指标权重计算流程
参考:https://www.zhihu.com/question/357680646/answer/1748591262
1、归一化
2、指标占比
3、计算熵
4、计算差异系数
5、计算权重
6、验证：权重和为1
样例：WeightScoreTest.scala
case class Room(name:String,x1:Double,x2:Double,x3:Double,x4:Double,x5:Double,x6:Double,x7:Double,x8:Double){
}
object Room{
// def apply(name: String, x1: Double, x2: Double, x3: Double, x4: Double, x5: Double, x6: Double, x7: Double, x8: Double): Room = new Room(name, x1, x2, x3, x4, x5, x6, x7, x8)
def apply(row:String)={
val r = row.split(" ")
new Room(r(0),r(1).toDouble,r(2).toDouble,r(3).toDouble,r(4).toDouble,r(5).toDouble,r(6).toDouble,r(7).toDouble,r(8).toDouble)
}
}
object WeightScoreTest {
/** l1个科室9项整体护理评价指标得分表 */
val samples =
"""
|A 100 90 100 84 90 100 100 100 100
|B 100 100 78.6 100 90 100 100 100 100
|C 75 100 85.7 100 90 100 100 100 100
|D 100 100 78.6 100 90 100 94.4 100 100
|E 100 90 100 100 100 90 100 100 80
|F 100 100 100 100 90 100 100 85.7 100
|G 100 100 78.6 100 90 100 55.6 100 100
|H 87.5 100 85.7 100 100 100 100 100 100
|I 100 100 92.9 100 80 100 100 100 100
|J 100 90 100 100 100 100 100 100 100
|K 100 100 92.9 100 90 100 100 100 100
|
""".stripMargin
def start(): Unit = {
val sparkConf = new SparkConf().setAppName("WeightScoreTest")
sparkConf.setMaster("local[*]")
val sparkContext = new SparkContext(sparkConf)
val sparkSessionBuilder = SparkSession.builder()
.enableHiveSupport()
.config(sparkConf)
.appName(sparkContext.appName)
val spark = sparkSessionBuilder.getOrCreate()
spark.udf.register("sumofsquares", new Sumofsquares())
val rooms = samples.split("\r\n").filter(StringUtils.isNoneBlank(_)).map(r=>{
Room(r)
}).toList.asJava
val df = spark.createDataFrame(rooms)
df.show(20)
//TODO 对每一列指标进行归一化，
val summary = df.summary("count", "mean", "max", "min", "stddev").cache()
var features = summary.columns.filterNot(r => r == "summary" || r == "name" )
val feaMaxMap = summary.filter("summary = 'max'").collect().head.getValuesMap[Double](features)
val feaMinMap = summary.filter("summary = 'min'").collect().head.getValuesMap[Double](features)
summary.show(20)
val feaMeanMap = summary.filter("summary = 'mean'").collect().head.getValuesMap[String](features)
val feaStdMap = summary.filter("summary = 'stddev'").collect().head.getValuesMap[String](features)
val df2 = df.selectExpr(features.map{ f =>
val maxVal = feaMaxMap.getOrElse(f, 1)
val minVal = feaMinMap.getOrElse(f, 0)
//s"($f - $minVal)/($maxVal - $minVal + 1e-6) as ${f}" //
if("name".equals(f)){
s"${f}"
}else {
s"($f - $minVal)/($maxVal - $minVal ) as ${f}"
}
}:_*)
df2.show(20)
// 然后计算权重
val diverse = features.map(f => calWeight(df2, f))
val s = diverse.sum + 1e-6
val weights = diverse.map(_ / s)
println(s"weights,list:${JSON.toJSONString(weights,false)}")
println(s"weights,sum:${weights.sum}")
println("features:"+JSON.toJSONString(features,false))
println("summary = 'max':"+JSON.toJSONString(feaMaxMap.asJava,false))
println("summary = 'min':"+JSON.toJSONString(feaMinMap.asJava,false))
println("summary = 'mean':"+JSON.toJSONString(feaMeanMap.asJava,false))
println("summary = 'stddev':"+JSON.toJSONString(feaStdMap.asJava,false))
}
def calWeight(dataDF:DataFrame, field: String):Double={
val scoreDf = dataDF.rdd.map{_.getAs[Any](field).toString.toDouble}//.select(field)
val sumIter=scoreDf.sum() + 1e-6
val scalar = -1.0/math.log(scoreDf.count())
val Ej = scoreDf.map{ v=>val l1value = math.abs(v)/sumIter
l1value * math.log(l1value + 1e-6)
}.sum * scalar
println(s"sum:${Ej}")
if(1 - Ej < 0) println("差异系数为负数")
1 - Ej // 差异系数*/
}
def main(args: Array[String]): Unit = {
start()
}
计算结果
/**数据集探索*/
val summary=
"""
