函數：pearsonr(x,y)

功能：
計算特征與目標變量之間的相關度

參數說明：
1）輸入：x為特征，y為目標變量.
2）輸出：r： 相關系數 [-1，1]之間，p-value: p值。
注： p值越小，表示相關系數越顯著，一般p值在500個樣本以上時有較高的可靠性。

pearson相關系數的計算公式為：

cov(X,Y)表示的是協方差
var(x)和var(y)表示的是方差

python實現

import numpy as np from scipy.stats import pearsonr import random np.random.seed(0) size=300 x=np.random.normal(0,1,size) print "Lower noise",pearsonr(x,x+np.random.normal(0,1,size)) print "Higher noise",pearsonr(x,x+np.random.normal(0,10,size))

輸出：

Lower noise (0.71824836862138408, 7.3240173129983507e-49) Higher noise (0.057964292079338155, 0.31700993885324752)

用pandas計算相關系數

corr()求解變量相關系數

df.head()Guba XQ BCI Count Value 0 0.021 0.098 0.175 0.077 0.057 1 0.031 0.097 0.192 0.087 0.069 2 0.018 0.101 0.193 0.075 0.069 3 0.017 0.112 0.203 0.077 0.063 4 0.042 0.158 0.222 0.335 0.567#1.pearson相關系數 df.corr()Guba XQ BCI Count Value Guba 1.000000 0.175604 -0.014611 0.200896 0.256166 XQ 0.175604 1.000000 -0.390358 0.654250 0.482809 BCI -0.014611 -0.390358 1.000000 -0.259319 -0.156440 Count 0.200896 0.654250 -0.259319 1.000000 0.832961 Value 0.256166 0.482809 -0.156440 0.832961 1.000000#2.Kendall Tau相關系數 df.corr('kendall')Guba XQ BCI Count Value Guba 1.000000 0.153904 -0.012438 0.133122 0.090707 XQ 0.153904 1.000000 -0.244304 0.374908 0.255377 BCI -0.012438 -0.244304 1.000000 -0.157442 -0.091950 Count 0.133122 0.374908 -0.157442 1.000000 0.720916 Value 0.090707 0.255377 -0.091950 0.720916 1.000000#3.spearman秩相關 df.corr('spearman')Guba XQ BCI Count Value Guba 1.000000 0.219124 -0.017204 0.189752 0.143163 XQ 0.219124 1.000000 -0.358981 0.563938 0.427756 BCI -0.017204 -0.358981 1.000000 -0.241880 -0.140010 Count 0.189752 0.563938 -0.241880 1.000000 0.877732 Value 0.143163 0.427756 -0.140010 0.877732 1.000000#4.顯著性檢驗 import scipy.stats as stats #輸出結果第一個值為pearsonr相關系數， #第二個為p-value，所以這里Guba列和Value值是顯著相關的 stats.pearsonr(df['Guba'],df['Value']) (0.256165703418037, 8.10519823509109e-07)

