加權(quán)線性回歸案例：預(yù)測鮑魚的年齡

點(diǎn)擊文章標(biāo)題即可獲取源代碼和筆記
數(shù)據(jù)集：https://download.csdn.net/download/weixin_44827418/12553408

1.導(dǎo)入數(shù)據(jù)集

數(shù)據(jù)集描述：

import pandas as pd import numpy as npabalone = pd.read_table("./datas/abalone.txt",header=None) abalone.columns=['性別','長度','直徑','高度','整體重量','肉重量','內(nèi)臟重量','殼重','年齡'] abalone.head() 性別長度直徑高度整體重量肉重量內(nèi)臟重量殼重年齡01234

1	0.455	0.365	0.095	0.5140	0.2245	0.1010	0.150	15
1	0.350	0.265	0.090	0.2255	0.0995	0.0485	0.070	7
-1	0.530	0.420	0.135	0.6770	0.2565	0.1415	0.210	9
1	0.440	0.365	0.125	0.5160	0.2155	0.1140	0.155	10
0	0.330	0.255	0.080	0.2050	0.0895	0.0395	0.055	7

abalone.shape (4177, 9) abalone.info() <class 'pandas.core.frame.DataFrame'> RangeIndex: 4177 entries, 0 to 4176 Data columns (total 9 columns):# Column Non-Null Count Dtype --- ------ -------------- ----- 0 性別 4177 non-null int64 1 長度 4177 non-null float642 直徑 4177 non-null float643 高度 4177 non-null float644 整體重量 4177 non-null float645 肉重量 4177 non-null float646 內(nèi)臟重量 4177 non-null float647 殼重 4177 non-null float648 年齡 4177 non-null int64 dtypes: float64(7), int64(2) memory usage: 293.8 KB abalone.describe() 性別長度直徑高度整體重量肉重量內(nèi)臟重量殼重年齡countmeanstdmin25%50%75%max

4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000
0.052909	0.523992	0.407881	0.139516	0.828742	0.359367	0.180594	0.238831	9.933684
0.822240	0.120093	0.099240	0.041827	0.490389	0.221963	0.109614	0.139203	3.224169
-1.000000	0.075000	0.055000	0.000000	0.002000	0.001000	0.000500	0.001500	1.000000
-1.000000	0.450000	0.350000	0.115000	0.441500	0.186000	0.093500	0.130000	8.000000
0.000000	0.545000	0.425000	0.140000	0.799500	0.336000	0.171000	0.234000	9.000000
1.000000	0.615000	0.480000	0.165000	1.153000	0.502000	0.253000	0.329000	11.000000
1.000000	0.815000	0.650000	1.130000	2.825500	1.488000	0.760000	1.005000	29.000000

2. 查看數(shù)據(jù)分布狀況

import numpy as np import pandas as pd import random import matplotlib as mpl import matplotlib.pyplot as plt plt.rcParams['font.sans-serif']=['simhei'] #顯示中文 plt.rcParams['axes.unicode_minus']=False # 用來正常顯示負(fù)號(hào) %matplotlib inline mpl.cm.rainbow(np.linspace(0,1,10)) array([[5.00000000e-01, 0.00000000e+00, 1.00000000e+00, 1.00000000e+00],[2.80392157e-01, 3.38158275e-01, 9.85162233e-01, 1.00000000e+00],[6.07843137e-02, 6.36474236e-01, 9.41089253e-01, 1.00000000e+00],[1.66666667e-01, 8.66025404e-01, 8.66025404e-01, 1.00000000e+00],[3.86274510e-01, 9.84086337e-01, 7.67362681e-01, 1.00000000e+00],[6.13725490e-01, 9.84086337e-01, 6.41213315e-01, 1.00000000e+00],[8.33333333e-01, 8.66025404e-01, 5.00000000e-01, 1.00000000e+00],[1.00000000e+00, 6.36474236e-01, 3.38158275e-01, 1.00000000e+00],[1.00000000e+00, 3.38158275e-01, 1.71625679e-01, 1.00000000e+00],[1.00000000e+00, 1.22464680e-16, 6.12323400e-17, 1.00000000e+00]]) mpl.cm.rainbow(np.linspace(0,1,10))[0] array([0.5, 0. , 1. , 1. ]) def dataPlot(dataSet):m,n = dataSet.shapefig = plt.figure(figsize=(8,20),dpi=100)colormap = mpl.cm.rainbow(np.linspace(0,1,n))for i in range(n):fig_ = fig.add_subplot(n,1,i+1)plt.scatter(range(m),dataSet.iloc[:,i].values,s=2,c=colormap[i])plt.title(dataSet.columns[i])plt.tight_layout(pad=1.2) # 調(diào)節(jié)子圖間的距離 # 運(yùn)行函數(shù)，查看數(shù)據(jù)分布： dataPlot(abalone) 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.

