奇异值检测和处理惩罚

本文先容数据奇异值检测和处理惩罚的常识。数据奇异值若是不检测和处理惩罚，会影响模子精确性，甚至对预测形成误导。</p> [TOC] <p>### 1 为什么要奇异值检测和处理惩罚<br /> 因为奇异值可以大大地方向可能改变拟合预计和预测。<br /> 举例说明：汽车数据集，比拟没有奇异值和有奇异值的简朴线性回归模子的拟合，然后做预测。</p> <p>**R代码**<br /> “`<br /> ## 汽车数据集<br /> data(cars)<br /> dim(cars)</p> <p>par(mfrow = c(1,2))<br /> ## 原始数据集<br /> cars1 <- cars[1:30, ] ## 景象一：没有奇异值<br /> plot(<br /> cars1$speed,<br /> cars1$dist,<br /> xlim = c(0, 28),<br /> ylim = c(0, 230),<br /> main = "没有奇异值 \n 简朴线性回归模子",<br /> xlab = "速度",<br /> ylab = "间隔",<br /> pch = "*",<br /> col = "red",<br /> cex = 2<br /> )<br /> abline(<br /> lm(dist ~ speed, data = cars1),<br /> col = "blue",<br /> lwd = 3,<br /> lty = 2<br /> )</p> <p>## 景象二：有奇异值<br /> ## 人工结构奇异值<br /> cars.outliers <- data.frame(<br /> speed = c(19, 19, 20, 20, 20),<br /> dist = c(190, 186, 210, 220, 218)<br /> )<br /> cars2 <- rbind(cars1, cars.outliers)<br /> plot(<br /> cars2$speed,<br /> cars2$dist,<br /> xlim = c(0, 28),<br /> ylim = c(0, 230),<br /> main = "有奇异值 \n 简朴线性回归模子",<br /> xlab = "速度",<br /> ylab = "间隔",<br /> pch = "*",<br /> col = "red",<br /> cex = 2<br /> )<br /> abline(<br /> lm(dist ~ speed, data = cars2),<br /> col = "blue",<br /> lwd = 3,<br /> lty = 2<br /> )<br /> “`<br /> **功效**<br /> </p> <p>**总结**<br /> 异常值导致预测模子斜率的变革，若是操作异常值数据拟合模子（右图），导致预测功效带来高误差。</p> <p>### 2 奇异值检测<br /> #### 2.1 单变量要领<br /> 对付持续变量，奇异值位于1.5IQR范畴之外。<br /> IQR = 75%四分位数-25%四分位数<br /> **R代码**<br /> “`<br /> ## 数据获取<br /> url <- "http://rstatistics.net/wp-content/uploads/2015/09/ozone.csv"<br /> inputData <- read.csv(url) </p> <p>## 异常值<br /> outlier.values <- boxplot.stats(<br /> inputData$pressure_height<br /> )$out<br /> print(outlier.values)</p> <p>par(mfrow=c(1,1))<br /> ## 异常值可视化<br /> boxplot(<br /> inputData$pressure_height,<br /> main = "Pressure Height",<br /> boxwex=0.1<br /> )<br /> mtext(<br /> paste("Outliers: ", paste(outlier.values, collapse=", ")),<br /> cex=0.6<br /> )<br /> “`<br /> **功效**<br /> </p> <p>#### 2.2 双变量要领<br /> 双变量x和y的盒子图，x是种别变量。<br /> **R代码**<br /> “`<br /> par(mfrow=c(1,2))<br /> boxplot(<br /> ozone_reading ~ Month,<br /> data = inputData,<br /> main = "Ozone reading across months"<br /> )<br /> boxplot(<br /> ozone_reading ~ Day_of_week,<br /> data = inputData,<br /> main = "Ozone reading for days of week"<br /> )<br /> “`<br /> **功效**<br /> <br /> **总结**<br /> 由图可知，月份对臭氧变革有影响，而礼拜没有。异常值见盒子图中空心圆圈。</p> <p>#### 2.3 多变量模子要领<br /> **Cooks Distance**，**简称CD**<br /> 计较每个样本（视察）对预测功效的影响水平。<br /> 一般环境，一个样本的CD大于4倍CD的平均值，则被当做对预测是有影响力，这样的样本，可以当做异常值处理惩罚。<br /> 代码<br /> “`<br /> mod <- lm(ozone_reading ~ ., data=inputData)<br /> cooksd <- cooks.distance(mod)<br /> par(mfrow=c(1,1))<br /> plot(<br /> cooksd,<br /> pch = "*",<br /> cex = 2,<br /> main = "Influential Obs by Cooks distance"<br /> )</p> <p>abline(<br /> h = 4 * mean(cooksd, na.rm = TRUE),<br /> col = "red"<br /> )<br /> text(<br /> x=1:length(cooksd)+1,<br /> y=cooksd,<br /> labels=ifelse(cooksd>4*mean(cooksd, na.rm=T),names(cooksd),""),<br /> col="red"<br /> )</p> <p>influential <- as.numeric(names(cooksd)[(cooksd > 4*mean(cooksd, na.rm=T))]) # influential row numbers<br /> View(head(inputData[influential, ]))<br /> “`<br /> **功效**<br /> </p> <p>#### 2.4 奇异值包：outliers<br /> outliers异常值包提供了很多有用函数来做异常值检测和处理惩罚，出格是outlier() 和scores() 函数。<br /> 奇异值包outliers的利用要领，阅读[**包文档**](https://cran.r-project.org/web/packages/outliers/outliers.pdf "包文档")。<br /> ### 3 奇异值处理惩罚<br /> 要领一：插值替换法<br /> 利用均值可能中位数可能众数填补<br /> 要领二：预测法<br /> 把异常值当做NA，然后操作NA的处理惩罚要领，拟合得当模子，预测出NA的值</p> <p>**参考资料：**<br /> 1 R做异常值检测：http://r-statistics.co/Outlier-Treatment-With-R.html</p> <p>您在阅读中，有什么发起可能想法，请评论。<br /> 想插手圈子，请加微信。</p> </div><!-- .entry-content --> </article><!-- #post-## -->  <div class="tagcloud"><ul class='wp-tag-cloud' role='list'><h3>关键字：</h3> </ul> </div> <div class="col-sm-6 col-box bg-gray-light-2 contact-form"> <div role="form" class="wpcf7" id="wpcf7-f17097-o1" lang="zh-CN" dir="ltr"> <div class="screen-reader-response"></div> <form 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