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# PyCM : Full analysis of confusion matrix

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.

### From Vector

``````>>> from pycm import *
>>> y_actu = [2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1, 2] # or y_actu = numpy.array([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] # or y_pred = numpy.array([0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 2])
>>> cm = ConfusionMatrix(actual_vector=y_actu, predict_vector=y_pred) # Create CM From Data
>>> cm.classes
[0, 1, 2]
>>> cm.table
{0: {0: 3, 1: 0, 2: 0}, 1: {0: 0, 1: 1, 2: 2}, 2: {0: 2, 1: 1, 2: 3}}
>>> print(cm)
Predict          0    1    2
Actual
0                3    0    0
1                0    1    2
2                2    1    3

Overall Statistics :

95% CI                                                           (0.30439,0.86228)
AUNP                                                             0.66667
AUNU                                                             0.69444
Bennett_S                                                        0.375
CBA                                                              0.47778
Chi-Squared                                                      6.6
Chi-Squared DF                                                   4
Conditional Entropy                                              0.95915
Cramer_V                                                         0.5244
Cross Entropy                                                    1.59352
Gwet_AC1                                                         0.38931
Hamming Loss                                                     0.41667
Joint Entropy                                                    2.45915
KL Divergence                                                    0.09352
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                                                         0.16667
Lambda B                                                         0.42857
Mutual Information                                               0.52421
NIR                                                              0.5
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                                                          0.38721
PPV_Macro                                                        0.56667
PPV_Micro                                                        0.58333
Phi-Squared                                                      0.55
RR                                                               4.0
Reference Entropy                                                1.5
Response Entropy                                                 1.48336
Scott_PI                                                         0.34426
Standard Error                                                   0.14232
Strength_Of_Agreement(Altman)                                    Fair
Strength_Of_Agreement(Cicchetti)                                 Poor
Strength_Of_Agreement(Fleiss)                                    Poor
Strength_Of_Agreement(Landis and Koch)                           Fair
TPR_Macro                                                        0.61111
TPR_Micro                                                        0.58333
Zero-one Loss                                                    5

Class Statistics :

Classes                                                          0                       1                       2
ACC(Accuracy)                                                    0.83333                 0.75                    0.58333
AUC(Area under the roc curve)                                    0.88889                 0.61111                 0.58333
BM(Informedness or bookmaker informedness)                       0.77778                 0.22222                 0.16667
CEN(Confusion entropy)                                           0.25                    0.49658                 0.60442
DOR(Diagnostic odds ratio)                                       None                    4.0                     2.0
ERR(Error rate)                                                  0.16667                 0.25                    0.41667
F0.5(F0.5 score)                                                 0.65217                 0.45455                 0.57692
F1(F1 score - harmonic mean of precision and sensitivity)        0.75                    0.4                     0.54545
F2(F2 score)                                                     0.88235                 0.35714                 0.51724
FDR(False discovery rate)                                        0.4                     0.5                     0.4
FN(False negative/miss/type 2 error)                             0                       2                       3
FNR(Miss rate or false negative rate)                            0.0                     0.66667                 0.5
FOR(False omission rate)                                         0.0                     0.2                     0.42857
FP(False positive/type 1 error/false alarm)                      2                       1                       2
FPR(Fall-out or false positive rate)                             0.22222                 0.11111                 0.33333
G(G-measure geometric mean of precision and sensitivity)         0.7746                  0.40825                 0.54772
IS(Information score)                                            1.26303                 1.0                     0.26303
J(Jaccard index)                                                 0.6                     0.25                    0.375
LR+(Positive likelihood ratio)                                   4.5                     3.0                     1.5
LR-(Negative likelihood ratio)                                   0.0                     0.75                    0.75
MCC(Matthews correlation coefficient)                            0.68313                 0.2582                  0.16903
MCEN(Modified confusion entropy)                                 0.26439                 0.5                     0.6875
MK(Markedness)                                                   0.6                     0.3                     0.17143
N(Condition negative)                                            9                       9                       6
NPV(Negative predictive value)                                   1.0                     0.8                     0.57143
P(Condition positive or support)                                 3                       3                       6
POP(Population)                                                  12                      12                      12
PPV(Precision or positive predictive value)                      0.6                     0.5                     0.6
PRE(Prevalence)                                                  0.25                    0.25                    0.5
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)                           0.77778                 0.88889                 0.66667
TON(Test outcome negative)                                       7                       10                      7
TOP(Test outcome positive)                                       5                       2                       5
TP(True positive/hit)                                            3                       1                       3
TPR(Sensitivity, recall, hit rate, or true positive rate)        1.0                     0.33333                 0.5
dInd(Distance index)                                             0.22222                 0.67586                 0.60093
sInd(Similarity index)                                           0.84287                 0.52209                 0.57508

>>> cm.matrix()
Predict          0        1        2
Actual
0                3        0        0
1                0        1        2
2                2        1        3

>>> cm.normalized_matrix()
Predict          0              1              2
Actual
0                1.0            0.0            0.0
1                0.0            0.33333        0.66667
2                0.33333        0.16667        0.5

>>> cm.matrix(one_vs_all=True,class_name=0)   # One-Vs-All, new in version 1.4
Predict          0    ~
Actual
0                3    0
~                2    7

