pycm 3.6

Multi-class confusion matrix library in Python

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Table of contents

• Overview
• Installation
• Usage
• Document
• Try PyCM in Your Browser
• Issues & Bug Reports
• Todo
• Outputs
• Dependencies
• Contribution
• Acknowledgments
• References
• Cite
• Authors
• License
• Show Your Support
• Changelog
• Code of Conduct

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 accurate evaluation of a large variety of classifiers.

Fig1. ConfusionMatrix Block Diagram

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Installation

⚠️ PyCM 2.4 is the last version to support Python 2.7 & Python 3.4

⚠️ Plotting capability requires Matplotlib (>= 3.0.0) or Seaborn (>= 0.9.1)

Source code

• Download Version 3.6 or Latest Source
• Run pip install -r requirements.txt or pip3 install -r requirements.txt (Need root access)
• Run python3 setup.py install or python setup.py install (Need root access)

PyPI

• Check Python Packaging User Guide
• Run pip install pycm==3.6 or pip3 install pycm==3.6 (Need root access)

Conda

• Check Conda Managing Package
• Update Conda using conda update conda (Need root access)
• Run conda install -c sepandhaghighi pycm (Need root access)

Easy install

• Run easy_install --upgrade pycm (Need root access)

MATLAB

• Download and install MATLAB (>=8.5, 64/32 bit)
• Download and install Python3.x (>=3.5, 64/32 bit)
  • Select Add to PATH option
  • Select Install pip option
• Run pip install pycm or pip3 install pycm (Need root access)
• Configure Python interpreter

>> pyversion PYTHON_EXECUTABLE_FULL_PATH

• Visit MATLAB Examples

Usage

From vector

>>> 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(actual_vector=y_actu, predict_vector=y_pred)
>>> 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}}
>>> cm.print_matrix()
Predict 0       1       2       
Actual
0       3       0       0       

1       0       1       2       

2       2       1       3   

>>> cm.print_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.stat(summary=True)
Overall Statistics : 

ACC Macro                                                         0.72222
F1 Macro                                                          0.56515
FPR Macro                                                         0.22222
Kappa                                                             0.35484
Overall ACC                                                       0.58333
PPV Macro                                                         0.56667
SOA1(Landis & Koch)                                               Fair
TPR Macro                                                         0.61111
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       
AUCI(AUC value interpretation)                                    Very Good     Fair          Poor          
F1(F1 score - harmonic mean of precision and sensitivity)         0.75          0.4           0.54545       
FN(False negative/miss/type 2 error)                              0             2             3             
FP(False positive/type 1 error/false alarm)                       2             1             2             
FPR(Fall-out or false positive rate)                              0.22222       0.11111       0.33333       
N(Condition negative)                                             9             9             6             
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           
TN(True negative/correct rejection)                               7             8             4             
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 

Direct CM

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

Class2       0            5            

>>> cm2.print_normalized_matrix()
Predict       Class1        Class2        
Actual
Class1        0.33333       0.66667       

Class2        0.0           1.0 

>>> cm2.stat(summary=True)
Overall Statistics : 

ACC Macro                                                         0.75
F1 Macro                                                          0.66667
FPR Macro                                                         0.33333
Kappa                                                             0.38462
Overall ACC                                                       0.75
PPV Macro                                                         0.85714
SOA1(Landis & Koch)                                               Fair
TPR Macro                                                         0.66667
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       
AUCI(AUC value interpretation)                                    Fair          Fair          
F1(F1 score - harmonic mean of precision and sensitivity)         0.5           0.83333       
FN(False negative/miss/type 2 error)                              2             0             
FP(False positive/type 1 error/false alarm)                       0             2             
FPR(Fall-out or false positive rate)                              0.0           0.66667       
N(Condition negative)                                             5             3             
P(Condition positive or support)                                  3             5             
POP(Population)                                                   8             8             
PPV(Precision or positive predictive value)                       1.0           0.71429       
TN(True negative/correct rejection)                               5             1             
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
     

• matrix() and normalized_matrix() renamed to print_matrix() and print_normalized_matrix() in version 1.5

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)

Relabel

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'])

Position

position method is added in version 2.8 in order to find the indexes of observations in predict_vector which made TP, TN, FP, FN.

