第10章 评价分类结果
10-1 准确度的陷阱和混淆矩阵
10-2 精准率和召回率
10-3 实现混淆矩阵，精准率和召回率
Notbook 示例
Notbook 源码
1 [1] 2 import numpy as np 3 from sklearn import datasets 4 [2] 5 digits = datasets.load_digits() 6 X = digits.data 7 y = digits.target.copy() 8 9 y[digits.target==9] = 1 10 y[digits.target!=9] = 0 11 [3] 12 from sklearn.model_selection import train_test_split 13 14 X_train, X_test, y_train, y_test = train_test_split(X, y,random_state=666) 15 [4] 16 X_train.shape 17 (1347, 64) 18 [5] 19 from sklearn.linear_model import LogisticRegression 20 21 log_reg = LogisticRegression() 22 log_reg.fit(X_train,y_train) 23 log_reg.score(X_test,y_test) 24 F:\anaconda\lib\site-packages\sklearn\linear_model\_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1): 25 STOP: TOTAL NO. of ITERATIONS REACHED LIMIT. 26 27 Increase the number of iterations (max_iter) or scale the data as shown in: 28 https://scikit-learn.org/stable/modules/preprocessing.html 29 Please also refer to the documentation for alternative solver options: 30 https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression 31 n_iter_i = _check_optimize_result( 32 33 0.9755555555555555 34 [6] 35 y_log_predict = log_reg.predict(X_test) 36 [7] 37 def TN(y_ture, y_predict): 38 assert len(y_ture) == len(y_predict) 39 return np.sum((y_ture == 0) & (y_predict == 0)) 40 41 TN(y_test,y_log_predict) 42 403 43 [8] 44 def FP(y_ture, y_predict): 45 assert len(y_ture) == len(y_predict) 46 return np.sum((y_ture == 0) & (y_predict == 1)) 47 48 FP(y_test,y_log_predict) 49 2 50 [9] 51 def FN(y_ture, y_predict): 52 assert len(y_ture) == len(y_predict) 53 return np.sum((y_ture == 1) & (y_predict == 0)) 54 55 FN(y_test,y_log_predict) 56 9 57 [10] 58 def TP(y_ture, y_predict): 59 assert len(y_ture) == len(y_predict) 60 return np.sum((y_ture == 1) & (y_predict == 1)) 61 62 TP(y_test,y_log_predict) 63 36 64 [11] 65 def confusion_matrix(y_true, y_predict): 66 return np.array([ 67 [TN(y_true,y_predict), FP(y_true,y_predict)], 68 [FN(y_true,y_predict), TP(y_true,y_predict)] 69 ]) 70 confusion_matrix(y_test, y_log_predict) 71 array([[403, 2], 72 [ 9, 36]]) 73 [12] 74 def precision_score(y_true, y_predict): 75 tp = TP(y_true, y_predict) 76 fp = FP(y_true, y_predict) 77 try: 78 return tp / (tp + fp) 79 except: 80 return 0.0 81 82 precision_score(y_test, y_log_predict) 83 0.9473684210526315 84 [13] 85 def recall_score(y_true, y_predict): 86 tp = TP(y_true, y_predict) 87 fn = FN(y_true, y_predict) 88 try: 89 return tp / (tp + fn) 90 except: 91 return 0.0 92 93 recall_score(y_test, y_log_predict) 94 0.8 95 scikit-learn 中的混淆矩阵，精准率和召回率 96 [14] 97 from sklearn.metrics import confusion_matrix 98 99 confusion_matrix(y_test, y_log_predict) 100 array([[403, 2], 101 [ 9, 36]], dtype=int64) 102 [15] 103 from sklearn.metrics import precision_score 104 105 precision_score(y_test,y_log_predict) 106 0.9473684210526315 107 [16] 108 from sklearn.metrics import recall_score 109 110 recall_score(y_test,y_log_predict) 111 0.8
10-4 F1 Score
10-5 Precision-Recall 平衡
Notbook 示例
Notbook 源码
