PyCM is a multi-class confusion matrix library written in Python that supports both input data vectors and direct matrix, and a proper tool for post-classification model evaluation that supports most classes and overall statistics parameters. PyCM is the swiss-army knife of confusion matrices, targeted mainly at data scientists that need a broad array of metrics for predictive models and an accurate evaluation of large variety of classifiers.
Fig1. ConfusionMatrix Block Diagram
pip install -r requirements.txt
or pip3 install -r requirements.txt
(Need root access)python3 setup.py install
or python setup.py install
(Need root access)pip install pycm==2.1
or pip3 install pycm==2.1
(Need root access)conda install -c sepandhaghighi pycm
(Need root access)easy_install --upgrade pycm
(Need root access)from pycm import *
y_actu = [2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1, 2]
y_pred = [0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 2]
cm = ConfusionMatrix(y_actu, y_pred,digit=5)
cm
pycm.ConfusionMatrix(classes: [0, 1, 2])
cm.actual_vector
[2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1, 2]
cm.predict_vector
[0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 2]
cm.classes
[0, 1, 2]
cm.class_stat
{'ACC': {0: 0.8333333333333334, 1: 0.75, 2: 0.5833333333333334}, 'AGM': {0: 0.837285964012303, 1: 0.6919986974962765, 2: 0.6071224016819726}, 'AM': {0: 2, 1: -1, 2: -1}, 'AUC': {0: 0.8888888888888888, 1: 0.611111111111111, 2: 0.5833333333333333}, 'AUCI': {0: 'Very Good', 1: 'Fair', 2: 'Poor'}, 'BCD': {0: 0.08333333333333333, 1: 0.041666666666666664, 2: 0.041666666666666664}, 'BM': {0: 0.7777777777777777, 1: 0.2222222222222221, 2: 0.16666666666666652}, 'CEN': {0: 0.25, 1: 0.49657842846620864, 2: 0.6044162769630221}, 'DOR': {0: 'None', 1: 3.999999999999998, 2: 1.9999999999999998}, 'DP': {0: 'None', 1: 0.331933069996499, 2: 0.16596653499824957}, 'DPI': {0: 'None', 1: 'Poor', 2: 'Poor'}, 'ERR': {0: 0.16666666666666663, 1: 0.25, 2: 0.41666666666666663}, 'F0.5': {0: 0.6521739130434783, 1: 0.45454545454545453, 2: 0.5769230769230769}, 'F1': {0: 0.75, 1: 0.4, 2: 0.5454545454545454}, 'F2': {0: 0.8823529411764706, 1: 0.35714285714285715, 2: 0.5172413793103449}, 'FDR': {0: 0.4, 1: 0.5, 2: 0.4}, 'FN': {0: 0, 1: 2, 2: 3}, 'FNR': {0: 0.0, 1: 0.6666666666666667, 2: 0.5}, 'FOR': {0: 0.0, 1: 0.19999999999999996, 2: 0.4285714285714286}, 'FP': {0: 2, 1: 1, 2: 2}, 'FPR': {0: 0.2222222222222222, 1: 0.11111111111111116, 2: 0.33333333333333337}, 'G': {0: 0.7745966692414834, 1: 0.408248290463863, 2: 0.5477225575051661}, 'GI': {0: 0.7777777777777777, 1: 0.2222222222222221, 2: 0.16666666666666652}, 'GM': {0: 0.8819171036881969, 1: 0.5443310539518174, 2: 0.5773502691896257}, 'IBA': {0: 0.9506172839506174, 1: 0.1316872427983539, 2: 0.2777777777777778}, 'IS': {0: 1.263034405833794, 1: 1.0, 2: 0.2630344058337938}, 'J': {0: 0.6, 1: 0.25, 2: 0.375}, 'LS': {0: 2.4, 1: 2.0, 2: 1.2}, 'MCC': {0: 0.6831300510639732, 1: 0.25819888974716115, 2: 0.1690308509457033}, 'MCEN': {0: 0.2643856189774724, 1: 0.5, 2: 0.6875}, 'MK': {0: 0.6000000000000001, 1: 0.30000000000000004, 2: 0.17142857142857126}, 'N': {0: 9, 1: 9, 2: 6}, 'NLR': {0: 0.0, 1: 0.7500000000000001, 2: 0.75}, 'NPV': {0: 1.0, 1: 0.8, 2: 0.5714285714285714}, 'OP': {0: 0.7083333333333334, 1: 0.2954545454545454, 2: 0.4404761904761905}, 'P': {0: 3, 1: 3, 2: 6}, 'PLR': {0: 4.5, 1: 2.9999999999999987, 2: 1.4999999999999998}, 'PLRI': {0: 'Poor', 1: 'Poor', 2: 'Poor'}, 'POP': {0: 12, 1: 12, 2: 12}, 'PPV': {0: 0.6, 1: 0.5, 2: 0.6}, 'PRE': {0: 0.25, 1: 0.25, 2: 0.5}, 'Q': {0: 'None', 1: 0.6, 2: 0.3333333333333333}, 'RACC': {0: 0.10416666666666667, 1: 0.041666666666666664, 2: 0.20833333333333334}, 'RACCU': {0: 0.1111111111111111, 1: 0.04340277777777778, 2: 0.21006944444444442}, 'TN': {0: 7, 1: 8, 2: 4}, 'TNR': {0: 0.7777777777777778, 1: 0.8888888888888888, 2: 0.6666666666666666}, 'TON': {0: 7, 1: 10, 2: 7}, 'TOP': {0: 5, 1: 2, 2: 5}, 'TP': {0: 3, 1: 1, 2: 3}, 'TPR': {0: 1.0, 1: 0.3333333333333333, 2: 0.5}, 'Y': {0: 0.7777777777777777, 1: 0.2222222222222221, 2: 0.16666666666666652}, 'dInd': {0: 0.2222222222222222, 1: 0.6758625033664689, 2: 0.6009252125773316}, 'sInd': {0: 0.8428651597363228, 1: 0.5220930407198541, 2: 0.5750817072006014}}
cm.overall_stat
{'95% CI': (0.30438856248221097, 0.8622781041844558), 'AUNP': 0.6666666666666666, 'AUNU': 0.6944444444444443, 'Bennett S': 0.37500000000000006, 'CBA': 0.4777777777777778, 'Chi-Squared': 6.6, 'Chi-Squared DF': 4, 'Conditional Entropy': 0.9591479170272448, 'Cramer V': 0.5244044240850757, 'Cross Entropy': 1.5935164295556343, 'Gwet AC1': 0.3893129770992367, 'Hamming Loss': 0.41666666666666663, 'Joint Entropy': 2.4591479170272446, 'KL Divergence': 0.09351642955563438, 'Kappa': 0.35483870967741943, 'Kappa 95% CI': (-0.07707577422109269, 0.7867531935759315), 'Kappa No Prevalence': 0.16666666666666674, 'Kappa Standard Error': 0.2203645326012817, 'Kappa Unbiased': 0.34426229508196726, 'Lambda A': 0.16666666666666666, 'Lambda B': 0.42857142857142855, 'Mutual Information': 0.5242078379544426, 'NIR': 0.5, 'Overall ACC': 0.5833333333333334, 'Overall CEN': 0.4638112995385119, 'Overall J': (1.225, 0.4083333333333334), 'Overall MCC': 0.36666666666666664, 'Overall MCEN': 0.5189369467580801, 'Overall RACC': 0.3541666666666667, 'Overall RACCU': 0.3645833333333333, 'P-Value': 0.38720703125, 'PPV Macro': 0.5666666666666668, 'PPV Micro': 0.5833333333333334, 'Pearson C': 0.5956833971812705, 'Phi-Squared': 0.5499999999999999, 'RCI': 0.3494718919696284, 'RR': 4.0, 'Reference Entropy': 1.5, 'Response Entropy': 1.4833557549816874, 'SOA1(Landis & Koch)': 'Fair', 'SOA2(Fleiss)': 'Poor', 'SOA3(Altman)': 'Fair', 'SOA4(Cicchetti)': 'Poor', 'Scott PI': 0.34426229508196726, 'Standard Error': 0.14231876063832777, 'TPR Macro': 0.611111111111111, 'TPR Micro': 0.5833333333333334, 'Zero-one Loss': 5}