計算兩列數據相關系數

import pandas as pd import pylab as plt #每小時的陣風風速平均值 all_gust_spd_mean_list = [8.21529411764706, 7.872941176470587, 7.829411764705882, 8.354117647058825, 9.025882352941174, 9.384523809523811, 9.57294117647059, 9.274117647058821, 9.050588235294118, 9.314117647058827, 8.924705882352939, 9.25176470588235, 8.978823529411764, 8.39176470588235, 7.715294117647061, 7.477647058823529, 7.272941176470586, 7.38470588235294, 7.396470588235295, 7.97261904761905, 7.716666666666666, 7.7809523809523835, 7.816666666666668, 7.897590361445783, 8.200000000000001, 8.04761904761905, 7.474999999999999, 9.855952380952383, 11.120000000000001, 10.979761904761906, 10.922619047619051, 10.841176470588234, 9.31566265060241, 8.867058823529415, 9.068235294117642, 8.774698795180722, 8.629411764705884, 8.292941176470586, 7.640000000000007, 7.422352941176469, 7.464705882352944, 8.210588235294113, 8.558823529411763, 8.93095238095238, 9.001176470588234, 8.538095238095238, 8.965882352941172, 9.855294117647057, 8.318918918918921, 9.217647058823525, 8.86470588235294, 8.840000000000002, 9.44235294117647, 9.352380952380953, 9.307058823529408, 9.64047619047619, 9.408333333333333, 9.585882352941175, 8.901190476190477, 7.698823529411764, 7.988235294117645, 9.091764705882353, 9.294117647058819, 8.996470588235297, 9.63764705882353, 9.091764705882353, 8.937647058823533, 8.838823529411764, 8.637647058823534, 8.46, 8.374117647058824, 8.24117647058823, 8.245238095238093, 8.365882352941174, 8.50235294117647, 8.291764705882352, 8.088235294117647, 7.889411764705883, 7.594117647058826, 7.216470588235293, 7.097647058823533, 7.305882352941181, 7.489411764705882, 6.815294117647058, 7.971428571428569, 7.424705882352936, 6.910588235294117, 6.071764705882354, 7.44117647058823, 7.667857142857143, 7.881176470588237, 7.929411764705881, 8.12142857142857, 8.822352941176472, 9.083529411764703, 9.028235294117646, 9.310714285714285, 9.035294117647057, 8.450588235294116, 8.414285714285713, 7.311764705882355, 6.840000000000001, 7.238095238095239, 6.641176470588236, 6.8047619047619055, 6.58705882352941, 6.826190476190474, 6.568235294117643, 7.060000000000001, 7.686904761904761, 8.348235294117643, 8.503529411764701, 8.287058823529414, 8.354117647058823, 7.624705882352941, 7.286904761904765, 7.361176470588235, 7.477647058823531, 7.343529411764706]#每小時的陣風風向標準差 all_gust_agl_dev_list = [0.7507438242046189, 0.768823513771462, 0.849877567310481, 0.8413581558472801, 0.8571319461950748, 0.8665002025305942, 0.9053739533298005, 0.8866979720735791, 0.8045677876888446, 0.873463882661469, 0.832383480871403, 0.778659970340069, 0.7357031045047981, 0.7974723911258534, 0.8039727543149432, 0.8709723763624072, 0.8727745464337923, 0.7896422160341138, 0.8165093346129041, 0.8821296270775546, 0.9193591477905156, 0.8546566314487358, 0.8595040204296921, 0.8075641299052398, 0.7996745617071098, 0.7930869411601498, 0.7578880032016914, 0.9107571156507569, 0.8461201382346486, 0.7553646348127085, 0.8510861123303187, 0.7282631202385544, 0.8588017730198183, 0.7923449370076744, 0.8265083209111689, 0.9599970229643688, 0.8195276021290412, 0.7882592259148272, 0.8036464793287409, 0.8237184691421926, 0.8846862360656914, 0.8136869244513337, 0.8516383375155133, 0.7760301715652644, 0.8644231334629017, 0.831330440569484, 0.8061342111854616, 0.7345896810176235, 1.205089147978776, 0.8266315966774649, 0.8137345300107962, 0.8186966603954983, 0.7836182115343135, 0.8406438908681332, 0.7717723331806998, 0.7932664155269176, 0.7266183593077442, 0.719063143819583, 0.8846434855533486, 0.817552510948495, 0.7571575934024827, 0.865326265251608, 0.9099784335052563, 0.8591794583996128, 0.9295389095340467, 0.8787300860744375, 0.8724277968300532, 0.95284132003256, 0.9288772059881606, 0.8690944948691984, 0.8327213470469693, 0.8339075062700629, 0.886835675339985, 0.8439137877550847, 0.7985495396895048, 0.8406267016063169, 0.8477871130878305, 0.8844025576348077, 0.9186363354492758, 0.8888539157167654, 0.9079462071375304, 0.8699806402308554, 0.8531937701209343, 0.8833108936555343, 0.9317958602705915, 0.9393618445471649, 0.9556065912926689, 0.967220118643412, 0.8882194173154115, 0.9361538853249073, 0.7872261833965604, 0.8608377368219552, 0.8787718518619395, 0.8169189082396561, 0.7965901553530427, 0.8838665737610132, 0.8844338861256802, 0.9008484784943429, 0.8612318707072047, 0.8623792153658019, 1.0033494995180463, 0.9901213381586231, 0.8780115045650467, 0.9172682690843976, 0.9653905755824115, 0.9199829176728873, 0.9180048223906779, 0.9172043382441968, 0.9267783259554074, 0.9231225672912022, 0.7945054721199195, 0.8655558517080688, 0.8306327906597787, 0.8457559701865576, 0.8038459124570336, 0.8519646989317945, 0.7735358658599594, 0.8612134954656397, 0.8879135146161856]g_s_m = pd.Series(all_gust_spd_mean_list) #利用Series將列表轉換成新的、pandas可處理的數據 g_a_d = pd.Series(all_gust_agl_dev_list)corr_gust = round(g_s_m.corr(g_a_d), 4) #計算標準差，round(a, 4)是保留a的前四位小數print('corr_gust :', corr_gust)#最后畫一下兩列表散點圖，直觀感受下，結合相關系數揣摩揣摩 plt.scatter(all_gust_spd_mean_list, all_gust_agl_dev_list) plt.title('corr_gust :' + str(corr_gust), fontproperties='SimHei') #給圖寫上title plt.show()