|+-------+----+----------------+-----------------+-----------------+-----------------+-----------------+------------------+------------------+-----------------+
||summary|name| x1| x2| x3| x4| x5| x6| x7| x8|
|+-------+----+----------------+-----------------+-----------------+-----------------+-----------------+------------------+------------------+-----------------+
|| count| 11| 11| 11| 11| 11| 11| 11| 11| 11|
|| mean|null|96.5909090909091|97.27272727272727|90.27272727272727|98.54545454545455|91.81818181818181| 99.0909090909091| 95.45454545454545| 98.7|
|| max| K| 100.0| 100.0| 100.0| 100.0| 100.0| 100.0| 100.0| 100.0|
|| min| A| 75.0| 90.0| 78.6| 84.0| 80.0| 90.0| 55.6| 85.7|
|| stddev|null|8.08337238353579|4.670993664969138|9.180750613004465|4.824181513244218|6.030226891555272|3.0151134457776365|13.324591073377345|4.311612227462018|
|+-------+----+----------------+-----------------+-----------------+-----------------+-----------------+------------------+------------------+-----------------+
|
""".stripMargin
/**指标标准化矩阵*/
val standString =
"""
|+---+---+-------------------+---+---+---+-----------------+------------------+
|| x1| x2| x3| x4| x5| x6| x7| x8|
|+---+---+-------------------+---+---+---+-----------------+------------------+
||1.0|0.0| 1.0000000000000002|0.0|0.5|1.0| 1.0|0.9999999999999998|
||1.0|1.0| 0.0|1.0|0.5|1.0| 1.0|0.9999999999999998|
||0.0|1.0|0.33177570093457986|1.0|0.5|1.0| 1.0|0.9999999999999998|
||1.0|1.0| 0.0|1.0|0.5|1.0|0.873873873873874|0.9999999999999998|
||1.0|0.0| 1.0000000000000002|1.0|1.0|0.0| 1.0|0.9999999999999998|
||1.0|1.0| 1.0000000000000002|1.0|0.5|1.0| 1.0| 0.0|
||1.0|1.0| 0.0|1.0|0.5|1.0| 0.0|0.9999999999999998|
||0.5|1.0|0.33177570093457986|1.0|1.0|1.0| 1.0|0.9999999999999998|
||1.0|1.0| 0.6682242990654211|1.0|0.0|1.0| 1.0|0.9999999999999998|
||1.0|0.0| 1.0000000000000002|1.0|1.0|1.0| 1.0|0.9999999999999998|
||1.0|1.0| 0.6682242990654211|1.0|0.5|1.0| 1.0|0.9999999999999998|
|+---+---+-------------------+---+---+---+-----------------+------------------+
""".stripMargin
val weightString =
"""
|weights,list:[0.08110818342879658,0.23453511631130167,0.2904122876143106,0.07019980217824295,0.11258311168727239,0.07019980217824295,0.07076012846443831,0.07019980217824295]
|weights,sum:0.9999982340408485
|features:["x1","x2","x3","x4","x5","x6","x7","x8"]
|summary = 'max':{"x8":"100.0","x3":"100.0","x7":"100.0","x2":"100.0","x5":"100.0","x6":"100.0","x1":"100.0","x4":"100.0"}
|summary = 'min':{"x8":"85.7","x3":"78.6","x7":"55.6","x2":"90.0","x5":"80.0","x6":"90.0","x1":"75.0","x4":"84.0"}
|summary = 'mean':{"x8":"98.7","x3":"90.27272727272727","x7":"95.45454545454545","x2":"97.27272727272727","x5":"91.81818181818181","x6":"99.0909090909091","x1":"96.5909090909091","x4":"98.54545454545455"}
|summary = 'stddev':{"x8":"4.311612227462018","x3":"9.180750613004465","x7":"13.324591073377345","x2":"4.670993664969138","x5":"6.030226891555272","x6":"3.0151134457776365","x1":"8.08337238353579","x4":"4.824181513244218"}
""".stripMargin
打分原理
根据分布情况求累积概率
累计概率（cumulativeprobability）即所有可能取值的概率之和。
正向指标 发生概率越大,分数越高
反向指标 发生概率越小,分数越高
```
import org.apache.commons.math3.distribution.{ExponentialDistribution, NormalDistribution}
NormalDist => new NormalDistribution(平均值, 标准差)
ExponDist => new ExponentialDistribution(平均值)
{if(-1 == effect) (1 - dist.cumulativeProbability(indexVal)) * 100
else 100 * dist.cumulativeProbability(indexVal)}.formatted("%.2f").toFloat
```
打分说明
反向指标打分：
求疲劳驾驶发生次数小于等于10次/100km的概率P(X <= 10) ,该指标分数 (1-p)*100
正向指标打分：
经济速度占比，经济负载占比
总分以及二级指标处理
总分：各个指标的分数*指标权重 相加
二级指标:分数 * ( 权重占比 即 权重/二级权重之和 ) 相加