cm.table
{0: {0: 3, 1: 0, 2: 0}, 1: {0: 0, 1: 1, 2: 2}, 2: {0: 2, 1: 1, 2: 3}}
cm.matrix
{0: {0: 3, 1: 0, 2: 0}, 1: {0: 0, 1: 1, 2: 2}, 2: {0: 2, 1: 1, 2: 3}}
cm.normalized_matrix
{0: {0: 1.0, 1: 0.0, 2: 0.0}, 1: {0: 0.0, 1: 0.33333, 2: 0.66667}, 2: {0: 0.33333, 1: 0.16667, 2: 0.5}}
cm.normalized_table
{0: {0: 1.0, 1: 0.0, 2: 0.0}, 1: {0: 0.0, 1: 0.33333, 2: 0.66667}, 2: {0: 0.33333, 1: 0.16667, 2: 0.5}}
import numpy
y_actu = numpy.array([2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1, 2])
y_pred = numpy.array([0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 2])
cm = ConfusionMatrix(y_actu, y_pred,digit=5)
cm
pycm.ConfusionMatrix(classes: [0, 1, 2])
cm2 = ConfusionMatrix(matrix={0: {0: 3, 1: 0, 2: 0}, 1: {0: 0, 1: 1, 2: 2}, 2: {0: 2, 1: 1, 2: 3}},digit=5)
cm2
pycm.ConfusionMatrix(classes: [0, 1, 2])
cm2.actual_vector
cm2.predict_vector
cm2.classes
[0, 1, 2]
cm2.class_stat
{'ACC': {0: 0.8333333333333334, 1: 0.75, 2: 0.5833333333333334}, 'AGM': {0: 0.837285964012303, 1: 0.6919986974962765, 2: 0.6071224016819726}, 'AM': {0: 2, 1: -1, 2: -1}, 'AUC': {0: 0.8888888888888888, 1: 0.611111111111111, 2: 0.5833333333333333}, 'AUCI': {0: 'Very Good', 1: 'Fair', 2: 'Poor'}, 'BCD': {0: 0.08333333333333333, 1: 0.041666666666666664, 2: 0.041666666666666664}, 'BM': {0: 0.7777777777777777, 1: 0.2222222222222221, 2: 0.16666666666666652}, 'CEN': {0: 0.25, 1: 0.49657842846620864, 2: 0.6044162769630221}, 'DOR': {0: 'None', 1: 3.999999999999998, 2: 1.9999999999999998}, 'DP': {0: 'None', 1: 0.331933069996499, 2: 0.16596653499824957}, 'DPI': {0: 'None', 1: 'Poor', 2: 'Poor'}, 'ERR': {0: 0.16666666666666663, 1: 0.25, 2: 0.41666666666666663}, 'F0.5': {0: 0.6521739130434783, 1: 0.45454545454545453, 2: 0.5769230769230769}, 'F1': {0: 0.75, 1: 0.4, 2: 0.5454545454545454}, 'F2': {0: 0.8823529411764706, 1: 0.35714285714285715, 2: 0.5172413793103449}, 'FDR': {0: 0.4, 1: 0.5, 2: 0.4}, 'FN': {0: 0, 1: 2, 2: 3}, 'FNR': {0: 0.0, 1: 0.6666666666666667, 2: 0.5}, 'FOR': {0: 0.0, 1: 0.19999999999999996, 2: 0.4285714285714286}, 'FP': {0: 2, 1: 1, 2: 2}, 'FPR': {0: 0.2222222222222222, 1: 0.11111111111111116, 2: 0.33333333333333337}, 'G': {0: 0.7745966692414834, 1: 0.408248290463863, 2: 0.5477225575051661}, 'GI': {0: 0.7777777777777777, 1: 0.2222222222222221, 2: 0.16666666666666652}, 'GM': {0: 0.8819171036881969, 1: 0.5443310539518174, 2: 0.5773502691896257}, 'IBA': {0: 0.9506172839506174, 1: 0.1316872427983539, 2: 0.2777777777777778}, 'IS': {0: 1.263034405833794, 1: 1.0, 2: 0.2630344058337938}, 'J': {0: 0.6, 1: 0.25, 2: 0.375}, 'LS': {0: 2.4, 1: 2.0, 2: 1.2}, 'MCC': {0: 0.6831300510639732, 1: 0.25819888974716115, 2: 0.1690308509457033}, 'MCEN': {0: 0.2643856189774724, 1: 0.5, 2: 0.6875}, 'MK': {0: 0.6000000000000001, 1: 0.30000000000000004, 2: 0.17142857142857126}, 'N': {0: 9, 1: 9, 2: 6}, 'NLR': {0: 0.0, 1: 0.7500000000000001, 2: 0.75}, 'NPV': {0: 1.0, 1: 0.8, 2: 0.5714285714285714}, 'OP': {0: 0.7083333333333334, 1: 0.2954545454545454, 2: 0.4404761904761905}, 'P': {0: 3, 1: 3, 2: 6}, 'PLR': {0: 4.5, 1: 2.9999999999999987, 2: 1.4999999999999998}, 'PLRI': {0: 'Poor', 1: 'Poor', 2: 'Poor'}, 'POP': {0: 12, 1: 12, 2: 12}, 'PPV': {0: 0.6, 1: 0.5, 2: 0.6}, 'PRE': {0: 0.25, 1: 0.25, 2: 0.5}, 'Q': {0: 'None', 1: 0.6, 2: 0.3333333333333333}, 'RACC': {0: 0.10416666666666667, 1: 0.041666666666666664, 2: 0.20833333333333334}, 'RACCU': {0: 0.1111111111111111, 1: 0.04340277777777778, 2: 0.21006944444444442}, 'TN': {0: 7, 1: 8, 2: 4}, 'TNR': {0: 0.7777777777777778, 1: 0.8888888888888888, 2: 0.6666666666666666}, 'TON': {0: 7, 1: 10, 2: 7}, 'TOP': {0: 5, 1: 2, 2: 5}, 'TP': {0: 3, 1: 1, 2: 3}, 'TPR': {0: 1.0, 1: 0.3333333333333333, 2: 0.5}, 'Y': {0: 0.7777777777777777, 1: 0.2222222222222221, 2: 0.16666666666666652}, 'dInd': {0: 0.2222222222222222, 1: 0.6758625033664689, 2: 0.6009252125773316}, 'sInd': {0: 0.8428651597363228, 1: 0.5220930407198541, 2: 0.5750817072006014}}
cm2.overall_stat
{'95% CI': (0.30438856248221097, 0.8622781041844558), 'AUNP': 0.6666666666666666, 'AUNU': 0.6944444444444443, 'Bennett S': 0.37500000000000006, 'CBA': 0.4777777777777778, 'Chi-Squared': 6.6, 'Chi-Squared DF': 4, 'Conditional Entropy': 0.9591479170272448, 'Cramer V': 0.5244044240850757, 'Cross Entropy': 1.5935164295556343, 'Gwet AC1': 0.3893129770992367, 'Hamming Loss': 0.41666666666666663, 'Joint Entropy': 2.4591479170272446, 'KL Divergence': 0.09351642955563438, 'Kappa': 0.35483870967741943, 'Kappa 95% CI': (-0.07707577422109269, 0.7867531935759315), 'Kappa No Prevalence': 0.16666666666666674, 'Kappa Standard Error': 0.2203645326012817, 'Kappa Unbiased': 0.34426229508196726, 'Lambda A': 0.16666666666666666, 'Lambda B': 0.42857142857142855, 'Mutual Information': 0.5242078379544426, 'NIR': 0.5, 'Overall ACC': 0.5833333333333334, 'Overall CEN': 0.4638112995385119, 'Overall J': (1.225, 0.4083333333333334), 'Overall MCC': 0.36666666666666664, 'Overall MCEN': 0.5189369467580801, 'Overall RACC': 0.3541666666666667, 'Overall RACCU': 0.3645833333333333, 'P-Value': 0.38720703125, 'PPV Macro': 0.5666666666666668, 'PPV Micro': 0.5833333333333334, 'Pearson C': 0.5956833971812705, 'Phi-Squared': 0.5499999999999999, 'RCI': 0.3494718919696284, 'RR': 4.0, 'Reference Entropy': 1.5, 'Response Entropy': 1.4833557549816874, 'SOA1(Landis & Koch)': 'Fair', 'SOA2(Fleiss)': 'Poor', 'SOA3(Altman)': 'Fair', 'SOA4(Cicchetti)': 'Poor', 'Scott PI': 0.34426229508196726, 'Standard Error': 0.14231876063832777, 'TPR Macro': 0.611111111111111, 'TPR Micro': 0.5833333333333334, 'Zero-one Loss': 5}
threshold
is added in version 0.9
for real value prediction.
For more information visit Example 3
file
is added in version 0.9.5
in order to load saved confusion matrix with .obj
format generated by save_obj
method.