根據以上程序，得到結果：

corr_gust : -0.3481

計算矩陣數據相關系數矩陣

import pandas as pd import numpy as npif __name__ == '__main__':unstrtf_lst = [[2.136, 1.778, 1.746, 2.565, 1.873, 2.413, 1.813, 1.72, 1.932, 1.987, 2.035, 2.178, 2.05, 2.016, 1.645, 1.756, 1.886, 2.106, 2.138, 1.914, 1.984, 1.906, 1.871, 1.939, 1.81, 1.93, 1.898, 1.802, 2.008, 1.724, 1.823, 1.636, 1.774, 2.055, 1.934, 1.629, 2.519, 2.093, 2.004, 1.793, 1.564, 1.962, 2.176, 1.846, 1.816, 2.018, 1.708, 2.465, 1.899, 1.523, 1.41, 2.102, 2.065, 2.402, 2.091, 1.867, 1.77, 1.466, 2.029, 1.659, 1.626, 1.977, 1.837, 2.13, 2.241, 2.184, 2.345, 1.833, 2.113, 1.764, 1.859, 1.868, 1.835, 1.906, 2.237, 1.846, 1.871, 1.769, 1.928, 1.831, 1.875, 2.039, 2.24, 1.835, 1.851], [2.171, 1.831, 1.714, 2.507, 1.793, 2.526, 1.829, 1.705, 1.954, 2.017, 2.022, 2.16, 2.059, 1.966, 1.661, 1.752, 1.884, 2.203, 2.182, 1.97, 2.003, 1.875, 1.852, 1.884, 1.774, 1.916, 1.936, 1.809, 1.926, 1.717, 1.841, 1.59, 1.781, 2.016, 1.898, 1.657, 2.458, 2.134, 2.032, 1.785, 1.575, 1.959, 2.11, 1.854, 1.826, 1.992, 1.706, 2.419, 1.854, 1.514, 1.37, 2.084, 2.024, 2.398, 1.955, 1.859, 1.759, 1.441, 2.059, 1.653, 1.583, 1.987, 1.84, 2.106, 2.262, 2.13, 2.371, 1.776, 2.117, 1.733, 1.814, 1.839, 1.822, 1.883, 2.23, 1.803, 1.894, 1.783, 1.911, 1.813, 1.85, 2.004, 2.191, 1.823, 1.809], [2.157, 1.873, 1.802, 2.761, 1.733, 2.506, 1.842, 1.765, 1.938, 2.058, 1.932, 2.196, 2.004, 2.126, 1.664, 1.698, 1.899, 2.073, 2.117, 2.083, 1.972, 1.969, 1.865, 1.937, 1.752, 1.939, 1.927, 1.804, 2.07, 1.725, 1.846, 1.5, 1.804, 2.1, 1.932, 1.773, 2.431, 2.088, 2.08, 1.812, 1.592, 1.953, 2.044, 2.019, 1.846, 2.061, 1.771, 2.254, 1.891, 1.536, 1.356, 1.952, 2.222, 2.427, 2.015, 1.873, 1.79, 1.384, 1.981, 1.665, 1.815, 2.006, 1.869, 2.102, 2.249, 2.27, 2.296, 1.814, 2.099, 1.702, 1.688, 1.89, 1.82, 1.927, 2.162, 1.825, 1.998, 1.811, 2.0, 1.842, 1.793, 2.115, 2.301, 1.789, 1.826], [2.127, 1.744, 1.747, 2.548, 1.939, 2.296, 1.808, 1.71, 1.901, 1.906, 2.074, 2.167, 