1 F1 Score 2 [18] 3 import numpy as np 4 import matplotlib.pyplot as plt 5 [4] 6 def f1_score(precision, recall): 7 try: 8 return 2 * precision * recall / ( precision + recall) 9 except: 10 return 0.0 11 [5] 12 precision = 0.5 13 recall =0.5 14 f1_score(precision,recall) 15 0.5 16 [6] 17 precision = 0.1 18 recall = 0.9 19 f1_score(precision,recall) 20 0.18000000000000002 21 [7] 22 precision = 0.0 23 recall = 0.9 24 f1_score(precision,recall) 25 0.0 26 [8] 27 from sklearn import datasets 28 29 digits = datasets.load_digits() 30 X = digits.data 31 y = digits.target.copy() 32 33 y[digits.target==9] = 1 34 y[digits.target!=9] = 0 35 [9] 36 from sklearn.model_selection import train_test_split 37 38 X_train, X_test, y_train, y_test = train_test_split(X, y,random_state=666) 39 [10] 40 from sklearn.linear_model import LogisticRegression 41 42 log_reg = LogisticRegression() 43 log_reg.fit(X_train,y_train) 44 log_reg.score(X_test,y_test) 45 F:\anaconda\lib\site-packages\sklearn\linear_model\_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1): 46 STOP: TOTAL NO. of ITERATIONS REACHED LIMIT. 47 48 Increase the number of iterations (max_iter) or scale the data as shown in: 49 https://scikit-learn.org/stable/modules/preprocessing.html 50 Please also refer to the documentation for alternative solver options: 51 https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression 52 n_iter_i = _check_optimize_result( 53 54 0.9755555555555555 55 [12] 56 y_predict = log_reg.predict(X_test) 57 [14] 58 from sklearn.metrics import confusion_matrix 59 60 confusion_matrix(y_test, y_predict) 61 array([[403, 2], 62 [ 9, 36]], dtype=int64) 63 [15] 64 from sklearn.metrics import precision_score 65 66 precision_score(y_test,y_predict) 67 0.9473684210526315 68 [16] 69 from sklearn.metrics import recall_score 70 71 recall_score(y_test,y_predict) 72 0.8 73 [17] 74 from sklearn.metrics import f1_score 75 76 f1_score(y_test, y_predict) 77 0.8674698795180723 78 [19] 79 log_reg.decision_function(X_test) 80 array([-21.39857276, -32.89731271, -16.41797156, -79.82318954, 81 -48.03305046, -24.18254017, -44.60990955, -24.24479014, 82 -1.14284305, -19.00457455, -65.82296325, -50.97066379, 83 -30.92082895, -45.94864685, -37.36152924, -29.51329291, 84 -36.92856241, -82.80968102, -37.63648469, -9.8788178 , 85 -9.26807376, -85.25151511, -16.75031683, -45.3443087 , 86 -5.02564992, -48.29794851, -11.65881308, -37.36076018, 87 -25.08299918, -13.59764839, -16.5953793 , -28.78598514, 88 -34.3678504 , -28.52337297, -8.11452445, -4.6022814 , 89 -21.94247061, -21.87781719, -31.17562964, -23.36466695, 90 -26.90556959, -62.23610493, -37.68704357, -66.36559349, 91 -20.10364224, -16.68553543, -18.16727295, -21.5492968 , 92 -28.96549149, -19.61417448, 2.41242539, 7.7293895 , 93 -34.87176036, -42.70947089, -25.63234617, -34.75112951, 94 -7.59781243, -49.51333048, -51.52646722, 19.66201134, 95 -10.09725489, -32.0060884 , -11.49932898, -1.42857622, 96 -48.69518674, -43.87320098, -24.83993002, -19.60221328, 97 -36.64215638, -3.52332398, -4.44425929, -19.2097096 , 98 -20.35743524, -40.89507478, -11.8601531 , -32.7541669 , 99 -35.7587069 , -28.5992766 , -55.41729445, -18.82659602, 100 4.56820284, -16.46610285, -76.77533257, -58.24489386, 101 -30.24372047, -29.42228053, -33.41709641, -8.41820483, 102 -47.91658806, -65.49746283, -16.90883929, -22.17253788, 103 -11.28533349, -18.66745327, -69.22403985, -46.39517132, 104 -39.45322992, -35.92419637, -17.72138133, -62.96856734, 105 -16.85788403, -55.14488072, -28.77104338, -68.47963152, 106 -68.85398745, -6.50137137, -25.51784658, -38.31116618, 107 -27.46927833, -15.54375029, -27.47815541, -20.3332547 , 108 12.07445747, -23.0874899 , -35.96861875, -29.87593015, 109 -68.95687582, -27.32891417, -54.23494371, -24.63214107, 110 -11.85499344, -47.3668394 , -2.75048074, -59.68909997, 111 -30.98860082, -8.98734123, -70.83680244, -56.97836911, 112 -20.07706325, -21.49966977, -68.28663666, -18.91058226, 113 -38.59829624, -57.36383144, -0.91081426, -22.51004028, 114 -22.66179993, -28.99910954, -32.78451092, -20.43310932, 115 -11.3535947 , 4.63057398, 6.26725227, 1.48867388, 116 -7.63736213, -39.24004802, 12.15620508, -74.5437931 , 117 -75.08648846, -49.97467006, -11.63081865, -47.61958938, 118 -75.41232907, -29.89880625, -63.93514052, -7.26078617, 119 -6.64271099, -18.2199428 , -32.47674504, -17.93503126, 120 -43.33439089, -32.70727873, -34.29947784, -72.74689478, 121 -15.19084634, 11.48054014, -56.40994066, -6.03930048, 122 -48.38612896, -16.44647469, -2.13693844, -11.85713489, 123 -33.26559831, -51.34042787, -10.38651041, -17.18846078, 124 -5.23982411, -25.19373985, -15.70686294, 3.5534034 , 125 -45.03772698, -12.58192379, -25.37999195, -16.56801256, 126 -22.17722688, -82.50131039, -5.8811552 , -20.25621041, 127 -20.46383207, -26.80997392, -25.98518361, -40.44912794, 128 -38.01122059, -26.9627282 , -23.75636279, -20.15726322, 129 -9.69213637, -19.6799691 , -42.49289639, -44.13469938, 130 -15.65386714, -64.03047268, -24.55648146, -56.30568399, 131 -13.01339393, -29.66652546, 3.89794499, -44.33546306, 132 -7.92245618, 1.14543666, -2.81814751, -11.92929586, 133 7.5086596 , -7.17718348, -46.39847023, -48.65871982, 134 -4.59959364, -19.05437356, -24.07254218, -48.76355552, 135 -15.01620526, -24.92137044, -16.69772054, -18.68326579, 136 -15.70208152, -16.86386928, -38.52705695, -31.09380281, 137 -9.37781861, -71.4453079 , -22.76526306, -14.43837784, 138 -23.08137726, -34.31916589, -0.89221103, -32.73888374, 139 -11.21723013, -18.6738182 , -8.21484026, -45.43305526, 140 -22.30560288, -62.38971913, -46.77028519, -65.15237525, 141 -33.22628484, -23.47536421, -28.51024714, -64.78914741, 142 1.45290051, -4.09358964, -25.64587602, -22.32038298, 143 -54.68656406, -16.3407006 , -12.06726537, -35.28199188, 144 -5.7391347 , -13.52396326, -72.2770459 , -6.16552202, 145 -1.16494995, -35.58095254, -24.15372831, -68.3152937 , 146 14.76606277, -63.0626057 , 9.9115143 , -24.1477828 , 147 -32.45732897, -14.38796233, -85.7282472 , -12.77864747, 148 8.99482139, -16.51791403, -36.67219629, -16.51511131, 149 -19.35718611, -32.583308 , -5.64342385, 7.68471894, 150 9.38946768, 5.85378475, -35.64899776, -12.98316031, 151 -54.42344306, -41.10888515, 5.63263711, -79.47912897, 152 -15.82650933, -19.23205602, -10.86309466, -42.52164565, 153 -19.81792269, -15.70492451, -17.99800508, -18.02255039, 154 -6.75867766, -20.78794591, -16.58125173, -70.42110518, 155 -9.21349451, -31.70399615, -19.67558207, -21.95918435, 156 -24.77110999, -16.38822309, -13.36794196, -22.93287663, 157 11.06093377, -15.37076191, -32.94045314, -13.74640562, 158 -50.35815794, -20.45538215, -56.2709184 , -28.68677373, 159 -21.86524573, -30.41664698, -69.26034763, -59.34711621, 160 14.34093357, 8.57797635, -25.66219805, 2.74054632, 161 4.9329685 , -19.66539612, -58.82488345, -10.00833742, 162 -28.80946298, -27.20346821, 6.28874155, -80.46777388, 163 -34.45717484, -50.28471677, -35.95066935, -48.6313621 , 164 -18.01210551, -62.3428243 , -3.09974615, -25.2635612 , 165 -64.10526345, -9.61660605, -21.76591374, 19.89900139, 166 -18.75262552, -4.46636384, -13.15019258, -21.64298339, 167 -43.10021867, -52.10329918, -28.53126446, -14.54900274, 168 -2.47647559, -6.12117544, 3.69187156, -15.0063578 , 169 -40.85876851, -26.64359518, 14.10780389, -17.68798006, 170 15.18161223, -33.09641501, 5.26048113, -14.27034463, 171 -53.58418085, -50.04146827, -30.668069 , -38.05244113, 172 -23.29209606, -24.6960092 , -13.57354354, -22.62553141, 173 -27.2290141 , -19.64733979, -28.1768732 , -19.93558149, 174 -29.85262347, -11.28766344, -17.24377394, -24.0310721 , 175 -24.35542295, 10.39150921, -17.21009704, -38.02155334, 176 -16.08422171, -37.57447399, -16.327524 , -69.12211344, 177 -33.67776297, -43.62662563, -26.61467625, -10.32511698, 178 -66.36070209, -31.9032331 , -45.56406403, -14.57833594, 179 -36.13656958, -14.94377141, -70.01819354, -11.35647733, 180 -40.86227952, -32.65545084, -19.77146533, -27.58157471, 181 -15.73466776, -31.57608305, -8.50558639, -21.38402622, 182 -34.07101343, -11.68747617, -36.42460337, -34.78640679, 183 -22.21781815, 4.77423291, -21.31044306, -4.45343862, 184 -20.8192745 , -32.26057776, -41.11472384, -25.0841837 , 185 -19.76245188, -47.86598828, -30.89389022, -45.55549885, 186 -71.52150073, -6.25498279, -32.5635314 , 2.27397922, 187 11.93710255, 7.1181192 , -31.36293349, -63.9582492 , 188 -23.78891268, -5.73651065, -32.42584299, -24.7138706 , 189 -67.69974056, -32.8331123 , -33.60887574, -31.53192719, 190 -51.97754435, -22.54575078, -7.74388421, -17.30052337, 191 -25.78866235, -32.37585686, -29.48393512, -66.43195243, 192 -45.70161834, -16.05036959]) 193 [20] 194 log_reg.decision_function(X_test)[:10] 195 array([-21.39857276, -32.89731271, -16.41797156, -79.82318954, 196 -48.03305046, -24.18254017, -44.60990955, -24.24479014, 197 -1.14284305, -19.00457455]) 198 [21] 199 log_reg.predict(X_test)[:10] 200 array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) 201 [22] 202 decision_scores = log_reg.decision_function(X_test) 203 [23] 204 np.min(decision_scores) 205 -85.72824719706493 206 [24] 207 np.max(decision_scores) 208 19.899001392471213 209 [25] 210 y_predict_2 = np.array(decision_scores >= 5, dtype='int') 211 [26] 212 confusion_matrix(y_test, y_predict_2) 213 array([[404, 1], 214 [ 21, 24]], dtype=int64) 215 [27] 216 precision_score(y_test,y_predict_2) 217 0.96 218 [28] 219 recall_score(y_test,y_predict_2) 220 0.5333333333333333 221 [29] 222 y_predict_3 = np.array(decision_scores >= -5, dtype='int') 223 [30] 224 confusion_matrix(y_test, y_predict_3) 225 array([[390, 15], 226 [ 5, 40]], dtype=int64) 227 [31] 228 precision_score(y_test,y_predict_3) 229 0.7272727272727273 230 [32] 231 recall_score(y_test,y_predict_3) 232 0.8888888888888888
10-6 scikit-learn 中的Precision-Recall曲线
Notbook 示例
Notbook 源码