For more information visit Example 4
sample_weight
is added in version 1.2
For more information visit Example 5
transpose
is added in version 1.2
in order to transpose input matrix (only in Direct CM
mode)
cm = ConfusionMatrix(matrix={0: {0: 3, 1: 0, 2: 0}, 1: {0: 0, 1: 1, 2: 2}, 2: {0: 2, 1: 1, 2: 3}},digit=5,transpose=True)
cm.print_matrix()
Predict 0 1 2 Actual 0 3 0 2 1 0 1 1 2 0 2 3
relabel
method is added in version 1.5
in order to change ConfusionMatrix classnames.
cm.relabel(mapping={0:"L1",1:"L2",2:"L3"})
cm
pycm.ConfusionMatrix(classes: ['L1', 'L2', 'L3'])
online_help
function is added in version 1.1
in order to open each statistics definition in web browser
>>> from pycm import online_help
>>> online_help("J")
>>> online_help("SOA1(Landis & Koch)")
>>> online_help(2)
online_help()
(without argument)online_help()
Please choose one parameter : Example : online_help("J") or online_help(2) 1-95% CI 2-ACC 3-AGM 4-AM 5-AUC 6-AUCI 7-AUNP 8-AUNU 9-BCD 10-BM 11-Bennett S 12-CBA 13-CEN 14-Chi-Squared 15-Chi-Squared DF 16-Conditional Entropy 17-Cramer V 18-Cross Entropy 19-DOR 20-DP 21-DPI 22-ERR 23-F0.5 24-F1 25-F2 26-FDR 27-FN 28-FNR 29-FOR 30-FP 31-FPR 32-G 33-GI 34-GM 35-Gwet AC1 36-Hamming Loss 37-IBA 38-IS 39-J 40-Joint Entropy 41-KL Divergence 42-Kappa 43-Kappa 95% CI 44-Kappa No Prevalence 45-Kappa Standard Error 46-Kappa Unbiased 47-LS 48-Lambda A 49-Lambda B 50-MCC 51-MCEN 52-MK 53-Mutual Information 54-N 55-NIR 56-NLR 57-NPV 58-OP 59-Overall ACC 60-Overall CEN 61-Overall J 62-Overall MCC 63-Overall MCEN 64-Overall RACC 65-Overall RACCU 66-P 67-P-Value 68-PLR 69-PLRI 70-POP 71-PPV 72-PPV Macro 73-PPV Micro 74-PRE 75-Pearson C 76-Phi-Squared 77-Q 78-RACC 79-RACCU 80-RCI 81-RR 82-Reference Entropy 83-Response Entropy 84-SOA1(Landis & Koch) 85-SOA2(Fleiss) 86-SOA3(Altman) 87-SOA4(Cicchetti) 88-Scott PI 89-Standard Error 90-TN 91-TNR 92-TON 93-TOP 94-TP 95-TPR 96-TPR Macro 97-TPR Micro 98-Y 99-Zero-one Loss 100-dInd 101-sInd
This option has been added in version 1.9
in order to recommend most related parameters considering the characteristics of the input dataset. The characteristics according to which the parameters are suggested are balance/imbalance and binary/multiclass. All suggestions can be categorized into three main groups: imbalanced dataset, binary classification for a balanced dataset, and multi-class classification for a balanced dataset. The recommendation lists have been gathered according to the respective paper of each parameter and the capabilities which had been claimed by the paper.
Fig2. Parameter Recommender Block Diagram
cm.imbalance
False
cm.binary
False
cm.recommended_list
['ERR', 'TPR Micro', 'TPR Macro', 'PPV Micro', 'PPV Macro', 'ACC', 'Overall ACC', 'MCC', 'Overall MCC', 'BCD', 'Hamming Loss', 'Zero-one Loss']
In version 2.0
a method for comparing several confusion matrices is introduced. This option is a combination of several overall and class-based benchmarks. Each of the benchmarks evaluates the performance of the classification algorithm from good to poor and give them a numeric score. The score of good performance is 1 and for the poor performance is 0.
After that, two scores are calculated for each confusion matrices, overall and class based. The overall score is the average of the score of four overall benchmarks which are Landis & Koch, Fleiss, Altman, and Cicchetti. And with a same manner, the class based score is the average of the score of three class-based benchmarks which are Positive Likelihood Ratio Interpretation, Discriminant Power Interpretation, and AUC value Interpretation. It should be notice that if one of the benchmarks returns none for one of the classes, that benchmarks will be eliminate in total averaging. If user set weights for the classes, the averaging over the value of class-based benchmark scores will transform to a weighted average.
If the user set the value of by_class
boolean input True
, the best confusion matrix is the one with the maximum class-based score. Otherwise, if a confusion matrix obtain the maximum of the both overall and class-based score, that will be the reported as the best confusion matrix but in any other cases the compare object doesn’t select best confusion matrix.
Fig3. Compare Block Diagram
cm2 = ConfusionMatrix(matrix={0:{0:2,1:50,2:6},1:{0:5,1:50,2:3},2:{0:1,1:7,2:50}})
cm3 = ConfusionMatrix(matrix={0:{0:50,1:2,2:6},1:{0:50,1:5,2:3},2:{0:1,1:55,2:2}})
cp = Compare({"cm2":cm2,"cm3":cm3})
print(cp)
Best : cm2 Rank Name Class-Score Overall-Score 1 cm2 4.15 1.48333 2 cm3 2.75 0.95
cp.scores
{'cm2': {'class': 4.15, 'overall': 1.48333}, 'cm3': {'class': 2.75, 'overall': 0.95}}
cp.sorted
['cm2', 'cm3']
cp.best
pycm.ConfusionMatrix(classes: [0, 1, 2])
cp.best_name
'cm2'
cp2 = Compare({"cm2":cm2,"cm3":cm3},by_class=True,weight={0:5,1:1,2:1})
print(cp2)
Best : cm3 Rank Name Class-Score Overall-Score 1 cm3 8.15 0.95 2 cm2 6.95 1.48333
actual_vector
: python list
or numpy array
of any stringable objectspredict_vector
: python list
or numpy array
of any stringable objectsmatrix
: dict
digit
: int
threshold
: FunctionType (function or lambda)
file
: File object
sample_weight
: python list
or numpy array
of numberstranspose
: bool
help(ConfusionMatrix)
for more informationcm_dict
: python dict
of ConfusionMatrix
object (str
: ConfusionMatrix
)by_class
: bool
weight
: python dict
of class weights (class_name
: float
)digit
: int
help(Compare)
for more informationA true positive test result is one that detects the condition when the condition is present (correctly identified) [3].
cm.TP
{'L1': 3, 'L2': 1, 'L3': 3}
A true negative test result is one that does not detect the condition when the condition is absent correctly rejected) [3].
cm.TN
{'L1': 7, 'L2': 8, 'L3': 4}
A false positive test result is one that detects the condition when the condition is absent (incorrectly identified) [3].
cm.FP
{'L1': 0, 'L2': 2, 'L3': 3}
A false negative test result is one that does not detect the condition when the condition is present (incorrectly rejected) [3].
cm.FN
{'L1': 2, 'L2': 1, 'L3': 2}
Number of positive samples. Also known as support (the number of occurrences of each class in y_true) [3].
cm.P
{'L1': 5, 'L2': 2, 'L3': 5}
Number of negative samples [3].
cm.N
{'L1': 7, 'L2': 10, 'L3': 7}
Number of positive outcomes [3].
cm.TOP
{'L1': 3, 'L2': 3, 'L3': 6}
Number of negative outcomes [3].
cm.TON
{'L1': 9, 'L2': 9, 'L3': 6}
For more information visit [3].
cm.POP
{'L1': 12, 'L2': 12, 'L3': 12}
Sensitivity (also called the true positive rate, the recall, or probability of detection in some fields) measures the proportion of positives that are correctly identified as such (e.g. the percentage of sick people who are correctly identified as having the condition) [3].
cm.TPR
{'L1': 0.6, 'L2': 0.5, 'L3': 0.6}
Specificity (also called the true negative rate) measures the proportion of negatives that are correctly identified as such (e.g. the percentage of healthy people who are correctly identified as not having the condition) [3].
cm.TNR
{'L1': 1.0, 'L2': 0.8, 'L3': 0.5714285714285714}
Predictive value positive is the proportion of positives that correspond to the presence of the condition [3].
cm.PPV
{'L1': 1.0, 'L2': 0.3333333333333333, 'L3': 0.5}
Predictive value negative is the proportion of negatives that correspond to the absence of the condition [3].
cm.NPV
{'L1': 0.7777777777777778, 'L2': 0.8888888888888888, 'L3': 0.6666666666666666}
The false negative rate is the proportion of positives which yield negative test outcomes with the test, i.e., the conditional probability of a negative test result given that the condition being looked for is present [3].
cm.FNR
{'L1': 0.4, 'L2': 0.5, 'L3': 0.4}
The false positive rate is the proportion of all negatives that still yield positive test outcomes, i.e., the conditional probability of a positive test result given an event that was not present [3].