可以從數(shù)據(jù)分布散點(diǎn)圖中看出：

1）除“性別”之外，其他數(shù)據(jù)明顯存在規(guī)律性排列

2）“高度”這一特征中，有兩個(gè)異常值

從看到的現(xiàn)象，我們可以采取以下兩種措施：

1） 切分訓(xùn)練集和測試集時(shí)，需要打亂原始數(shù)據(jù)集來進(jìn)行隨機(jī)挑選

2） 剔除"高度"這一特征中的異常值

abalone['高度']<0.4 0 True 1 True 2 True 3 True 4 True... 4172 True 4173 True 4174 True 4175 True 4176 True Name: 高度, Length: 4177, dtype: bool aba = abalone.loc[abalone['高度']<0.4,:] #再次查看數(shù)據(jù)集的分布 dataPlot(aba) 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.

2. 切分訓(xùn)練集和測試集

""" 函數(shù)功能：隨機(jī)切分訓(xùn)練集和測試集 參數(shù)說明：dataSet：原始數(shù)據(jù)集rate:訓(xùn)練集比例 返回：train,test：切分好的訓(xùn)練集和測試集 """ def randSplit(dataSet,rate):l = list(dataSet.index) # 將原始數(shù)據(jù)集的索引提取出來，存到列表中random.seed(123) # 設(shè)置隨機(jī)數(shù)種子random.shuffle(l) # 隨機(jī)打亂數(shù)據(jù)集中的索引dataSet.index = l # 把打亂后的索引重新賦值給數(shù)據(jù)集中的索引，# 索引打亂了就相當(dāng)于打亂了原始數(shù)據(jù)集中的數(shù)據(jù)m = dataSet.shape[0] # 原始數(shù)據(jù)集樣本總數(shù)n = int(m*rate) # 訓(xùn)練集樣本數(shù)量train = dataSet.loc[range(n),:] # 從打亂了的原始數(shù)據(jù)集中提取出訓(xùn)練集數(shù)據(jù)test = dataSet.loc[range(n,m),:] # 從打亂了的原始數(shù)據(jù)集中提取出測試集數(shù)據(jù)train.index = range(train.shape[0]) # 重置train訓(xùn)練數(shù)據(jù)集中的索引test.index = range(test.shape[0]) # 重置test測試數(shù)據(jù)集中的索引dataSet.index = range(dataSet.shape[0]) # 重置原始數(shù)據(jù)集中的索引return train,test train,test = randSplit(aba,0.8) #探索訓(xùn)練集 train.head() 性別長度直徑高度整體重量肉重量內(nèi)臟重量殼重年齡01234

-1	0.590	0.470	0.170	0.9000	0.3550	0.1905	0.2500	11
1	0.560	0.450	0.145	0.9355	0.4250	0.1645	0.2725	11
-1	0.635	0.535	0.190	1.2420	0.5760	0.2475	0.3900	14
1	0.505	0.390	0.115	0.5585	0.2575	0.1190	0.1535	8
1	0.510	0.410	0.145	0.7960	0.3865	0.1815	0.1955	8

train.shape (3340, 9) abalone.describe() 性別長度直徑高度整體重量肉重量內(nèi)臟重量殼重年齡countmeanstdmin25%50%75%max