1 [8] 2 import numpy as np 3 import matplotlib.pyplot as plt 4 from sklearn import datasets 5 [2] 6 digits = datasets.load_digits() 7 X = digits.data 8 y = digits.target.copy() 9 10 y[digits.target==9] = 1 11 y[digits.target!=9] = 0 12 [3] 13 from sklearn.model_selection import train_test_split 14 15 X_train, X_test, y_train, y_test = train_test_split(X, y,random_state=666) 16 [5] 17 from sklearn.linear_model import LogisticRegression 18 19 log_reg = LogisticRegression() 20 log_reg.fit(X_train,y_train) 21 decision_score = log_reg.decision_function(X_test) 22 F:\anaconda\lib\site-packages\sklearn\linear_model\_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1): 23 STOP: TOTAL NO. of ITERATIONS REACHED LIMIT. 24 25 Increase the number of iterations (max_iter) or scale the data as shown in: 26 https://scikit-learn.org/stable/modules/preprocessing.html 27 Please also refer to the documentation for alternative solver options: 28 https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression 29 n_iter_i = _check_optimize_result( 30 31 [6] 32 from sklearn.metrics import precision_score 33 from sklearn.metrics import recall_score 34 35 precisions = [] 36 recallls = [] 37 thresholds = np.arange(np.min(decision_score), np.max(decision_score),0.1) 38 for threshold in thresholds: 39 y_predict = np.array(decision_score >= threshold,dtype='int') 40 precisions.append(precision_score(y_test, y_predict)) 41 recallls.append(recall_score(y_test,y_predict)) 42 [9] 43 plt.plot(thresholds,precisions) 44 plt.plot(thresholds,recallls) 45 [<matplotlib.lines.Line2D at 0x1bf900a73a0>] 46 47 Precision-Recall 曲线 48 [10] 49 plt.plot(precisions, recallls) 50 51 [<matplotlib.lines.Line2D at 0x1bf9016b4c0>] 52 53 scikit-learn 中的Precision-Recall曲线 54 [11] 55 from sklearn.metrics import precision_recall_curve 56 57 precisions, recallls, thresholds = precision_recall_curve(y_test,decision_score) 58 [12] 59 precisions.shape 60 (151,) 61 [13] 62 recallls.shape 63 (151,) 64 [14] 65 thresholds.shape 66 (150,) 67 [15] 68 plt.plot(thresholds,precisions[:-1]) 69 plt.plot(thresholds,recallls[:-1]) 70 [<matplotlib.lines.Line2D at 0x1bf901f6fa0>] 71 72 [16] 73 plt.plot(precisions, recallls) 74 [<matplotlib.lines.Line2D at 0x1bf901e8160>]
10-7 ROC
Notbook 示例
Notbook 源码
1 ROC曲线 2 [1] 3 import numpy as np 4 import matplotlib.pyplot as plt 5 from sklearn import datasets 6 [2] 7 digits = datasets.load_digits() 8 X = digits.data 9 y = digits.target.copy() 10 11 y[digits.target==9] = 1 12 y[digits.target!=9] = 0 13 [3] 14 from sklearn.model_selection import train_test_split 15 16 X_train, X_test, y_train, y_test = train_test_split(X, y,random_state=666) 17 [4] 18 from sklearn.linear_model import LogisticRegression 19 20 log_reg = LogisticRegression() 21 log_reg.fit(X_train,y_train) 22 decision_score = log_reg.decision_function(X_test) 23 F:\anaconda\lib\site-packages\sklearn\linear_model\_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1): 24 STOP: TOTAL NO. of ITERATIONS REACHED LIMIT. 