The false positive rate is equal to the significance level. The specificity of the test is equal to 1 minus the false positive rate.
cm.FPR
{'L1': 0.0, 'L2': 0.19999999999999996, 'L3': 0.4285714285714286}
The false discovery rate (FDR) is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. FDR-controlling procedures are designed to control the expected proportion of "discoveries" (rejected null hypotheses) that are false (incorrect rejections) [3].
cm.FDR
{'L1': 0.0, 'L2': 0.6666666666666667, 'L3': 0.5}
False omission rate (FOR) is a statistical method used in multiple hypothesis testing to correct for multiple comparisons and it is the complement of the negative predictive value. It measures the proportion of false negatives which are incorrectly rejected [3].
cm.FOR
{'L1': 0.2222222222222222, 'L2': 0.11111111111111116, 'L3': 0.33333333333333337}
The accuracy is the number of correct predictions from all predictions made [3].
cm.ACC
{'L1': 0.8333333333333334, 'L2': 0.75, 'L3': 0.5833333333333334}
The accuracy is the number of incorrect predictions from all predictions made [3].
cm.ERR
{'L1': 0.16666666666666663, 'L2': 0.25, 'L3': 0.41666666666666663}
In statistical analysis of classification, the F1 score (also F-score or F-measure) is a measure of a test's accuracy. It considers both the precision p and the recall r of the test to compute the score. The F1 score is the harmonic average of the precision and recall, where F1 score reaches its best value at 1 (perfect precision and recall) and worst at 0 [3].
cm.F1
{'L1': 0.75, 'L2': 0.4, 'L3': 0.5454545454545454}
cm.F05
{'L1': 0.8823529411764706, 'L2': 0.35714285714285715, 'L3': 0.5172413793103449}
cm.F2
{'L1': 0.6521739130434783, 'L2': 0.45454545454545453, 'L3': 0.5769230769230769}
cm.F_beta(beta=4)
{'L1': 0.6144578313253012, 'L2': 0.4857142857142857, 'L3': 0.5930232558139535}
The Matthews correlation coefficient is used in machine learning as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975. It takes into account true and false positives and negatives and is generally regarded as a balanced measure which can be used even if the classes are of very different sizes.The MCC is in essence a correlation coefficient between the observed and predicted binary classifications; it returns a value between −1 and +1. A coefficient of +1 represents a perfect prediction, 0 no better than random prediction and −1 indicates total disagreement between prediction and observation [27].
cm.MCC
{'L1': 0.6831300510639732, 'L2': 0.25819888974716115, 'L3': 0.1690308509457033}
The informedness of a prediction method as captured by a contingency matrix is defined as the probability that the prediction method will make a correct decision as opposed to guessing and is calculated using the bookmaker algorithm [2].
cm.BM
{'L1': 0.6000000000000001, 'L2': 0.30000000000000004, 'L3': 0.17142857142857126}
In statistics and psychology, the social science concept of markedness is quantified as a measure of how much one variable is marked as a predictor or possible cause of another, and is also known as Δp (deltaP) in simple two-choice cases [2].
cm.MK
{'L1': 0.7777777777777777, 'L2': 0.2222222222222221, 'L3': 0.16666666666666652}
Likelihood ratios are used for assessing the value of performing a diagnostic test. They use the sensitivity and specificity of the test to determine whether a test result usefully changes the probability that a condition (such as a disease state) exists. The first description of the use of likelihood ratios for decision rules was made at a symposium on information theory in 1954 [28].
cm.PLR
{'L1': 'None', 'L2': 2.5000000000000004, 'L3': 1.4}
Likelihood ratios are used for assessing the value of performing a diagnostic test. They use the sensitivity and specificity of the test to determine whether a test result usefully changes the probability that a condition (such as a disease state) exists. The first description of the use of likelihood ratios for decision rules was made at a symposium on information theory in 1954 [28].
cm.NLR
{'L1': 0.4, 'L2': 0.625, 'L3': 0.7000000000000001}
The diagnostic odds ratio is a measure of the effectiveness of a diagnostic test. It is defined as the ratio of the odds of the test being positive if the subject has a disease relative to the odds of the test being positive if the subject does not have the disease [28].
cm.DOR
{'L1': 'None', 'L2': 4.000000000000001, 'L3': 1.9999999999999998}
Prevalence is a statistical concept referring to the number of cases of a disease that are present in a particular population at a given time (Reference Likelihood) [14].
cm.PRE
{'L1': 0.4166666666666667, 'L2': 0.16666666666666666, 'L3': 0.4166666666666667}
Geometric mean of precision and sensitivity, also known as Fowlkes–Mallows index [3].
cm.G
{'L1': 0.7745966692414834, 'L2': 0.408248290463863, 'L3': 0.5477225575051661}
The expected accuracy from a strategy of randomly guessing categories according to reference and response distributions [24].
cm.RACC
{'L1': 0.10416666666666667, 'L2': 0.041666666666666664, 'L3': 0.20833333333333334}
The expected accuracy from a strategy of randomly guessing categories according to the average of the reference and response distributions [25].
cm.RACCU
{'L1': 0.1111111111111111, 'L2': 0.04340277777777778, 'L3': 0.21006944444444442}
The Jaccard index, also known as Intersection over Union and the Jaccard similarity coefficient (originally coined coefficient de communauté by Paul Jaccard), is a statistic used for comparing the similarity and diversity of sample sets [29].
cm.J
{'L1': 0.6, 'L2': 0.25, 'L3': 0.375}
cm.IS
{'L1': 1.2630344058337937, 'L2': 0.9999999999999998, 'L3': 0.26303440583379367}
CEN based upon the concept of entropy for evaluating classifier performances. By exploiting the misclassification information of confusion matrices, the measure evaluates the confusion level of the class distribution of misclassified samples. Both theoretical analysis and statistical results show that the proposed measure is more discriminating than accuracy and RCI while it remains relatively consistent with the two measures. Moreover, it is more capable of measuring how the samples of different classes have been separated from each other. Hence the proposed measure is more precise than the two measures and can substitute for them to evaluate classifiers in classification applications [17].
cm.CEN
{'L1': 0.25, 'L2': 0.49657842846620864, 'L3': 0.6044162769630221}
Modified version of CEN [19].
cm.MCEN
{'L1': 0.2643856189774724, 'L2': 0.5, 'L3': 0.6875}
Thus, AUC corresponds to the arithmetic mean of sensitivity and specificity values of each class [23].
cm.AUC
{'L1': 0.8, 'L2': 0.65, 'L3': 0.5857142857142856}
Euclidean distance of a ROC point from the top left corner of the ROC space, which can take values between 0 (perfect classification) and sqrt(2) [23].
cm.dInd
{'L1': 0.4, 'L2': 0.5385164807134504, 'L3': 0.5862367008195198}
sInd is comprised between 0 (no correct classifications) and 1 (perfect classification) [23].
cm.sInd
{'L1': 0.717157287525381, 'L2': 0.6192113447068046, 'L3': 0.5854680534700882}
Discriminant power (DP) is a measure that summarizes sensitivity and specificity. The DP has been used mainly in feature selection over imbalanced data [33].
cm.DP
{'L1': 'None', 'L2': 0.33193306999649924, 'L3': 0.1659665349982495}
Youden’s index, evaluates the algorithm’s ability to avoid failure; it’s derived from sensitivity and specificity and denotes a linear correspondence balanced accuracy. As Youden’s index is a linear transformation of the mean sensitivity and specificity, its values are difficult to interpret, we retain that a higher value of Y indicates better ability to avoid failure. Youden’s index has been conventionally used to evaluate tests diagnostic, improve efficiency of Telemedical prevention [33] [34].
cm.Y
{'L1': 0.6000000000000001, 'L2': 0.30000000000000004, 'L3': 0.17142857142857126}
For more information visit [33].
PLR | Model contribution |
1 > | Negligible |
1 - 5 | Poor |
5 - 10 | Fair |
> 10 | Good |
cm.PLRI
{'L1': 'None', 'L2': 'Poor', 'L3': 'Poor'}
For more information visit [33].
DP | Model contribution |
1 > | Poor |
1 - 2 | Limited |
2 - 3 | Fair |
> 3 | Good |
cm.DPI
{'L1': 'None', 'L2': 'Poor', 'L3': 'Poor'}
For more information visit [33].