4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000
0.052909	0.523992	0.407881	0.139516	0.828742	0.359367	0.180594	0.238831	9.933684
0.822240	0.120093	0.099240	0.041827	0.490389	0.221963	0.109614	0.139203	3.224169
-1.000000	0.075000	0.055000	0.000000	0.002000	0.001000	0.000500	0.001500	1.000000
-1.000000	0.450000	0.350000	0.115000	0.441500	0.186000	0.093500	0.130000	8.000000
0.000000	0.545000	0.425000	0.140000	0.799500	0.336000	0.171000	0.234000	9.000000
1.000000	0.615000	0.480000	0.165000	1.153000	0.502000	0.253000	0.329000	11.000000
1.000000	0.815000	0.650000	1.130000	2.825500	1.488000	0.760000	1.005000	29.000000

train.describe() #統(tǒng)計(jì)描述 性別長度直徑高度整體重量肉重量內(nèi)臟重量殼重年齡countmeanstdmin25%50%75%max

3340.000000	3340.000000	3340.000000	3340.000000	3340.000000	3340.000000	3340.000000	3340.000000	3340.000000
0.060479	0.522754	0.406886	0.138790	0.824906	0.358151	0.179732	0.237158	9.911976
0.819021	0.120300	0.099372	0.038441	0.488535	0.222422	0.109036	0.137920	3.223534
-1.000000	0.075000	0.055000	0.000000	0.002000	0.001000	0.000500	0.001500	1.000000
-1.000000	0.450000	0.350000	0.115000	0.439000	0.184375	0.092000	0.130000	8.000000
0.000000	0.540000	0.420000	0.140000	0.796750	0.335500	0.171000	0.232000	9.000000
1.000000	0.615000	0.480000	0.165000	1.147250	0.498500	0.250500	0.325000	11.000000
1.000000	0.780000	0.630000	0.250000	2.825500	1.488000	0.760000	1.005000	27.000000

dataPlot(train) #查看訓(xùn)練集數(shù)據(jù)分布 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.

#探索測試集 test.head() 性別長度直徑高度整體重量肉重量內(nèi)臟重量殼重年齡01234

1	0.630	0.470	0.150	1.1355	0.5390	0.2325	0.3115	12
-1	0.585	0.445	0.140	0.9130	0.4305	0.2205	0.2530	10
-1	0.390	0.290	0.125	0.3055	0.1210	0.0820	0.0900	7
1	0.525	0.410	0.130	0.9900	0.3865	0.2430	0.2950	15
1	0.625	0.475	0.160	1.0845	0.5005	0.2355	0.3105	10

test.shape (835, 9) test.describe() 性別長度直徑高度整體重量肉重量內(nèi)臟重量殼重年齡countmeanstdmin25%50%75%max

835.000000	835.000000	835.000000	835.000000	835.000000	835.000000	835.000000	835.000000	835.000000
0.022754	0.528808	0.411737	0.140784	0.842714	0.363370	0.183749	0.245320	10.022754
0.834341	0.119166	0.098627	0.038664	0.495990	0.218938	0.111510	0.143925	3.230284
-1.000000	0.130000	0.100000	0.015000	0.013000	0.004500	0.003000	0.004000	3.000000
-1.000000	0.450000	0.350000	0.115000	0.458000	0.192000	0.096500	0.132750	8.000000
0.000000	0.550000	0.430000	0.140000	0.810000	0.339000	0.170500	0.235000	10.000000
1.000000	0.620000	0.485000	0.170000	1.177250	0.510750	0.259250	0.337000	11.000000
1.000000	0.815000	0.650000	0.250000	2.555000	1.145500	0.590000	0.815000	29.000000

dataPlot(test) 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points. 'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'. Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.