2.113, 2.044, 1.632, 1.821, 1.94, 2.076, 2.114, 1.837, 1.978, 1.904, 1.872, 1.98, 1.886, 1.923, 1.875, 1.799, 1.992, 1.704, 1.812, 1.715, 1.756, 2.061, 1.94, 1.554, 2.592, 2.065, 1.983, 1.802, 1.57, 1.955, 2.215, 1.765, 1.796, 2.006, 1.662, 2.573, 1.915, 1.543, 1.439, 2.16, 2.012, 2.42, 2.268, 1.886, 1.767, 1.527, 2.073, 1.65, 1.567, 2.016, 1.819, 2.153, 2.225, 2.237, 2.327, 1.877, 2.115, 1.804, 1.939, 1.867, 1.84, 1.905, 2.302, 1.883, 1.798, 1.725, 1.893, 1.846, 1.916, 2.025, 2.268, 1.867, 1.877], [2.089, 1.664, 1.72, 2.441, 2.031, 2.321, 1.773, 1.702, 1.935, 1.968, 2.119, 2.191, 2.023, 1.925, 1.621, 1.75, 1.822, 2.074, 2.139, 1.764, 1.982, 1.873, 1.895, 1.955, 1.829, 1.945, 1.853, 1.794, 2.046, 1.75, 1.793, 1.741, 1.752, 2.042, 1.965, 1.532, 2.598, 2.086, 1.923, 1.771, 1.517, 1.98, 2.338, 1.743, 1.794, 2.014, 1.693, 2.618, 1.938, 1.5, 1.476, 2.216, 2.003, 2.361, 2.13, 1.85, 1.764, 1.513, 2.001, 1.669, 1.538, 1.897, 1.819, 2.163, 2.226, 2.099, 2.386, 1.865, 2.121, 1.818, 2.0, 1.876, 1.858, 1.908, 2.254, 1.874, 1.791, 1.759, 1.908, 1.822, 1.944, 2.012, 2.201, 1.863, 1.892]]column_lst = ['whole_year', 'spring', 'summer', 'autumn', 'winter']# 計算列表兩兩間的相關系數data_dict = {} # 創建數據字典，為生成Dataframe做準備for col, gf_lst in zip(column_lst, unstrtf_lst):data_dict[col] = gf_lstunstrtf_df = pd.DataFrame(data_dict)cor1 = unstrtf_df.corr() # 計算相關系數，得到一個矩陣print(cor1)print(unstrtf_df.columns.tolist())

結果如下：

whole_year spring summer autumn winter whole_year 1.000000 0.986011 0.943254 0.980358 0.965415 spring 0.986011 1.000000 0.944394 0.945710 0.930887 summer 0.943254 0.944394 1.000000 0.876008 0.833568 autumn 0.980358 0.945710 0.876008 1.000000 0.977426 winter 0.965415 0.930887 0.833568 0.977426 1.000000

用numpy計算相關系數

import numpy as np # 這里u1是一個矩陣，可以自己構造，也可以來自dataframe類型：比如u1=a_df.values np.corrcoef(u1) # 計算矩陣所有行的相關系數 np.corrcoef(u1.T) # 計算矩陣所有列的相關系數 np.around(np.corrcoef(u1), decimals=3) # 這里是將矩陣結果保留3位小數

總結

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