PyCM – the swiss-army knife of confusion matrices
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Table of contents
- Overview
- Installation
- Usage
- Document
- Issues & Bug Reports
- Todo
- Outputs
- Dependencies
- Contribution
- References
- Cite
- Authors
- License
- Donate
- Changelog
Overview
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. PyCM Block Diagram
Installation
Source Code
- Download Version 1.4 or Latest Source
- Run
pip install -r requirements.txtorpip3 install -r requirements.txt(Need root access) - Run
python3 setup.py installorpython setup.py install(Need root access)
PyPI
- Check Python Packaging User Guide
- Run
pip install pycm --upgradeorpip3 install pycm --upgrade(Need root access)
Easy Install
- Run
easy_install --upgrade pycm(Need root access)
Usage
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
Activation Threshold
threshold is added in Version 0.9 for real value prediction.
For more information visit Example3
Load From File
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 Example4
Sample Weights
sample_weight is added in Version 1.2
For more information visit Example5
Transpose
transpose is added in Version 1.2 in order to transpose input matrix (only in Direct CM mode)
Online Help
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("Strength_Of_Agreement(Landis and Koch)")
>>> online_help(2)
- list of items are available by calling
online_help()(without argument)
Acceptable Data Types
-
actual_vector: pythonlistor numpyarrayof any stringable objects -
predict_vector: pythonlistor numpyarrayof any stringable objects -
matrix:dict -
digit:int -
threshold:FunctionType (function or lambda) -
file:File object -
sample_weight: pythonlistor numpyarrayof any stringable objects -
transpose:bool
- run
help(ConfusionMatrix)forConfusionMatrixobject details
For more information visit here
Issues & Bug Reports
Just fill an issue and describe it. We'll check it ASAP! or send an email to [email protected] .
Todo
Moved here
Outputs
Dependencies
Contribution
Changes and improvements are more than welcome!
:heart:
Feel free to fork and open a pull request. Please make your changes in a specific branch and request to pull into dev
Remember to write a few tests for your code before sending pull requests.
References
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.
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- Wei, J.-M., Yuan, X.-Y., Hu, Q.-H., Wang, S.-Q.: A novel measure for evaluating classifiers. Expert Systems with Applications, Vol 37, 3799–3809 (2010).
18- Kononenko I. and Bratko I. Information-based evaluation criterion for classifier’s performance. Machine Learning, 6:67–80, 1991.
19- Delgado R., Núñez-González J.D. (2019) Enhancing Confusion Entropy as Measure for Evaluating Classifiers. In: Graña M. et al. (eds) International Joint Conference SOCO’18-CISIS’18-ICEUTE’18. SOCO’18-CISIS’18-ICEUTE’18 2018. Advances in Intelligent Systems and Computing, vol 771. Springer, Cham
20- Gorodkin J (2004) Comparing two K-category assignments by a K-category correlation coefficient. Computational Biology and Chemistry 28: 367–374
21- Freitas C.O.A., de Carvalho J.M., Oliveira J., Aires S.B.K., Sabourin R. (2007) Confusion Matrix Disagreement for Multiple Classifiers. In: Rueda L., Mery D., Kittler J. (eds) Progress in Pattern Recognition, Image Analysis and Applications. CIARP 2007. Lecture Notes in Computer Science, vol 4756. Springer, Berlin, Heidelberg
22- Branco P., Torgo L., Ribeiro R.P. (2017) Relevance-Based Evaluation Metrics for Multi-class Imbalanced Domains. In: Kim J., Shim K., Cao L., Lee JG., Lin X., Moon YS. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2017. Lecture Notes in Computer Science, vol 10234. Springer, Cham
23- Ballabio, D., Grisoni, F. and Todeschini, R. (2018). Multivariate comparison of classification performance measures. Chemometrics and Intelligent Laboratory Systems, 174, pp.33-44.
24- Cohen, Jacob. 1960. A coefficient of agreement for nominal scales. Educational And Psychological Measurement 20:37-46
25- Siegel, Sidney and N. John Castellan, Jr. 1988. Nonparametric Statistics for the Behavioral Sciences. McGraw Hill.
26- Cramér, Harald. 1946. Mathematical Methods of Statistics. Princeton: Princeton University Press, page 282 (Chapter 21. The two-dimensional case)
27- Matthews, B. W. (1975). "Comparison of the predicted and observed secondary structure of T4 phage lysozyme". Biochimica et Biophysica Acta (BBA) - Protein Structure. 405 (2): 442–451.
28- Swets JA. (1973). "The relative operating characteristic in Psychology". Science. 182 (14116): 990–1000.
29- Jaccard, Paul (1901), "Étude comparative de la distribution florale dans une portion des Alpes et des Jura", Bulletin de la Société Vaudoise des Sciences Naturelles, 37: 547–579.
30- Thomas M. Cover and Joy A. Thomas. 2006. Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing). Wiley-Interscience, New York, NY, USA.
31- Keeping, E.S. (1962) Introduction to Statistical Inference. D. Van Nostrand, Princeton, NJ.
Cite
If you use PyCM in your research , please cite this JOSS paper :
Haghighi, S., Jasemi, M., Hessabi, S. and Zolanvari, A. (2018). PyCM: Multiclass confusion matrix library in Python. Journal of Open Source Software, 3(25), p.729.
@article{Haghighi2018,
doi = {10.21105/joss.00729},
url = {https://doi.org/10.21105/joss.00729},
year = {2018},
month = {may},
publisher = {The Open Journal},
volume = {3},
number = {25},
pages = {729},
author = {Sepand Haghighi and Masoomeh Jasemi and Shaahin Hessabi and Alireza Zolanvari},
title = {{PyCM}: Multiclass confusion matrix library in Python},
journal = {Journal of Open Source Software}
}
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