AUC | Model performance |
0.5 - 0.6 | Poor |
0.6 - 0.7 | Fair |
0.7 - 0.8 | Good |
0.8 - 0.9 | Very Good |
0.9 - 1.0 | Excellent |
cm.AUCI
{'L1': 'Very Good', 'L2': 'Fair', 'L3': 'Poor'}
A chance-standardized variant of the AUC is given by Gini coefficient, taking values between 0 (no difference between the score distributions of the two classes) and 1 (complete separation between the two distributions). Gini coefficient is widespread use metric in imbalanced data learning [33].
cm.GI
{'L1': 0.6000000000000001, 'L2': 0.30000000000000004, 'L3': 0.17142857142857126}
cm.LS
{'L1': 2.4, 'L2': 2.0, 'L3': 1.2}
Difference between automatic and manual classification
cm.AM
{'L1': -2, 'L2': 1, 'L3': 1}
In ecology and biology, the Bray–Curtis dissimilarity, named after J. Roger Bray and John T. Curtis, is a statistic used to quantify the compositional dissimilarity between two different sites, based on counts at each site [37].
cm.BCD
{'L1': 0.08333333333333333, 'L2': 0.041666666666666664, 'L3': 0.041666666666666664}
Optimized precision is a type of hybrid threshold metrics and has been proposed as a discriminator for building an optimized heuristic classifier. This metric is a combination of accuracy, sensitivity and specificity metrics. The sensitivity and specificity metric were used for stabilizing and optimizing the accuracy performance when dealing with imbalanced class of twoclass problems [40] [42].
cm.OP
{'L1': 0.5833333333333334, 'L2': 0.5192307692307692, 'L3': 0.5589430894308943}
cm.IBA
{'L1': 0.36, 'L2': 0.27999999999999997, 'L3': 0.35265306122448975}
cm.IBA_alpha(0.5)
{'L1': 0.48, 'L2': 0.34, 'L3': 0.3477551020408163}
cm.IBA_alpha(0.1)
{'L1': 0.576, 'L2': 0.388, 'L3': 0.34383673469387754}
cm.GM
{'L1': 0.7745966692414834, 'L2': 0.6324555320336759, 'L3': 0.5855400437691198}
In statistics, Yule's Q, also known as the coefficient of colligation, is a measure of association between two binary variables [45].
cm.Q
{'L1': 'None', 'L2': 0.6, 'L3': 0.3333333333333333}
An adjusted version of geometric mean of specificity and sensitivity [46].
cm.AGM
{'L1': 0.8576400016262, 'L2': 0.708612108382005, 'L3': 0.5803410802752335}
Kappa is a statistic which measures inter-rater agreement for qualitative (categorical) items. It is generally thought to be a more robust measure than simple percent agreement calculation, as kappa takes into account the possibility of the agreement occurring by chance [24].
cm.Kappa
0.35483870967741943
The unbiased kappa value is defined in terms of total accuracy and a slightly different computation of expected likelihood that averages the reference and response probabilities [25].
cm.KappaUnbiased
0.34426229508196726
The kappa statistic adjusted for prevalence [14].
cm.KappaNoPrevalence
0.16666666666666674
cm.Kappa_SE
0.2203645326012817
cm.Kappa_CI
(-0.07707577422109269, 0.7867531935759315)
Pearson's chi-squared test is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is suitable for unpaired data from large samples [10].
cm.Chi_Squared
6.6000000000000005
Number of degrees of freedom of this confusion matrix for the chi-squared statistic [10].
cm.DF
4
In statistics, the phi coefficient (or mean square contingency coefficient) is a measure of association for two binary variables. Introduced by Karl Pearson, this measure is similar to the Pearson correlation coefficient in its interpretation. In fact, a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient [10].
cm.Phi_Squared
0.55
In statistics, Cramér's V (sometimes referred to as Cramér's phi) is a measure of association between two nominal variables, giving a value between 0 and +1 (inclusive). It is based on Pearson's chi-squared statistic and was published by Harald Cramér in 1946 [26].
cm.V
0.5244044240850758
The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation [31].
cm.SE
0.14231876063832777
In statistics, a confidence interval (CI) is a type of interval estimate (of a population parameter) that is computed from the observed data. The confidence level is the frequency (i.e., the proportion) of possible confidence intervals that contain the true value of their corresponding parameter. In other words, if confidence intervals are constructed using a given confidence level in an infinite number of independent experiments, the proportion of those intervals that contain the true value of the parameter will match the confidence level [31].
cm.CI
(0.30438856248221097, 0.8622781041844558)
Bennett, Alpert & Goldstein’s S is a statistical measure of inter-rater agreement. It was created by Bennett et al. in 1954. Bennett et al. suggested adjusting inter-rater reliability to accommodate the percentage of rater agreement that might be expected by chance was a better measure than simple agreement between raters [8].
cm.S
0.37500000000000006
Scott's pi (named after William A. Scott) is a statistic for measuring inter-rater reliability for nominal data in communication studies. Textual entities are annotated with categories by different annotators, and various measures are used to assess the extent of agreement between the annotators, one of which is Scott's pi. Since automatically annotating text is a popular problem in natural language processing, and goal is to get the computer program that is being developed to agree with the humans in the annotations it creates, assessing the extent to which humans agree with each other is important for establishing a reasonable upper limit on computer performance [7].
cm.PI
0.34426229508196726
AC1 was originally introduced by Gwet in 2001 (Gwet, 2001). The interpretation of AC1 is similar to generalized kappa (Fleiss, 1971), which is used to assess interrater reliability of when there are multiple raters. Gwet (2002) demonstrated that AC1 can overcome the limitations that kappa is sensitive to trait prevalence and rater's classification probabilities (i.e., marginal probabilities), whereas AC1 provides more robust measure of interrater reliability [6].
cm.AC1
0.3893129770992367
The entropy of the decision problem itself as defined by the counts for the reference. The entropy of a distribution is the average negative log probability of outcomes [30].
cm.ReferenceEntropy
1.4833557549816874
The entropy of the response distribution. The entropy of a distribution is the average negative log probability of outcomes [30].
cm.ResponseEntropy
1.5
The cross-entropy of the response distribution against the reference distribution. The cross-entropy is defined by the negative log probabilities of the response distribution weighted by the reference distribution [30].
cm.CrossEntropy
1.5833333333333335
The entropy of the joint reference and response distribution as defined by the underlying matrix [30].
cm.JointEntropy
2.4591479170272446
The entropy of the distribution of categories in the response given that the reference category was as specified [30].
cm.ConditionalEntropy
0.9757921620455572
cm.KL
0.09997757835164581
Mutual information is defined Kullback-Lieblier divergence, between the product of the individual distributions and the joint distribution. Mutual information is symmetric. We could also subtract the conditional entropy of the reference given the response from the reference entropy to get the same result [11] [30].
cm.MutualInformation
0.5242078379544428
In probability theory and statistics, Goodman & Kruskal's lambda is a measure of proportional reduction in error in cross tabulation analysis [12].
cm.LambdaA
0.42857142857142855
In probability theory and statistics, Goodman & Kruskal's lambda is a measure of proportional reduction in error in cross tabulation analysis [13].
cm.LambdaB
0.16666666666666666
For more information visit [1].
Kappa | Strength of Agreement |
0 > | Poor |
0 - 0.20 | Slight |
0.21 – 0.40 | Fair |
0.41 – 0.60 | Moderate |
0.61 – 0.80 | Substantial |
0.81 – 1.00 | Almost perfect |
cm.SOA1
'Fair'
For more information visit [4].
Kappa | Strength of Agreement |
0.40 > | Poor |
0.4 - 0.75 | Intermediate to Good |
More than 0.75 | Excellent |
cm.SOA2
'Poor'
For more information visit [5].
Kappa | Strength of Agreement |
0.2 > | Poor |
0.21 – 0.40 | Fair |
0.41 – 0.60 | Moderate |
0.61 – 0.80 | Good |
0.81 – 1.00 | Very Good |
cm.SOA3
'Fair'
For more information visit [9].
Kappa | Strength of Agreement |
0.4 > | Poor |
0.4 – 0.59 | Fair |
0.6 – 0.74 | Good |
0.74 – 1.00 | Excellent |
cm.SOA4
'Poor'
For more information visit [3].
cm.Overall_ACC
0.5833333333333334
For more information visit [24].
cm.Overall_RACC
0.3541666666666667
For more information visit [25].
cm.Overall_RACCU
0.3645833333333333
For more information visit [3].
cm.PPV_Micro
0.5833333333333334
For more information visit [3].
cm.TPR_Micro
0.5833333333333334
For more information visit [3].
cm.PPV_Macro
0.611111111111111
For more information visit [3].
cm.TPR_Macro
0.5666666666666668
For more information visit [29].
cm.Overall_J
(1.225, 0.4083333333333334)
The hamming_loss computes the average Hamming loss or Hamming distance between two sets of samples [31].
cm.HammingLoss
0.41666666666666663
For more information visit [31].
cm.ZeroOneLoss
5
The no information error rate is the error rate when the input and output are independent.
cm.NIR
0.4166666666666667
For more information visit [31].
cm.PValue
0.18926430237560654
For more information visit [17].
cm.Overall_CEN
0.4638112995385119
For more information visit [19].
cm.Overall_MCEN
0.5189369467580801
cm.Overall_MCC
0.36666666666666664
For more information visit [21].
cm.RR
4.0
For more information visit [22].
cm.CBA
0.4777777777777778
When dealing with multiclass problems, a global measure of classification performances based on the ROC approach (AUNU) has been proposed as the average of single-class measures [23].
cm.AUNU
0.6785714285714285
Another option (AUNP) is that of averaging the AUCi values with weights proportional to the number of samples experimentally belonging to each class, that is, the a priori class distribution [23].