>>> cm.position()
{0: {'FN': [], 'FP': [0, 7], 'TP': [1, 4, 9], 'TN': [2, 3, 5, 6, 8, 10, 11]}, 1: {'FN': [5, 10], 'FP': [3], 'TP': [6], 'TN': [0, 1, 2, 4, 7, 8, 9, 11]}, 2: {'FN': [0, 3, 7], 'FP': [5, 10], 'TP': [2, 8, 11], 'TN': [1, 4, 6, 9]}}

To array

to_array method is added in version 2.9 in order to returns the confusion matrix in the form of a NumPy array. This can be helpful to apply different operations over the confusion matrix for different purposes such as aggregation, normalization, and combination.

>>> cm.to_array()
array([[3, 0, 0],
       [0, 1, 2],
       [2, 1, 3]])
>>> cm.to_array(normalized=True)
array([[1.     , 0.     , 0.     ],
       [0.     , 0.33333, 0.66667],
       [0.33333, 0.16667, 0.5    ]])
>>> cm.to_array(normalized=True,one_vs_all=True, class_name="L1")
array([[1.     , 0.     ],
       [0.22222, 0.77778]])

Combine

combine method is added in version 3.0 in order to merge two confusion matrices. This option will be useful in mini-batch learning.

>>> cm_combined = cm2.combine(cm3)
>>> cm_combined.print_matrix()
Predict      Class1       Class2       
Actual
Class1       2            4            

Class2       0            10           

Plot

plot method is added in version 3.0 in order to plot a confusion matrix using Matplotlib or Seaborn.

>>> cm.plot()

>>> from matplotlib import pyplot as plt
>>> cm.plot(cmap=plt.cm.Greens,number_label=True,plot_lib="matplotlib")

>>> cm.plot(cmap=plt.cm.Reds,normalized=True,number_label=True,plot_lib="seaborn")

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("SOA1(Landis & Koch)")
>>> online_help(2)

• List of items are available by calling online_help() (without argument)
• If PyCM website is not available, set alt_link = True (new in version 2.4)

Parameter recommender

This option has been added in version 1.9 to recommend the most related parameters considering the characteristics of the input dataset. The suggested parameters are selected according to some characteristics of the input such as being balance/imbalance and binary/multi-class. 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.

>>> cm.imbalance
False
>>> cm.binary
False
>>> cm.recommended_list
['MCC', 'TPR Micro', 'ACC', 'PPV Macro', 'BCD', 'Overall MCC', 'Hamming Loss', 'TPR Macro', 'Zero-one Loss', 'ERR', 'PPV Micro', 'Overall ACC']

is_imbalanced parameter has been added in version 3.3, so the user can indicate whether the concerned dataset is imbalanced or not. As long as the user does not provide any information in this regard, the automatic detection algorithm will be used.

>>> cm = ConfusionMatrix(y_actu, y_pred, is_imbalanced = True)
>>> cm.imbalance
True
>>> cm = ConfusionMatrix(y_actu, y_pred, is_imbalanced = False)
>>> cm.imbalance
False

Compare

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 and poor performances are 1 and 0, respectively.

After that, two scores are calculated for each confusion matrices, overall and class-based. The overall score is the average of the score of six overall benchmarks which are Landis & Koch, Fleiss, Altman, Cicchetti, Cramer, and Matthews. In the same manner, the class-based score is the average of the score of six class-based benchmarks which are Positive Likelihood Ratio Interpretation, Negative Likelihood Ratio Interpretation, Discriminant Power Interpretation, AUC value Interpretation, Matthews Correlation Coefficient Interpretation and Yule's Q Interpretation. It should be noticed that if one of the benchmarks returns none for one of the classes, that benchmarks will be eliminated in total averaging. If the user sets weights for the classes, the averaging over the value of class-based benchmark scores will transform to a weighted average.

If the user sets 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 obtains the maximum of both overall and class-based scores, that will be reported as the best confusion matrix, but in any other case, the compared object doesn’t select the best confusion matrix.