``````

### Direct CM

``````>>> from pycm import *
>>> cm2 = ConfusionMatrix(matrix={"Class1": {"Class1": 1, "Class2":2}, "Class2": {"Class1": 0, "Class2": 5}}) # Create CM Directly
>>> cm2
pycm.ConfusionMatrix(classes: ['Class1', 'Class2'])
>>> print(cm2)
Predict          Class1    Class2
Actual
Class1           1         2
Class2           0         5

Overall Statistics :

95% CI                                                           (0.44994,1.05006)
AUNP                                                             0.66667
AUNU                                                             0.66667
Bennett_S                                                        0.5
CBA                                                              0.52381
Chi-Squared                                                      1.90476
Chi-Squared DF                                                   1
Conditional Entropy                                              0.34436
Cramer_V                                                         0.48795
Cross Entropy                                                    1.2454
Gwet_AC1                                                         0.6
Hamming Loss                                                     0.25
Joint Entropy                                                    1.29879
KL Divergence                                                    0.29097
Kappa                                                            0.38462
Kappa 95% CI                                                     (-0.354,1.12323)
Kappa No Prevalence                                              0.5
Kappa Standard Error                                             0.37684
Kappa Unbiased                                                   0.33333
Lambda A                                                         0.33333
Lambda B                                                         0.0
Mutual Information                                               0.1992
NIR                                                              0.625
Overall_ACC                                                      0.75
Overall_CEN                                                      0.44812
Overall_J                                                        (1.04762,0.52381)
Overall_MCC                                                      0.48795
Overall_MCEN                                                     0.29904
Overall_RACC                                                     0.59375
Overall_RACCU                                                    0.625
P-Value                                                          0.36974
PPV_Macro                                                        0.85714
PPV_Micro                                                        0.75
Phi-Squared                                                      0.2381
RR                                                               4.0
Reference Entropy                                                0.95443
Response Entropy                                                 0.54356
Scott_PI                                                         0.33333
Standard Error                                                   0.15309
Strength_Of_Agreement(Altman)                                    Fair
Strength_Of_Agreement(Cicchetti)                                 Poor
Strength_Of_Agreement(Fleiss)                                    Poor
Strength_Of_Agreement(Landis and Koch)                           Fair
TPR_Macro                                                        0.66667
TPR_Micro                                                        0.75
Zero-one Loss                                                    2

Class Statistics :

Classes                                                          Class1                  Class2
ACC(Accuracy)                                                    0.75                    0.75
AUC(Area under the roc curve)                                    0.66667                 0.66667
BM(Informedness or bookmaker informedness)                       0.33333                 0.33333
CEN(Confusion entropy)                                           0.5                     0.43083
DOR(Diagnostic odds ratio)                                       None                    None
ERR(Error rate)                                                  0.25                    0.25
F0.5(F0.5 score)                                                 0.71429                 0.75758
F1(F1 score - harmonic mean of precision and sensitivity)        0.5                     0.83333
F2(F2 score)                                                     0.38462                 0.92593
FDR(False discovery rate)                                        0.0                     0.28571
FN(False negative/miss/type 2 error)                             2                       0
FNR(Miss rate or false negative rate)                            0.66667                 0.0
FOR(False omission rate)                                         0.28571                 0.0
FP(False positive/type 1 error/false alarm)                      0                       2
FPR(Fall-out or false positive rate)                             0.0                     0.66667
G(G-measure geometric mean of precision and sensitivity)         0.57735                 0.84515
IS(Information score)                                            1.41504                 0.19265
J(Jaccard index)                                                 0.33333                 0.71429
LR+(Positive likelihood ratio)                                   None                    1.5
LR-(Negative likelihood ratio)                                   0.66667                 0.0
MCC(Matthews correlation coefficient)                            0.48795                 0.48795
MCEN(Modified confusion entropy)                                 0.38998                 0.51639
MK(Markedness)                                                   0.71429                 0.71429
N(Condition negative)                                            5                       3
NPV(Negative predictive value)                                   0.71429                 1.0
P(Condition positive or support)                                 3                       5
POP(Population)                                                  8                       8
PPV(Precision or positive predictive value)                      1.0                     0.71429
PRE(Prevalence)                                                  0.375                   0.625
RACC(Random accuracy)                                            0.04688                 0.54688
RACCU(Random accuracy unbiased)                                  0.0625                  0.5625
TN(True negative/correct rejection)                              5                       1
TNR(Specificity or true negative rate)                           1.0                     0.33333
TON(Test outcome negative)                                       7                       1
TOP(Test outcome positive)                                       1                       7
TP(True positive/hit)                                            1                       5
TPR(Sensitivity, recall, hit rate, or true positive rate)        0.33333                 1.0
dInd(Distance index)                                             0.66667                 0.66667
sInd(Similarity index)                                           0.5286                  0.5286

>>> cm3 = ConfusionMatrix(matrix={"Class1": {"Class1": 1, "Class2":0}, "Class2": {"Class1": 2, "Class2": 5}},transpose=True) # Transpose Matrix
>>> cm3.matrix()
Predict          Class1    Class2
Actual
Class1           1         2
Class2           0         5

``````