异常值（outlier）

• 简介

在数据挖掘的过程中，我们可能会经常遇到一些偏离于预测趋势之外的数据，通常我们称之为异常值。

通常将这样的一些数据的出现归为误差。有很多情况会出现误差，具体的情况需要就对待：

传感器故障　　　->　　忽略

数据输入错误　　->　　忽略

反常事件　　　　->　　重视

• 异常值检测/删除算法

1、训练数据

2、异常值检测，找出训练集中访问最多的点，去除这些点（一般约10%的异常数据）

3、再训练

需要多次重复2、3步骤

例：对数据第一次使用回归后的拟合

　

误差点的出现使拟合线相对偏离，将误差点去除后进行一次回归：

　　　　

去除误差点后的回归线很好的对数据进行了拟合

• 代码实现

环境：MacOS mojave　　10.14.3

Python　　3.7.0

使用库：scikit-learn    0.19.2

原始数据集：

　　　　

对原始数据进行一次回归：

　　　　

删除10%的异常值后进行一次回归：
　　　　

outlier_removal_regression.py　　主程序

#!/usr/bin/python

import random
import numpy
import matplotlib.pyplot as plt
import pickle

from outlier_cleaner import outlierCleaner

class StrToBytes:
    def __init__(self, fileobj):
        self.fileobj = fileobj
    def read(self, size):
        return self.fileobj.read(size).encode()
    def readline(self, size=-1):
        return self.fileobj.readline(size).encode()


### load up some practice data with outliers in it
ages = pickle.load(StrToBytes(open("practice_outliers_ages.pkl", "r") ) )
net_worths = pickle.load(StrToBytes(open("practice_outliers_net_worths.pkl", "r") ) )



### ages and net_worths need to be reshaped into 2D numpy arrays
### second argument of reshape command is a tuple of integers: (n_rows, n_columns)
### by convention, n_rows is the number of data points
### and n_columns is the number of features
ages       = numpy.reshape( numpy.array(ages), (len(ages), 1))
net_worths = numpy.reshape( numpy.array(net_worths), (len(net_worths), 1))
from sklearn.cross_validation import train_test_split
ages_train, ages_test, net_worths_train, net_worths_test = train_test_split(ages, net_worths, test_size=0.1, random_state=42)

### fill in a regression here!  Name the regression object reg so that
### the plotting code below works, and you can see what your regression looks like


from sklearn import linear_model
reg = linear_model.LinearRegression()
reg.fit(ages_train,net_worths_train)
print (reg.coef_)
print (reg.intercept_)
print (reg.score(ages_test,net_worths_test) )



try:
    plt.plot(ages, reg.predict(ages), color="blue")
except NameError:
    pass
plt.scatter(ages, net_worths)
plt.show()


### identify and remove the most outlier-y points
cleaned_data = []
try:
    predictions = reg.predict(ages_train)
    cleaned_data = outlierCleaner( predictions, ages_train, net_worths_train )

except NameError:
    print ("your regression object doesn't exist, or isn't name reg")
    print ("can't make predictions to use in identifying outliers")







### only run this code if cleaned_data is returning data
if len(cleaned_data) > 0:
    ages, net_worths, errors = zip(*cleaned_data)
    ages       = numpy.reshape( numpy.array(ages), (len(ages), 1))
    net_worths = numpy.reshape( numpy.array(net_worths), (len(net_worths), 1))

    ### refit your cleaned data!
    try:
        reg.fit(ages, net_worths)
        plt.plot(ages, reg.predict(ages), color="blue")
        print (reg.coef_)
        print (reg.intercept_)
        print (reg.score(ages_test,net_worths_test) )
    except NameError:
        print ("you don't seem to have regression imported/created,")
        print ("   or else your regression object isn't named reg")
        print ("   either way, only draw the scatter plot of the cleaned data")
    plt.scatter(ages, net_worths)
    plt.xlabel("ages")
    plt.ylabel("net worths")
    plt.show()


else:
    print ("outlierCleaner() is returning an empty list, no refitting to be done")

outlier_cleaner.py　　清除10%的异常值

import numpy as np
import math
 
def outlierCleaner(predictions, ages, net_worths):
    """
        Clean away the 10% of points that have the largest
        residual errors (difference between the prediction
        and the actual net worth).
        Return a list of tuples named cleaned_data where 
        each tuple is of the form (age, net_worth, error).
    """
    
    cleaned_data = []
 
 
    ages = ages.reshape((1,len(ages)))[0]
    net_worths = net_worths.reshape((1,len(ages)))[0]
    predictions = predictions.reshape((1,len(ages)))[0]
    # zip() 函数用于将可迭代的对象作为参数，将对象中对应的元素打包成一个个元组，然后返回由这些元组组成的列表。
    cleaned_data = zip(ages,net_worths,abs(net_worths-predictions))
    #按照error大小排序
    cleaned_data = sorted(cleaned_data , key=lambda x: (x[2]))
    #ceil() 函数返回数字的上入整数，计算要删除的元素个数
    cleaned_num = int(-1 * math.ceil(len(cleaned_data)* 0.1))
    #切片
    cleaned_data = cleaned_data[:cleaned_num]
    
    return cleaned_data

同时得到这两次回归的拟合优度：

第一次：0.8782624703664675

第二次：0.983189455395532

可见，去除异常值对于预测数据具有重要作用