>>> 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    0.50278           0.425
2     cm3    0.33611           0.33056

>>> cp.best
pycm.ConfusionMatrix(classes: [0, 1, 2])
>>> cp.sorted
['cm2', 'cm3']
>>> cp.best_name
'cm2'

Acceptable data types

ConfusionMatrix

1. actual_vector : python list or numpy array of any stringable objects
2. predict_vector : python list or numpy array of any stringable objects
3. matrix : dict
4. digit: int
5. threshold : FunctionType (function or lambda)
6. file : File object
7. sample_weight : python list or numpy array of numbers
8. transpose : bool
9. classes : python list
10. is_imbalanced : bool

• Run help(ConfusionMatrix) for ConfusionMatrix object details

Compare

1. cm_dict : python dict of ConfusionMatrix object (str : ConfusionMatrix)
2. by_class : bool
3. class_weight : python dict of class weights (class_name : float)
4. class_benchmark_weight: python dict of class benchmark weights (class_benchmark_name : float)
5. overall_benchmark_weight: python dict of overall benchmark weights (overall_benchmark_name : float)
6. digit: int

• Run help(Compare) for Compare object details

For more information visit here

Try PyCM in your browser!

PyCM can be used online in interactive Jupyter Notebooks via the Binder or Colab services! Try it out now! :

• Check Examples in Document folder

Issues & bug reports

1. Fill an issue and describe it. We'll check it ASAP!
   • Please complete the issue template
2. Discord : https://discord.com/invite/zqpU2b3J3f
3. Website : https://www.pycm.io
4. Mailing List : https://mail.python.org/mailman3/lists/pycm.python.org/
5. Email : [e-mail]

Outputs

1. HTML
2. CSV
3. PyCM
4. OBJ
5. COMP

Dependencies

master	dev

Acknowledgments

NLnet foundation has supported the PyCM project from version 3.6 to 4.0 through the NGI Assure Fund. This fund is set up by NLnet foundation with funding from the European Commission's Next Generation Internet program, administered by DG Communications Networks, Content, and Technology under grant agreement No 957073.

 

References

1- J. R. Landis and G. G. Koch, "The measurement of observer agreement for categorical data," biometrics, pp. 159-174, 1977.

2- D. M. Powers, "Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation," arXiv preprint arXiv:2010.16061, 2020.

3- C. Sammut and G. I. Webb, Encyclopedia of machine learning. Springer Science & Business Media, 2011.

4- J. L. Fleiss, "Measuring nominal scale agreement among many raters," Psychological bulletin, vol. 76, no. 5, p. 378, 1971.

5- D. G. Altman, Practical statistics for medical research. CRC press, 1990.

6- K. L. Gwet, "Computing inter-rater reliability and its variance in the presence of high agreement," British Journal of Mathematical and Statistical Psychology, vol. 61, no. 1, pp. 29-48, 2008.

7- W. A. Scott, "Reliability of content analysis: The case of nominal scale coding," Public opinion quarterly, pp. 321-325, 1955.

8- E. M. Bennett, R. Alpert, and A. Goldstein, "Communications through limited-response questioning," Public Opinion Quarterly, vol. 18, no. 3, pp. 303-308, 1954.

9- D. V. Cicchetti, "Guidelines, criteria, and rules of thumb for evaluating normed and standardized assessment instruments in psychology," Psychological assessment, vol. 6, no. 4, p. 284, 1994.

10- R. B. Davies, "Algorithm AS 155: The distribution of a linear combination of χ2 random variables," Applied Statistics, pp. 323-333, 1980.

11- S. Kullback and R. A. Leibler, "On information and sufficiency," The annals of mathematical statistics, vol. 22, no. 1, pp. 79-86, 1951.

12- L. A. Goodman and W. H. Kruskal, "Measures of association for cross classifications, IV: Simplification of asymptotic variances," Journal of the American Statistical Association, vol. 67, no. 338, pp. 415-421, 1972.