cm.AUNP
0.6857142857142857
cm.RCI
0.3533932006492363
cm.C
0.5956833971812706
print(cm)
Predict L1 L2 L3 Actual L1 3 0 2 L2 0 1 1 L3 0 2 3 Overall Statistics : 95% CI (0.30439,0.86228) AUNP 0.68571 AUNU 0.67857 Bennett S 0.375 CBA 0.47778 Chi-Squared 6.6 Chi-Squared DF 4 Conditional Entropy 0.97579 Cramer V 0.5244 Cross Entropy 1.58333 Gwet AC1 0.38931 Hamming Loss 0.41667 Joint Entropy 2.45915 KL Divergence 0.09998 Kappa 0.35484 Kappa 95% CI (-0.07708,0.78675) Kappa No Prevalence 0.16667 Kappa Standard Error 0.22036 Kappa Unbiased 0.34426 Lambda A 0.42857 Lambda B 0.16667 Mutual Information 0.52421 NIR 0.41667 Overall ACC 0.58333 Overall CEN 0.46381 Overall J (1.225,0.40833) Overall MCC 0.36667 Overall MCEN 0.51894 Overall RACC 0.35417 Overall RACCU 0.36458 P-Value 0.18926 PPV Macro 0.61111 PPV Micro 0.58333 Pearson C 0.59568 Phi-Squared 0.55 RCI 0.35339 RR 4.0 Reference Entropy 1.48336 Response Entropy 1.5 SOA1(Landis & Koch) Fair SOA2(Fleiss) Poor SOA3(Altman) Fair SOA4(Cicchetti) Poor Scott PI 0.34426 Standard Error 0.14232 TPR Macro 0.56667 TPR Micro 0.58333 Zero-one Loss 5 Class Statistics : Classes L1 L2 L3 ACC(Accuracy) 0.83333 0.75 0.58333 AGM(Adjusted geometric mean) 0.85764 0.70861 0.58034 AM(Difference between automatic and manual classification) -2 1 1 AUC(Area under the roc curve) 0.8 0.65 0.58571 AUCI(AUC value interpretation) Very Good Fair Poor BCD(Bray-Curtis dissimilarity) 0.08333 0.04167 0.04167 BM(Informedness or bookmaker informedness) 0.6 0.3 0.17143 CEN(Confusion entropy) 0.25 0.49658 0.60442 DOR(Diagnostic odds ratio) None 4.0 2.0 DP(Discriminant power) None 0.33193 0.16597 DPI(Discriminant power interpretation) None Poor Poor ERR(Error rate) 0.16667 0.25 0.41667 F0.5(F0.5 score) 0.88235 0.35714 0.51724 F1(F1 score - harmonic mean of precision and sensitivity) 0.75 0.4 0.54545 F2(F2 score) 0.65217 0.45455 0.57692 FDR(False discovery rate) 0.0 0.66667 0.5 FN(False negative/miss/type 2 error) 2 1 2 FNR(Miss rate or false negative rate) 0.4 0.5 0.4 FOR(False omission rate) 0.22222 0.11111 0.33333 FP(False positive/type 1 error/false alarm) 0 2 3 FPR(Fall-out or false positive rate) 0.0 0.2 0.42857 G(G-measure geometric mean of precision and sensitivity) 0.7746 0.40825 0.54772 GI(Gini index) 0.6 0.3 0.17143 GM(G-mean geometric mean of specificity and sensitivity) 0.7746 0.63246 0.58554 IBA(Index of balanced accuracy) 0.36 0.28 0.35265 IS(Information score) 1.26303 1.0 0.26303 J(Jaccard index) 0.6 0.25 0.375 LS(Lift score) 2.4 2.0 1.2 MCC(Matthews correlation coefficient) 0.68313 0.2582 0.16903 MCEN(Modified confusion entropy) 0.26439 0.5 0.6875 MK(Markedness) 0.77778 0.22222 0.16667 N(Condition negative) 7 10 7 NLR(Negative likelihood ratio) 0.4 0.625 0.7 NPV(Negative predictive value) 0.77778 0.88889 0.66667 OP(Optimized precision) 0.58333 0.51923 0.55894 P(Condition positive or support) 5 2 5 PLR(Positive likelihood ratio) None 2.5 1.4 PLRI(Positive likelihood ratio interpretation) None Poor Poor POP(Population) 12 12 12 PPV(Precision or positive predictive value) 1.0 0.33333 0.5 PRE(Prevalence) 0.41667 0.16667 0.41667 Q(Yule Q - coefficient of colligation) None 0.6 0.33333 RACC(Random accuracy) 0.10417 0.04167 0.20833 RACCU(Random accuracy unbiased) 0.11111 0.0434 0.21007 TN(True negative/correct rejection) 7 8 4 TNR(Specificity or true negative rate) 1.0 0.8 0.57143 TON(Test outcome negative) 9 9 6 TOP(Test outcome positive) 3 3 6 TP(True positive/hit) 3 1 3 TPR(Sensitivity, recall, hit rate, or true positive rate) 0.6 0.5 0.6 Y(Youden index) 0.6 0.3 0.17143 dInd(Distance index) 0.4 0.53852 0.58624 sInd(Similarity index) 0.71716 0.61921 0.58547
cm.print_matrix()
Predict L1 L2 L3 Actual L1 3 0 2 L2 0 1 1 L3 0 2 3
cm.matrix
{'L1': {'L1': 3, 'L2': 0, 'L3': 2}, 'L2': {'L1': 0, 'L2': 1, 'L3': 1}, 'L3': {'L1': 0, 'L2': 2, 'L3': 3}}
cm.print_matrix(one_vs_all=True,class_name = "L1")
Predict L1 ~ Actual L1 3 2 ~ 0 7
one_vs_all
: One-Vs-All mode flag (type : bool
)class_name
: target class name for One-Vs-All mode (type : any valid type
)cm.print_normalized_matrix()
Predict L1 L2 L3 Actual L1 0.6 0.0 0.4 L2 0.0 0.5 0.5 L3 0.0 0.4 0.6
cm.normalized_matrix
{'L1': {'L1': 0.6, 'L2': 0.0, 'L3': 0.4}, 'L2': {'L1': 0.0, 'L2': 0.5, 'L3': 0.5}, 'L3': {'L1': 0.0, 'L2': 0.4, 'L3': 0.6}}
cm.print_normalized_matrix(one_vs_all=True,class_name = "L1")
Predict L1 ~ Actual L1 0.6 0.4 ~ 0.0 1.0
one_vs_all
: One-Vs-All mode flag (type : bool
)class_name
: target class name for One-Vs-All mode (type : any valid type
)cm.stat()
Overall Statistics : 95% CI (0.30439,0.86228) AUNP 0.68571 AUNU 0.67857 Bennett S 0.375 CBA 0.47778 Chi-Squared 6.6 Chi-Squared DF 4 Conditional Entropy 0.97579 Cramer V 0.5244 Cross Entropy 1.58333 Gwet AC1 0.38931 Hamming Loss 0.41667 Joint Entropy 2.45915 KL Divergence 0.09998 Kappa 0.35484 Kappa 95% CI (-0.07708,0.78675) Kappa No Prevalence 0.16667 Kappa Standard Error 0.22036 Kappa Unbiased 0.34426 Lambda A 0.42857 Lambda B 0.16667 Mutual Information 0.52421 NIR 0.41667 Overall ACC 0.58333 Overall CEN 0.46381 Overall J (1.225,0.40833) Overall MCC 0.36667 Overall MCEN 0.51894 Overall RACC 0.35417 Overall RACCU 0.36458 P-Value 0.18926 PPV Macro 0.61111 PPV Micro 0.58333 Pearson C 0.59568 Phi-Squared 0.55 RCI 0.35339 RR 4.0 Reference Entropy 1.48336 Response Entropy 1.5 SOA1(Landis & Koch) Fair SOA2(Fleiss) Poor SOA3(Altman) Fair SOA4(Cicchetti) Poor Scott PI 0.34426 Standard Error 0.14232 TPR Macro 0.56667 TPR Micro 0.58333 Zero-one Loss 5 Class Statistics : Classes L1 L2 L3 ACC(Accuracy) 0.83333 0.75 0.58333 AGM(Adjusted geometric mean) 0.85764 0.70861 0.58034 AM(Difference between automatic and manual classification) -2 1 1 AUC(Area under the roc curve) 0.8 0.65 0.58571 AUCI(AUC value interpretation) Very Good Fair Poor BCD(Bray-Curtis dissimilarity) 0.08333 0.04167 0.04167 BM(Informedness or bookmaker informedness) 0.6 0.3 0.17143 CEN(Confusion entropy) 0.25 0.49658 0.60442 DOR(Diagnostic odds ratio) None 4.0 2.0 DP(Discriminant power) None 0.33193 0.16597 DPI(Discriminant power interpretation) None Poor Poor ERR(Error rate) 0.16667 0.25 0.41667 F0.5(F0.5 score) 0.88235 0.35714 0.51724 F1(F1 score - harmonic mean of precision and sensitivity) 0.75 0.4 0.54545 F2(F2 score) 0.65217 0.45455 0.57692 FDR(False discovery rate) 0.0 0.66667 0.5 FN(False negative/miss/type 2 error) 2 1 2 FNR(Miss rate or false negative rate) 0.4 0.5 0.4 FOR(False omission rate) 0.22222 0.11111 0.33333 FP(False positive/type 1 error/false alarm) 0 2 3 FPR(Fall-out or false positive rate) 0.0 0.2 0.42857 G(G-measure geometric mean of precision and sensitivity) 0.7746 0.40825 0.54772 GI(Gini index) 0.6 0.3 0.17143 GM(G-mean geometric mean of specificity and sensitivity) 0.7746 0.63246 0.58554 IBA(Index of balanced accuracy) 0.36 0.28 0.35265 IS(Information score) 1.26303 1.0 0.26303 J(Jaccard index) 0.6 0.25 0.375 LS(Lift score) 2.4 2.0 1.2 MCC(Matthews correlation coefficient) 0.68313 0.2582 0.16903 MCEN(Modified confusion entropy) 0.26439 0.5 0.6875 MK(Markedness) 0.77778 0.22222 0.16667 N(Condition negative) 7 10 7 NLR(Negative likelihood ratio) 0.4 0.625 0.7 NPV(Negative predictive value) 0.77778 0.88889 0.66667 OP(Optimized precision) 0.58333 0.51923 0.55894 P(Condition positive or support) 5 2 5 PLR(Positive likelihood ratio) None 2.5 1.4 PLRI(Positive likelihood ratio interpretation) None Poor Poor POP(Population) 12 12 12 PPV(Precision or positive predictive value) 1.0 0.33333 0.5 PRE(Prevalence) 0.41667 0.16667 0.41667 Q(Yule Q - coefficient of colligation) None 0.6 0.33333 RACC(Random accuracy) 0.10417 0.04167 0.20833 RACCU(Random accuracy unbiased) 0.11111 0.0434 0.21007 TN(True negative/correct rejection) 7 8 4 TNR(Specificity or true negative rate) 1.0 0.8 0.57143 TON(Test outcome negative) 9 9 6 TOP(Test outcome positive) 3 3 6 TP(True positive/hit) 3 1 3 TPR(Sensitivity, recall, hit rate, or true positive rate) 0.6 0.5 0.6 Y(Youden index) 0.6 0.3 0.17143 dInd(Distance index) 0.4 0.53852 0.58624 sInd(Similarity index) 0.71716 0.61921 0.58547