25 26 Increase the number of iterations (max_iter) or scale the data as shown in: 27 https://scikit-learn.org/stable/modules/preprocessing.html 28 Please also refer to the documentation for alternative solver options: 29 https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression 30 n_iter_i = _check_optimize_result( 31 32 [5] 33 from playML.metrics import FPR, TPR 34 35 fprs = [] 36 tprs = [] 37 thresholds = np.arange(np.min(decision_score), np.max(decision_score),0.1) 38 for threshold in thresholds: 39 y_predict = np.array(decision_score >= threshold,dtype='int') 40 fprs.append(FPR(y_test, y_predict)) 41 tprs.append(TPR(y_test,y_predict)) 42 [6] 43 plt.plot(fprs,tprs) 44 [<matplotlib.lines.Line2D at 0x1600c413820>] 45 46 scikit-learn中的ROC 47 [7] 48 from sklearn.metrics import roc_curve 49 50 fps, tps, thresholds = roc_curve(y_test,decision_score) 51 [8] 52 plt.plot(fprs,tprs) 53 [<matplotlib.lines.Line2D at 0x1600c190cd0>] 54 55 [9] 56 from sklearn.metrics import roc_auc_score 57 58 roc_auc_score(y_test,decision_score) 59 0.9823868312757201
10-8 多分类问题中的混淆矩阵
Notbook 示例
Notbook 源码
多分类问题中的混淆矩阵 [2] import numpy as np import matplotlib.pyplot as plt from sklearn import datasets [5] digits = datasets.load_digits() X = digits.data y = digits.target.copy() [6] from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split(X, y,random_state=666) [8] from sklearn.linear_model import LogisticRegression log_reg = LogisticRegression() log_reg.fit(X_train,y_train) log_reg.score(X_test,y_test) F:\anaconda\lib\site-packages\sklearn\linear_model\_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1): STOP: TOTAL NO. of ITERATIONS REACHED LIMIT. Increase the number of iterations (max_iter) or scale the data as shown in: https://scikit-learn.org/stable/modules/preprocessing.html Please also refer to the documentation for alternative solver options: https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression n_iter_i = _check_optimize_result( 0.9711111111111111 [9] y_predict = log_reg.predict(X_test) [10] from sklearn.metrics import precision_score precision_score(y_test,y_predict,average='micro') 0.9711111111111111 [11] from sklearn.metrics import confusion_matrix confusion_matrix(y_test,y_predict) array([[46, 0, 0, 0, 0, 0, 0, 0, 0, 0], [ 0, 40, 0, 0, 0, 0, 0, 0, 0, 0], [ 0, 0, 50, 0, 0, 0, 0, 0, 0, 0], [ 0, 0, 1, 50, 0, 0, 0, 0, 1, 1], [ 0, 0, 0, 0, 47, 0, 0, 0, 1, 0], [ 0, 0, 0, 0, 0, 37, 0, 1, 0, 0], [ 0, 0, 0, 0, 0, 1, 38, 0, 0, 0], [ 0, 0, 0, 0, 0, 0, 0, 43, 0, 0], [ 0, 0, 0, 0, 1, 2, 0, 1, 44, 0], [ 0, 0, 0, 1, 0, 2, 0, 0, 0, 42]], dtype=int64) [12] cfm = confusion_matrix(y_test,y_predict) plt.matshow(cfm, cmap=plt.cm.gray) <matplotlib.image.AxesImage at 0x1cdcf0153d0> [14] row_sums = np.sum(cfm, axis=1) err_matrix = cfm / row_sums np.fill_diagonal(err_matrix,0) err_matrix array([[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [0. , 0. , 0.02 , 0. , 0. , 0. , 0. , 0. , 0.02083333, 0.02222222], [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.02083333, 0. ], [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.02325581, 0. , 0. ], [0. , 0. , 0. , 0. , 0. , 0.02631579, 0. , 0. , 0. , 0. ], [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [0. , 0. , 0. , 0. , 0.02083333, 0.05263158, 0. , 0.02325581, 0. , 0. ], [0. , 0. , 0. , 0.01886792, 0. , 0.05263158, 0. , 0. , 0. , 0. ]]) [15] plt.matshow(err_matrix, cmap=plt.cm.gray) <matplotlib.image.AxesImage at 0x1cdcf386550>
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