13- L. A. Goodman and W. H. Kruskal, "Measures of association for cross classifications III: Approximate sampling theory," Journal of the American Statistical Association, vol. 58, no. 302, pp. 310-364, 1963.

14- T. Byrt, J. Bishop, and J. B. Carlin, "Bias, prevalence and kappa," Journal of clinical epidemiology, vol. 46, no. 5, pp. 423-429, 1993.

15- M. Shepperd, D. Bowes, and T. Hall, "Researcher bias: The use of machine learning in software defect prediction," IEEE Transactions on Software Engineering, vol. 40, no. 6, 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," Information Sciences, vol. 340, pp. 250-261, 2016.

17- J.-M. Wei, X.-J. Yuan, Q.-H. Hu, and S.-Q. Wang, "A novel measure for evaluating classifiers," Expert Systems with Applications, vol. 37, no. 5, pp. 3799-3809, 2010.

18- I. Kononenko and I. Bratko, "Information-based evaluation criterion for classifier's performance," Machine learning, vol. 6, no. 1, pp. 67-80, 1991.

19- R. Delgado and J. D. Núnez-González, "Enhancing confusion entropy as measure for evaluating classifiers," in The 13th International Conference on Soft Computing Models in Industrial and Environmental Applications, 2018: Springer, pp. 79-89.

20- J. Gorodkin, "Comparing two K-category assignments by a K-category correlation coefficient," Computational biology and chemistry, vol.28, no. 5-6, 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, 2007: Springer, pp. 387-396.

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, 2017: Springer, pp. 698-710.

23- D. Ballabio, F. Grisoni, and R. Todeschini, "Multivariate comparison of classification performance measures," Chemometrics and Intelligent Laboratory Systems, vol. 174, pp. 33-44, 2018.

24- J. Cohen, "A coefficient of agreement for nominal scales," Educational and psychological measurement, vol. 20, no. 1, pp. 37-46, 1960.

25- S. Siegel, "Nonparametric statistics for the behavioral sciences," 1956.

26- H. Cramér, Mathematical methods of statistics. Princeton university press, 1999.

27- B. W. Matthews, "Comparison of the predicted and observed secondary structure of T4 phage lysozyme," Biochimica et Biophysica Acta (BBA)-Protein Structure, vol. 405, no. 2, pp. 442-451, 1975.

28- J. A. 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," Science, vol. 182, no. 4116, pp. 990-1000, 1973.

29- P. Jaccard, "Étude comparative de la distribution florale dans une portion des Alpes et des Jura," Bull Soc Vaudoise Sci Nat, vol. 37, pp. 547-579, 1901.

30- T. M. Cover and J. A. Thomas, Elements of Information Theory. John Wiley & Sons, 2012.

31- E. S. Keeping, Introduction to statistical inference. 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, 2001: SIAM, pp. 1-18.

33- M. Bekkar, H. K. Djemaa, and T. A. Alitouche, "Evaluation measures for models assessment over imbalanced data sets," J Inf Eng Appl, vol. 3, no. 10, 2013.

34- W. J. Youden, "Index for rating diagnostic tests," Cancer, vol. 3, no. 1, pp. 32-35, 1950.

35- S. Brin, R. Motwani, J. D. Ullman, and S. Tsur, "Dynamic itemset counting and implication rules for market basket data," in Proceedings of the 1997 ACM SIGMOD international conference on Management of data, 1997, pp. 255-264.

36- S. Raschka, "MLxtend: Providing machine learning and data science utilities and extensions to Python's scientific computing stack," Journal of open source software, vol. 3, no. 24, p. 638, 2018.

37- J. R. Bray and J. T. Curtis, "An ordination of the upland forest communities of southern Wisconsin," Ecological monographs, vol. 27, no. 4, pp. 325-349, 1957.

38- J. L. Fleiss, J. Cohen, and B. S. Everitt, "Large sample standard errors of kappa and weighted kappa," Psychological bulletin, vol. 72, no. 5, p. 323, 1969.

39- M. Felkin, "Comparing classification results between n-ary and binary problems," in Quality Measures in Data Mining: Springer, 2007, pp. 277-301.