cm.stat(overall_param=["Kappa"],class_param=["ACC","AUC","TPR"])
Overall Statistics : Kappa 0.35484 Class Statistics : Classes L1 L2 L3 ACC(Accuracy) 0.83333 0.75 0.58333 AUC(Area under the roc curve) 0.8 0.65 0.58571 TPR(Sensitivity, recall, hit rate, or true positive rate) 0.6 0.5 0.6
cm.stat(overall_param=["Kappa"],class_param=["ACC","AUC","TPR"],class_name=["L1","L3"])
Overall Statistics : Kappa 0.35484 Class Statistics : Classes L1 L3 ACC(Accuracy) 0.83333 0.58333 AUC(Area under the roc curve) 0.8 0.58571 TPR(Sensitivity, recall, hit rate, or true positive rate) 0.6 0.6
overall_param
: overall statistics names for print (type : list
)class_param
: class statistics names for print (type : list
)class_name
: class names for print (sub set of classes) (type : list
)cp.print_report()
Best : cm2 Rank Name Class-Score Overall-Score 1 cm2 4.15 1.48333 2 cm3 2.75 0.95
print(cp)
Best : cm2 Rank Name Class-Score Overall-Score 1 cm2 4.15 1.48333 2 cm3 2.75 0.95
import os
if "Document_Files" not in os.listdir():
os.mkdir("Document_Files")
cm.save_stat(os.path.join("Document_Files","cm1"))
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1.pycm', 'Status': True}
cm.save_stat(os.path.join("Document_Files","cm1_filtered"),overall_param=["Kappa"],class_param=["ACC","AUC","TPR"])
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_filtered.pycm', 'Status': True}
cm.save_stat(os.path.join("Document_Files","cm1_filtered2"),overall_param=["Kappa"],class_param=["ACC","AUC","TPR"],class_name=["L1"])
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_filtered2.pycm', 'Status': True}
cm.save_stat("cm1asdasd/")
{'Message': "[Errno 2] No such file or directory: 'cm1asdasd/.pycm'", 'Status': False}
name
: output file name (type : str
)address
: flag for address return (type : bool
)overall_param
: overall statistics names for save (type : list
)class_param
: class statistics names for save (type : list
)class_name
: class names for print (sub set of classes) (type : list
)cm.save_html(os.path.join("Document_Files","cm1"))
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1.html', 'Status': True}
cm.save_html(os.path.join("Document_Files","cm1_filtered"),overall_param=["Kappa"],class_param=["ACC","AUC","TPR"])
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_filtered.html', 'Status': True}
cm.save_html(os.path.join("Document_Files","cm1_filtered2"),overall_param=["Kappa"],class_param=["ACC","AUC","TPR"],class_name=["L1"])
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_filtered2.html', 'Status': True}
cm.save_html(os.path.join("Document_Files","cm1_colored"),color=(255, 204, 255))
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_colored.html', 'Status': True}
cm.save_html(os.path.join("Document_Files","cm1_colored2"),color="Crimson")
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_colored2.html', 'Status': True}
cm.save_html(os.path.join("Document_Files","cm1_normalized"),color="Crimson",normalize=True)
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_normalized.html', 'Status': True}
cm.save_html("cm1asdasd/")
{'Message': "[Errno 2] No such file or directory: 'cm1asdasd/.html'", 'Status': False}
name
: output file name (type : str
)address
: flag for address return (type : bool
)overall_param
: overall statistics names for save (type : list
)class_param
: class statistics names for save (type : list
)class_name
: class names for print (sub set of classes) (type : list
)color
: matrix color (R,G,B) (type : tuple
/str
)cm.save_csv(os.path.join("Document_Files","cm1"))
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1.csv', 'Status': True}
cm.save_csv(os.path.join("Document_Files","cm1_filtered"),class_param=["ACC","AUC","TPR"])
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_filtered.csv', 'Status': True}
cm.save_csv(os.path.join("Document_Files","cm1_filtered2"),class_param=["ACC","AUC","TPR"],normalize=True)
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_filtered2.csv', 'Status': True}
cm.save_csv(os.path.join("Document_Files","cm1_filtered3"),class_param=["ACC","AUC","TPR"],class_name=["L1"])
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1_filtered3.csv', 'Status': True}
cm.save_csv("cm1asdasd/")
{'Message': "[Errno 2] No such file or directory: 'cm1asdasd/.csv'", 'Status': False}
name
: output file name (type : str
)address
: flag for address return (type : bool
)class_param
: class statistics names for save (type : list
)class_name
: class names for print (sub set of classes) (type : list
)matrix_save
: flag for saving matrix in seperate CSV file (type : bool
)normalize
: flag for saving normalized matrix instead of matrix (type : bool
)cm.save_obj(os.path.join("Document_Files","cm1"))
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cm1.obj', 'Status': True}
cm.save_obj("cm1asdasd/")
{'Message': "[Errno 2] No such file or directory: 'cm1asdasd/.obj'", 'Status': False}
name
: output file name (type : str
)address
: flag for address return (type : bool
)cp.save_report(os.path.join("Document_Files","cp"))
{'Message': 'D:\\For Asus Laptop\\projects\\pycm\\Document\\Document_Files\\cp.comp', 'Status': True}
cp.save_report("cm1asdasd/")
{'Message': "[Errno 2] No such file or directory: 'cm1asdasd/.comp'", 'Status': False}
name
: output file name (type : str
)address
: flag for address return (type : bool
)try:
cm2=ConfusionMatrix(y_actu, 2)
except pycmVectorError as e:
print(str(e))
The type of input vectors is assumed to be a list or a NumPy array
try:
cm3=ConfusionMatrix(y_actu, [1,2,3])
except pycmVectorError as e:
print(str(e))
Input vectors must have same length
try:
cm_4 = ConfusionMatrix([], [])
except pycmVectorError as e:
print(str(e))
Input vectors are empty
try:
cm_5 = ConfusionMatrix([1,1,1,], [1,1,1,1])
except pycmVectorError as e:
print(str(e))
Input vectors must have same length
try:
cm3=ConfusionMatrix(matrix={})
except pycmMatrixError as e:
print(str(e))
Input confusion matrix format error
try:
cm_4=ConfusionMatrix(matrix={1:{1:2,"1":2},"1":{1:2,"1":3}})
except pycmMatrixError as e:
print(str(e))
Type of the input matrix classes is assumed be the same
try:
cm_5=ConfusionMatrix(matrix={1:{1:2}})
except pycmVectorError as e:
print(str(e))
Number of the classes is lower than 2
try:
cp=Compare([cm2,cm3])
except pycmCompareError as e:
print(str(e))
The input type is considered to be dictionary but it's not!
try:
cp=Compare({"cm1":cm,"cm2":cm2})
except pycmCompareError as e:
print(str(e))
The domain of all ConfusionMatrix objects must be same! The sample size or the number of classes are different.
try:
cp=Compare({"cm1":[],"cm2":cm2})
except pycmCompareError as e:
print(str(e))
The input is considered to consist of pycm.ConfusionMatrix object but it's not!
try:
cp=Compare({"cm2":cm2})
except pycmCompareError as e:
print(str(e))
Lower than two confusion matrices is given for comparing. The minimum number of confusion matrix for comparing is 2.
try:
cp=Compare({"cm1":cm2,"cm2":cm3},by_class=True,weight={1:2,2:0})
except pycmCompareError as e:
print(str(e))
The weight type must be dictionary and also must be set for all classes.