3.構(gòu)建輔助函數(shù)

''' 函數(shù)功能：輸入DF數(shù)據(jù)集（最后一列為標(biāo)簽），返回特征矩陣和標(biāo)簽矩陣 ''' def get_Mat(dataSet):xMat = np.mat(dataSet.iloc[:,:-1].values)yMat = np.mat(dataSet.iloc[:,-1].values).Treturn xMat,yMat ''' 函數(shù)功能：數(shù)據(jù)集可視化 ''' def plotShow(dataSet):xMat,yMat = get_Mat(dataSet)plt.scatter(xMat.A[:,1],yMat.A,c='b',s=5)plt.show() ''' 函數(shù)功能：計(jì)算回歸系數(shù) 參數(shù)說明：dataSet:原始數(shù)據(jù)集 返回：ws:回歸系數(shù) ''' def standRegres(dataSet):xMat,yMat = get_Mat(dataSet)xTx = xMat.T * xMatif np.linalg.det(xTx) == 0:print('矩陣為奇異矩陣，無法求逆！')returnws = xTx.I*(xMat.T*yMat) # xTx.I ，用來求逆矩陣return ws """ 函數(shù)功能：計(jì)算誤差平方和SSE 參數(shù)說明：dataSet：真實(shí)值regres：求回歸系數(shù)的函數(shù) 返回：SSE：誤差平方和 """ def sseCal(dataSet, regres):xMat,yMat = get_Mat(dataSet)ws = regres(dataSet)yHat = xMat*wssse = ((yMat.A.flatten() - yHat.A.flatten())**2).sum()# return sse

以ex0數(shù)據(jù)集為例，查看函數(shù)運(yùn)行結(jié)果：

ex0 = pd.read_table("./datas/ex0.txt",header=None) ex0.head() 01201234

1.0	0.067732	3.176513
1.0	0.427810	3.816464
1.0	0.995731	4.550095
1.0	0.738336	4.256571
1.0	0.981083	4.560815

#簡單線性回歸的SSE sseCal(ex0, standRegres) 1.3552490816814902

構(gòu)建相關(guān)系數(shù)R2計(jì)算函數(shù)

""" 函數(shù)功能：計(jì)算相關(guān)系數(shù)R2 """ def rSquare(dataSet,regres):xMat,yMat=get_Mat(dataSet)sse = sseCal(dataSet,regres)sst = ((yMat.A-yMat.mean())**2).sum()# r2 = 1 - sse / sstreturn r2

同樣以ex0數(shù)據(jù)集為例，查看函數(shù)運(yùn)行結(jié)果：

#簡單線性回歸的R2 rSquare(ex0, standRegres) 0.9731300889856916 ''' 函數(shù)功能：計(jì)算局部加權(quán)線性回歸的預(yù)測值 參數(shù)說明：testMat:測試集xMat:訓(xùn)練集的特征矩陣yMat:訓(xùn)練集的標(biāo)簽矩陣返回：yHat：函數(shù)預(yù)測值 ''' def LWLR(testMat,xMat,yMat,k=1.0):n = testMat.shape[0] # 測試數(shù)據(jù)集行數(shù)m = xMat.shape[0] # 訓(xùn)練集特征矩陣行數(shù)weights = np.mat(np.eye(m)) # 用單位矩陣來初始化權(quán)重矩陣，yHat = np.zeros(n) # 用0矩陣來初始化預(yù)測值矩陣for i in range(n):for j in range(m):diffMat = testMat[i] - xMat[j]weights[j,j] = np.exp(diffMat*diffMat.T / (-2*k**2))xTx = xMat.T*(weights*xMat)if np.linalg.det(xTx) == 0:print('矩陣為奇異矩陣，無法求逆')returnws = xTx.I*(xMat.T*(weights*yMat))yHat[i] = testMat[i] * wsreturn ws,yHat

4.構(gòu)建加權(quán)線性模型

因?yàn)閿?shù)據(jù)量太大，計(jì)算速度極慢，所以此處選擇訓(xùn)練集的前100個(gè)數(shù)據(jù)作為訓(xùn)練集，測試集的前100個(gè)數(shù)據(jù)作為測試集。