40- R. Ranawana and V. Palade, "Optimized precision-a new measure for classifier performance evaluation," in 2006 IEEE International Conference on Evolutionary Computation, 2006: IEEE, pp. 2254-2261.

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, 2009: Springer, pp. 441-448.

42- P. Branco, L. Torgo, and R. P. Ribeiro, "A survey of predictive modeling on imbalanced domains," ACM Computing Surveys (CSUR), vol. 49, no. 2, pp. 1-50, 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. Conover, Practical nonparametric statistics. John Wiley & Sons, 1998.

45- G. U. Yule, "On the methods of measuring association between two attributes," Journal of the Royal Statistical Society, vol. 75, no. 6, pp. 579-652, 1912.

46- R. Batuwita and V. Palade, "A new performance measure for class imbalance learning. application to bioinformatics problems," in 2009 International Conference on Machine Learning and Applications, 2009: IEEE, pp. 545-550.

47- D. K. Lee, "Alternatives to P value: confidence interval and effect size," Korean journal of anesthesiology, vol. 69, no. 6, p. 555, 2016.

48- M. A. Raslich, R. J. Markert, and S. A. Stutes, "Selecting and interpreting diagnostic tests," Biochemia Medica, vol. 17, no. 2, pp. 151-161, 2007.

49- D. E. Hinkle, W. Wiersma, and S. G. Jurs, Applied statistics for the behavioral sciences. Houghton Mifflin College Division, 2003.

50- A. Maratea, A. Petrosino, and M. Manzo, "Adjusted F-measure and kernel scaling for imbalanced data learning," Information Sciences, vol. 257, pp. 331-341, 2014.

51- L. Mosley, "A balanced approach to the multi-class imbalance problem," 2013.

52- M. Vijaymeena and K. Kavitha, "A survey on similarity measures in text mining," Machine Learning and Applications: An International Journal, vol. 3, no. 2, pp. 19-28, 2016.

53- Y. Otsuka, "The faunal character of the Japanese Pleistocene marine Mollusca, as evidence of climate having become colder during the Pleistocene in Japan," Biogeograph Soc Japan, vol. 6, no. 16, pp. 165-170, 1936.

54- A. Tversky, "Features of similarity," Psychological review, vol. 84, no. 4, p. 327, 1977.

55- K. Boyd, K. H. Eng, and C. D. Page, "Area under the precision-recall curve: point estimates and confidence intervals," in Joint European conference on machine learning and knowledge discovery in databases, 2013: Springer, pp. 451-466.

56- J. Davis and M. Goadrich, "The relationship between Precision-Recall and ROC curves," in Proceedings of the 23rd international conference on Machine learning, 2006, pp. 233-240.

57- M. Kuhn, "Building predictive models in R using the caret package," J Stat Softw, vol. 28, no. 5, pp. 1-26, 2008.

58- V. Labatut and H. Cherifi, "Accuracy measures for the comparison of classifiers," arXiv preprint arXiv:1207.3790, 2012.

59- S. Wallis, "Binomial confidence intervals and contingency tests: mathematical fundamentals and the evaluation of alternative methods," Journal of Quantitative Linguistics, vol. 20, no. 3, pp. 178-208, 2013.

60- D. Altman, D. Machin, T. Bryant, and M. Gardner, Statistics with confidence: confidence intervals and statistical guidelines. John Wiley & Sons, 2013.

61- J. A. Hanley and B. J. McNeil, "The meaning and use of the area under a receiver operating characteristic (ROC) curve," Radiology, vol. 143, no. 1, pp. 29-36, 1982.

62- E. B. Wilson, "Probable inference, the law of succession, and statistical inference," Journal of the American Statistical Association, vol. 22, no. 158, pp. 209-212, 1927.

63- A. Agresti and B. A. Coull, "Approximate is better than “exact” for interval estimation of binomial proportions," The American Statistician, vol. 52, no. 2, pp. 119-126, 1998.

64- C. S. Peirce, "The numerical measure of the success of predictions," Science, no. 93, pp. 453-454, 1884.