1- J. R. Landis, G. G. Koch, “The measurement of observer agreement for categorical data. Biometrics,” in International Biometric Society, pp. 159–174, 1977.
2- D. M. W. Powers, “Evaluation: from precision, recall and f-measure to roc, informedness, markedness & correlation,” in Journal of Machine Learning Technologies, pp.37-63, 2011.
3- C. Sammut, G. Webb, “Encyclopedia of Machine Learning” in Springer, 2011.
4- J. L. Fleiss, “Measuring nominal scale agreement among many raters,” in Psychological Bulletin, pp. 378-382, 1971.
5- D.G. Altman, “Practical Statistics for Medical Research,” in Chapman and Hall, 1990.
6- K. L. Gwet, “Computing inter-rater reliability and its variance in the presence of high agreement,” in The British Journal of Mathematical and Statistical Psychology, pp. 29–48, 2008.”
7- W. A. Scott, “Reliability of content analysis: The case of nominal scaling,” in Public Opinion Quarterly, pp. 321–325, 1955.
8- E. M. Bennett, R. Alpert, and A. C. Goldstein, “Communication through limited response questioning,” in The Public Opinion Quarterly, pp. 303–308, 1954.
9- D. V. Cicchetti, "Guidelines, criteria, and rules of thumb for evaluating normed and standardized assessment instruments in psychology," in Psychological Assessment, pp. 284–290, 1994.
10- R.B. Davies, "Algorithm AS155: The Distributions of a Linear Combination of χ2 Random Variables," in Journal of the Royal Statistical Society, pp. 323–333, 1980.
11- S. Kullback, R. A. Leibler "On information and sufficiency," in Annals of Mathematical Statistics, pp. 79–86, 1951.
12- L. A. Goodman, W. H. Kruskal, "Measures of Association for Cross Classifications, IV: Simplification of Asymptotic Variances," in Journal of the American Statistical Association, pp. 415–421, 1972.
13- L. A. Goodman, W. H. Kruskal, "Measures of Association for Cross Classifications III: Approximate Sampling Theory," in Journal of the American Statistical Association, pp. 310–364, 1963.
14- T. Byrt, J. Bishop and J. B. Carlin, “Bias, prevalence, and kappa,” in Journal of Clinical Epidemiology pp. 423-429, 1993.
15- M. Shepperd, D. Bowes, and T. Hall, “Researcher Bias: The Use of Machine Learning in Software Defect Prediction,” in IEEE Transactions on Software Engineering, pp. 603-616, 2014.
16- X. Deng, Q. Liu, Y. Deng, and S. Mahadevan, “An improved method to construct basic probability assignment based on the confusion matrix for classification problem, ” in Information Sciences, pp.250-261, 2016.
17- J.-M. Wei, X.-J. Yuan, Q.-H. Hu, and S.-Q. J. E. S. w. A. Wang, "A novel measure for evaluating classifiers," in Expert Systems with Applications, pp. 3799-3809, 2010.
18- I. Kononenko and I. J. M. L. Bratko, "Information-based evaluation criterion for classifier's performance," in Machine Learning, pp. 67-80, 1991.
19- R. Delgado and J. D. Núñez-González, "Enhancing Confusion Entropy as Measure for Evaluating Classifiers," in The 13th International Conference on Soft Computing Models in Industrial and Environmental Applications, pp. 79-89, 2018: Springer.
20- J. J. C. b. Gorodkin and chemistry, "Comparing two K-category assignments by a K-category correlation coefficient," in Computational Biology and chemistry, pp. 367-374, 2004.
21- C. O. Freitas, J. M. De Carvalho, J. Oliveira, S. B. Aires, and R. Sabourin, "Confusion matrix disagreement for multiple classifiers," in Iberoamerican Congress on Pattern Recognition, pp. 387-396, 2007.
22- P. Branco, L. Torgo, and R. P. Ribeiro, "Relevance-based evaluation metrics for multi-class imbalanced domains," in Pacific-Asia Conference on Knowledge Discovery and Data Mining, pp. 698-710, 2017. Springer.
23- D. Ballabio, F. Grisoni, R. J. C. Todeschini, and I. L. Systems, "Multivariate comparison of classification performance measures," in Chemometrics and Intelligent Laboratory Systems, pp. 33-44, 2018.
24- J. J. E. Cohen and p. measurement, "A coefficient of agreement for nominal scales," in Educational and Psychological Measurement, pp. 37-46, 1960.
25- S. Siegel, "Nonparametric statistics for the behavioral sciences," in New York : McGraw-Hill, 1956.
26- H. Cramér, "Mathematical methods of statistics (PMS-9),"in Princeton university press, 2016.
27- B. W. J. B. e. B. A.-P. S. Matthews, "Comparison of the predicted and observed secondary structure of T4 phage lysozyme," in Biochimica et Biophysica Acta (BBA) - Protein Structure, pp. 442-451, 1975.
28- J. A. J. S. Swets, "The relative operating characteristic in psychology: a technique for isolating effects of response bias finds wide use in the study of perception and cognition," in American Association for the Advancement of Science, pp. 990-1000, 1973.
29- P. J. B. S. V. S. N. Jaccard, "Étude comparative de la distribution florale dans une portion des Alpes et des Jura," in Bulletin de la Société vaudoise des sciences naturelles, pp. 547-579, 1901.
30- T. M. Cover and J. A. Thomas, "Elements of information theory," in John Wiley & Sons, 2012.
31- E. S. Keeping, "Introduction to statistical inference," in Courier Corporation, 1995.
32- V. Sindhwani, P. Bhattacharya, and S. Rakshit, "Information theoretic feature crediting in multiclass support vector machines," in Proceedings of the 2001 SIAM International Conference on Data Mining, pp. 1-18, 2001.
33- M. Bekkar, H. K. Djemaa, and T. A. J. J. I. E. A. Alitouche, "Evaluation measures for models assessment over imbalanced data sets," in Journal of Information Engineering and Applications, 2013.
34- W. J. J. C. Youden, "Index for rating diagnostic tests," in Cancer, pp. 32-35, 1950.
35- S. Brin, R. Motwani, J. D. Ullman, and S. J. A. S. R. Tsur, "Dynamic itemset counting and implication rules for market basket data," in Proceedings of the 1997 ACM SIGMOD international conference on Management of datavol, pp. 255-264, 1997.
36- S. J. T. J. o. O. S. S. Raschka, "MLxtend: Providing machine learning and data science utilities and extensions to Python’s scientific computing stack," in Journal of Open Source Software, 2018.
37- J. BRAy and J. CuRTIS, "An ordination of upland forest communities of southern Wisconsin.-ecological Monographs," in journal of Ecological Monographs, 1957.
38- J. L. Fleiss, J. Cohen, and B. S. J. P. B. Everitt, "Large sample standard errors of kappa and weighted kappa," in Psychological Bulletin, p. 323, 1969.
39- M. Felkin, "Comparing classification results between n-ary and binary problems," in Quality Measures in Data Mining: Springer, pp. 277-301, 2007.
40- R. Ranawana and V. Palade, "Optimized Precision-A new measure for classifier performance evaluation," in 2006 IEEE International Conference on Evolutionary Computation, pp. 2254-2261, 2006.
41- V. García, R. A. Mollineda, and J. S. Sánchez, "Index of balanced accuracy: A performance measure for skewed class distributions," in Iberian Conference on Pattern Recognition and Image Analysis, pp. 441-448, 2009.
42- P. Branco, L. Torgo, and R. P. J. A. C. S. Ribeiro, "A survey of predictive modeling on imbalanced domains," in Journal ACM Computing Surveys (CSUR), p. 31, 2016.
43- K. Pearson, "Notes on Regression and Inheritance in the Case of Two Parents," in Proceedings of the Royal Society of London, p. 240-242, 1895.
44- W. J. I. Conover, New York, "Practical Nonparametric Statistics," in John Wiley and Sons, 1999.
45- Yule, G. U, "On the methods of measuring association between two attributes." in Journal of the Royal Statistical Society, pp. 579-652, 1912.
46- Batuwita, R. and Palade, V, "A new performance measure for class imbalance learning. application to bioinformatics problems," in Machine Learning and Applications, pp.545–550, 2009.