分分析(Principal Component Analysis, PCA) + * `通俗理解：就是找出一个最主要的特征，然后进行分析。` + * `例如： 考察一个人的智力情况，就直接看数学成绩就行(存在：数学、语文、英语成绩)` + * a.将数据从原来的坐标系转换到了新的坐标系，新的坐标系的选择是由数据本身决定的。 + * b.第一个新坐标轴选择的是原始数据中`方差最大`的方向 + * c.第二个新坐标轴的选择和第一个坐标轴`正交(orthogonal 如果是二维空间就叫垂直)`且具有`最大方差`的方向。 + * d.该过程一直重复，重复次数为原始数据中特征的数目。 + * 我们会发现，大部分方差都包含在最前面的几个新坐标轴中。因此，我们可以忽略余下的坐标轴，即对数据进行了降维处理。 +* 2) 因子分析(Factor Analysis) + * `通俗理解：将多个实测变量转换为少数几个综合指标,它反映一种降维的思想.通过降维将相关性高的变量聚在一起,从而减少需要分析的变量的数量,而减少问题分析的复杂性` + * `例如： 考察一个人的整体情况，就直接组合3样成绩(隐变量)，看平均成绩就行(存在：数学、语文、英语成绩)` + * 应用的领域：社会科学、金融和其他领域 + * 在因子分析中，我们 + * 假设观察数据的生成中有一些观察不到的隐变量(latent variable)。 + * 假设观察数据是这些隐变量和某些噪音的线性组合。 + * 那么隐变量的数据可能比观察数据的数目少，也就说通过找到隐变量就可以实现数据的降维。 +* 3) 独立成分分析(Independ Component Analysis, ICA) + * `通俗理解：PCA(主成分分析)寻找的是，使得投影之后，尽量保留原有信息量的投影方向。 ICA(独立主成分分析)寻找的是，使得投影之后，数据之间相互独立的投影方向。` + * `例如：我们去ktv唱歌，想辨别唱的是哪首歌，PCA就是搜录歌词；而ICA是对歌词按人进行完全的拆分。` + * ICA假设数据是从N个数据源生成的，这一点和因子分析有些类似。 + * 假设数据为多个数据源的混合观察结果，这些数据源之间在统计上是相互独立的，而在PCA中只假设数据是不相关的。 + * 同因子分析一样，如果数据源的数目少于观察数据的数目，则可以实现降维过程。 + +## 2 主成分分析(PCA) + +> PCA的优缺点 + +* 优点：降低数据的复杂性，识别最重要的多个特征。 +* 缺点：不一定需要，且可能损失有用信息。 +* 适用数据类型：数值型数据。 + +> 通过PCA进行降维处理，我们就可以同时获得SVM和决策树的优点： + +* 一方面，得到了和决策树一样简单的分类器，同时分类间隔和SVM一样好。 + * 1.第一个主成分就是来自于数据差异性最大(即 方差最大)的方向提取出来 + * 2.第二个主成分就是来自于数据差异性次大的方向，并且该方向于第一个主成分方向正交。 + * 3.通过数据集的协方差矩阵及其特征值分析，我们就可以得到这些主成分的值。 + * 一旦得到了协方差矩阵的特征向量，我们就可以保留最大的N个值。这些特征向量也给出了N个最重要特征的真实结构。我们可以通过将数据乘上这N个特征向量而将它转换到新的空间。 +* 例如下图： +* ![应用PCA降维](/images/13.PCA/应用PCA降维.png) + +## 3 对半导体数据进行降维处理 + + \ No newline at end of file diff --git a/docs/3.决策树.md b/docs/3.决策树.md index 3d6e6ed7..7f0bd058 100644 --- a/docs/3.决策树.md +++ b/docs/3.决策树.md @@ -24,4 +24,4 @@ * 基尼不纯度(Gini impurity) [本书不做过多的介绍] * 简单来说：就是从一个数据集中随机选取子项，度量其被错误分类到其他分组里的概率。 * 流程介绍图 -* ![决策树流程介绍图](./3.决策树流程介绍图.jpg) +* ![决策树流程介绍图](/images/3.DecisionTree/决策树流程介绍图.jpg) diff --git a/docs/7.利用AdaBoost元算法提高分类.md b/docs/7.利用AdaBoost元算法提高分类.md index e9cdc3a7..3c6d6621 100644 --- a/docs/7.利用AdaBoost元算法提高分类.md +++ b/docs/7.利用AdaBoost元算法提高分类.md @@ -32,18 +32,18 @@ * 单层决策树(decision stump, 也称决策树桩)是一种简单的决策树。 * 过拟合(overfitting, 也称为过学习) * 发现测试错误率在达到一个最小值之后有开始上升，这种现象称为过拟合。 - * ![过拟合](./7.过拟合.png) + * ![过拟合](/images/7.AdaBoost/过拟合.png) * 非均衡分类问题 * 现象： * 判断马是否能继续生存 * 过滤垃圾邮件 * ROC曲线: 最佳的分类器应该尽可能地处于左上角 - * ![ROC曲线](./7.ROC曲线.png) + * ![ROC曲线](/images/7.AdaBoost/ROC曲线.png) * 对不同的ROC曲线进行比较的一个指标是曲线下的面积(Area Unser the Curve, AUC). * AUC给出的是分类器的平均性能值，当然它并不能完全代替对整条曲线的观察。 * 一个完美分类器的AUC为1，而随机猜测的AUC则为0.5。 * 基于代价函数的分类器决策控制：`TP*(-5)+FN*1+FP*50+TN*0` - * ![代价函数](./7.代价函数.png) + * ![代价函数](/images/7.AdaBoost/代价函数.png) * 欠抽样(undersampling)或者过抽样(oversampling) * 欠抽样: 意味着删除样例 * 过抽样: 意味着复制样例(重复使用) diff --git a/docs/1.机器学习基础-选择算法.png b/images/1.MLFoundation/机器学习基础-选择算法.png similarity index 100% rename from docs/1.机器学习基础-选择算法.png rename to images/1.MLFoundation/机器学习基础-选择算法.png diff --git a/docs/1.机器学习基础训练过程.png b/images/1.MLFoundation/机器学习基础训练过程.png similarity index 100% rename from docs/1.机器学习基础训练过程.png rename to images/1.MLFoundation/机器学习基础训练过程.png diff --git a/docs/11.交易清单.png b/images/11.Apriori/交易清单.png similarity index 100% rename from docs/11.交易清单.png rename to 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a/docs/7.过拟合.png b/images/7.AdaBoost/过拟合.png similarity index 100% rename from docs/7.过拟合.png rename to images/7.AdaBoost/过拟合.png diff --git a/src/python/13.PCA/pca.py b/src/python/13.PCA/pca.py new file mode 100644 index 00000000..86ee7958 --- /dev/null +++ b/src/python/13.PCA/pca.py @@ -0,0 +1,45 @@ +#!/usr/bin/python +# coding:utf8 + +''' +Created on Jun 1, 2011 +Update on 2017-04-06 +@author: Peter Harrington/片刻 +''' +print(__doc__) +from numpy import * + + +def loadDataSet(fileName, delim='\t'): + fr = open(fileName) + stringArr = [line.strip().split(delim) for line in fr.readlines()] + datArr = [map(float,line) for line in stringArr] + return mat(datArr) + + +def pca(dataMat, topNfeat=9999999): + meanVals = mean(dataMat, axis=0) + meanRemoved = dataMat - meanVals #remove mean + covMat = cov(meanRemoved, rowvar=0) + eigVals,eigVects = linalg.eig(mat(covMat)) + eigValInd = argsort(eigVals) #sort, sort goes smallest to largest + eigValInd = eigValInd[:-(topNfeat+1):-1] #cut off unwanted dimensions + redEigVects = eigVects[:,eigValInd] #reorganize eig vects largest to smallest + lowDDataMat = meanRemoved * redEigVects#transform data into new dimensions + reconMat = (lowDDataMat * redEigVects.T) + meanVals + return lowDDataMat, reconMat + + +def replaceNanWithMean(): + datMat = loadDataSet('secom.data', ' ') + numFeat = shape(datMat)[1] + for i in range(numFeat): + meanVal = mean(datMat[nonzero(~isnan(datMat[:,i].A))[0],i]) #values that are not NaN (a number) + datMat[nonzero(isnan(datMat[:,i].A))[0],i] = meanVal #set NaN values to mean + return datMat + + +if __name__ == "__main__": + dataMat = loadDataSet('data/13.PCA/testSet.txt') + lowDmat, reconMat = pca(dataMat, 1) + print shape(lowDmat)