65- E. W. Steyerberg, B. Van Calster, and M. J. Pencina, "Performance measures for prediction models and markers: evaluation of predictions and classifications," Revista Española de Cardiología (English Edition), vol. 64, no. 9, pp. 788-794, 2011.

66- A. J. Vickers and E. B. Elkin, "Decision curve analysis: a novel method for evaluating prediction models," Medical Decision Making, vol. 26, no. 6, pp. 565-574, 2006.

67- G. W. Bohrnstedt and D. Knoke,"Statistics for social data analysis," 1982.

68- W. M. Rand, "Objective criteria for the evaluation of clustering methods," Journal of the American Statistical association, vol. 66, no. 336, pp. 846-850, 1971.

69- J. M. Santos and M. Embrechts, "On the use of the adjusted rand index as a metric for evaluating supervised classification," in International conference on artificial neural networks, 2009: Springer, pp. 175-184.

70- J. Cohen, "Weighted kappa: nominal scale agreement provision for scaled disagreement or partial credit," Psychological bulletin, vol. 70, no. 4, p. 213, 1968.

71- R. Bakeman and J. M. Gottman, Observing interaction: An introduction to sequential analysis. Cambridge university press, 1997.

72- S. Bangdiwala, "A graphical test for observer agreement," in 45th International Statistical Institute Meeting, 1985, vol. 1985, p. 307.

73- K. Bangdiwala and H. Bryan, "Using SAS software graphical procedures for the observer agreement chart," in Proceedings of the SAS Users Group International Conference, 1987, vol. 12, pp. 1083-1088.

74- A. F. Hayes and K. Krippendorff, "Answering the call for a standard reliability measure for coding data," Communication methods and measures, vol. 1, no. 1, pp. 77-89, 2007.

75- M. Aickin, "Maximum likelihood estimation of agreement in the constant predictive probability model, and its relation to Cohen's kappa," Biometrics, pp. 293-302, 1990.

76- N. A. Macmillan and C. D. Creelman, Detectiontheory: A user's guide. Psychology press, 2004.

77- D. J. Hand, P. Christen, and N. Kirielle, "F*: an interpretable transformation of the F-measure," Machine Learning, vol. 110, no. 3, pp. 451-456, 2021.

78- G. W. Brier, "Verification of forecasts expressed in terms of probability," Monthly weather review, vol. 78, no. 1, pp. 1-3, 1950.

79- L. Buitinck et al., "API design for machine learning software: experiences from the scikit-learn project," arXiv preprint arXiv:1309.0238, 2013.

80- R. W. Hamming, "Error detecting and error correcting codes," The Bell system technical journal, vol. 29, no. 2, pp. 147-160, 1950.

81- S. S. Choi, S. H. Cha, and C. C. Tappert, "A survey of binary similarity and distance measures," Journal of systemics, cybernetics and informatics, vol. 8, no. 1, pp. 43-48, 2010.

82- J. Braun-Blanquet, "Plant sociology. The study of plant communities," Plant sociology. The study of plant communities. First ed., 1932.

83- C. C. Little, "Abydos Documentation," 2020.

Cite

If you use PyCM in your research, we would appreciate citations to the following 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}
}

Download PyCM.bib

JOSS
Zenodo
Researchgate

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Changelog

All notable changes to this project will be documented in this file.

The format is based on Keep a Changelog and this project adheres to Semantic Versioning.

Unreleased

3.6 - 2022-08-17

Added

• Hamming distance
• Braun-Blanquet similarity

Changed

• classes parameter added to matrix_params_from_table function
• Matrices with numpy.integer elements are now accepted
• Arrays added to matrix parameter accepting formats
• Website changed to http://www.pycm.io
• Document modified
• README.md modified

3.5 - 2022-04-27

Added

• Anaconda workflow
• Custom iterating setting
• Custom casting setting

Changed

• plot method updated
• class_statistics function modified
• overall_statistics function modified
• BCD_calc function modified
• CONTRIBUTING.md updated
• CODE_OF_CONDUCT.md updated
• Document modified