""" 函數(shù)功能：繪制不同k取值下，訓(xùn)練集和測試集的SSE曲線 """ def ssePlot(train,test):X0,Y0 = get_Mat(train)X1,Y1 =get_Mat(test)train_sse = []test_sse = []for k in np.arange(0.2,10,0.5):ws1,yHat1 = LWLR(X0[:99],X0[:99],Y0[:99],k) sse1 = ((Y0[:99].A.T - yHat1)**2).sum() train_sse.append(sse1)ws2,yHat2 = LWLR(X1[:99],X0[:99],Y0[:99],k) sse2 = ((Y1[:99].A.T - yHat2)**2).sum() test_sse.append(sse2)plt.figure(figsize=(20,8),dpi=100)plt.plot(np.arange(0.2,10,0.5),train_sse,color='b')# plt.plot(np.arange(0.2,10,0.5),test_sse,color='r') plt.xlabel('不同k取值')plt.ylabel('SSE')plt.legend(['train_sse','test_sse'])

運(yùn)行結(jié)果：

ssePlot(train,test)

這個(gè)圖的解讀應(yīng)該是這樣的：從右往左看，當(dāng)K取較大值時(shí)，模型比較穩(wěn)定，隨著K值的減小，訓(xùn)練集的SSE開始逐漸減小，當(dāng)K取到2左右，訓(xùn)練集的SSE與測試集的SSE相等，當(dāng)K繼續(xù)減小時(shí)，訓(xùn)練集的SSE也越來越小，也就是說，模型在訓(xùn)練集上的表現(xiàn)越來越好，但是，模型在測試集上的表現(xiàn)卻越來越差了，這就說明模型開始出現(xiàn)過擬合了。其實(shí)，這個(gè)圖與前面不同k值的結(jié)果圖是吻合的，K=1.0,
0.01, 0.003這三張圖也表明隨著K的減小，模型會(huì)逐漸出現(xiàn)過擬合。所以這里可以看出，K在2左右的取值最佳。

我們再將K=2帶入局部線性回歸模型中，然后查看預(yù)測結(jié)果：

train,test = randSplit(aba,0.8) # 隨機(jī)切分原始數(shù)據(jù)集，得到訓(xùn)練集和測試集 trainX,trainY = get_Mat(train) # 將切分好的訓(xùn)練集分成特征矩陣和標(biāo)簽矩陣 testX,testY = get_Mat(test) # 將切分好的測試集分成特征矩陣和標(biāo)簽矩陣 ws0,yHat0 = LWLR(testX,trainX,trainY,k=2)

繪制真實(shí)值與預(yù)測值之間的關(guān)系圖

y=testY.A.flatten() plt.scatter(y,yHat0,c='b',s=5); # ;等效于plt.show()

通過上圖可知，橫坐標(biāo)為真實(shí)值，縱坐標(biāo)為預(yù)測值，形成的圖像為呈現(xiàn)一個(gè)“喇叭形”，隨著橫坐標(biāo)真實(shí)值逐漸變大，縱坐標(biāo)預(yù)測值也越來越大，說明隨著真實(shí)值的增加，預(yù)測值偏差越來越大

封裝一個(gè)函數(shù)來計(jì)算SSE和R方，方便后續(xù)調(diào)用

""" 函數(shù)功能：計(jì)算加權(quán)線性回歸的SSE和R方 """ def LWLR_pre(dataSet):train,test = randSplit(dataSet,0.8)# trainX,trainY = get_Mat(train)testX,testY = get_Mat(test)ws,yHat = LWLR(testX,trainX,trainY,k=2)# sse = ((testY.A.T - yHat)**2).sum()# sst = ((testY.A-testY.mean())**2).sum() # r2 = 1 - sse / sstreturn sse,r2

查看模型預(yù)測結(jié)果

LWLR_pre(aba) (4152.777097646255, 0.5228101340130846)

從結(jié)果可以看出，SSE達(dá)4000+，相關(guān)系數(shù)只有0.52，模型效果并不是很好。

總結(jié)

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