3.4 - 2022-01-26

Added

• Colab badge
• Discord badge
• brier_score method

Changed

• J (Jaccard index) section in Document.ipynb updated
• save_obj method updated
• Python 3.10 added to test.yml
• Example-3 updated
• Docstrings of the functions updated
• CONTRIBUTING.md updated

3.3 - 2021-10-27

Added

• __compare_weight_handler__ function

Changed

• is_imbalanced parameter added to ConfusionMatrix __init__ method
• class_benchmark_weight and overall_benchmark_weight parameters added to Compare __init__ method
• statistic_recommend function modified
• Compare weight parameter renamed to class_weight
• Document modified
• License updated
• AUTHORS.md updated
• README.md modified
• Block diagrams updated

3.2 - 2021-08-11

Added

• classes_filter function

Changed

• classes parameter added to matrix_params_calc function
• classes parameter added to __obj_vector_handler__ function
• classes parameter added to ConfusionMatrix __init__ method
• name parameter removed from html_init function
• shortener parameter added to html_table function
• shortener parameter added to save_html method
• Document modified
• HTML report modified

3.1 - 2021-03-11

Added

• requirements-splitter.py
• sensitivity_index method

Changed

• Test system modified
• overall_statistics function modified
• HTML report modified
• Document modified
• References format updated
• CONTRIBUTING.md updated

3.0 - 2020-10-26

Added

• plot_test.py
• axes_gen function
• add_number_label function
• plot method
• combine method
• matrix_combine function

Changed

• Document modified
• README.md modified
• Example-2 deprecated
• Example-7 deprecated
• Error messages modified

2.9 - 2020-09-23

Added

• notebook_check.py
• to_array method
• __copy__ method
• copy method

Changed

• average method refactored

2.8 - 2020-07-09

Added

• label_map attribute
• positions attribute
• position method
• Krippendorff's Alpha
• Aickin's Alpha
• weighted_alpha method

Changed

• Single class bug fixed
• CLASS_NUMBER_ERROR error type changed to pycmMatrixError
• relabel method bug fixed
• Document modified
• README.md modified

2.7 - 2020-05-11

Added

• average method
• weighted_average method
• weighted_kappa method
• pycmAverageError class
• Bangdiwala's B
• MATLAB examples
• Github action

Changed

• Document modified
• README.md modified
• relabel method bug fixed
• sparse_table_print function bug fixed
• matrix_check function bug fixed
• Minor bug in Compare class fixed
• Class names mismatch bug fixed

2.6 - 2020-03-25

Added

• custom_rounder function
• complement function
• sparse_matrix attribute
• sparse_normalized_matrix attribute
• Net benefit (NB)
• Yule's Q interpretation (QI)
• Adjusted Rand index (ARI)
• TNR micro/macro
• FPR micro/macro
• FNR micro/macro

Changed

• sparse parameter added to print_matrix,print_normalized_matrix and save_stat methods
• header parameter added to save_csv method
• Handler functions moved to pycm_handler.py
• Error objects moved to pycm_error.py
• Verified tests references updated
• Verified tests moved to verified_test.py
• Test system modified
• CONTRIBUTING.md updated
• Namespace optimized
• README.md modified
• Document modified
• print_normalized_matrix method modified
• normalized_table_calc function modified
• setup.py modified
• summary mode updated
• Dockerfile updated
• Python 3.8 added to .travis.yaml and appveyor.yml

Removed

• PC_PI_calc function

2.5 - 2019-10-16

Added

• __version__ variable
• Individual classification success index (ICSI)
• Classification success index (CSI)
• Example-8 (Confidence interval)
• install.sh
• autopep8.sh
• Dockerfile
• CI method (supported statistics : ACC,AUC,Overall ACC,Kappa,TPR,TNR,PPV,NPV,PLR,NLR,PRE)

Changed

• test.sh moved to .travis folder
• Python 3.4 support dropped
• Python 2.7 support dropped
• AUTHORS.md updated
• save_stat,save_csv and save_html methods Non-ASCII character bug fixed
• Mixed type input vectors bug fixed
• CONTRIBUTING.md updated
• Example-3 updated
• README.md modified
• Document modified
• CI attribute renamed to CI95
• kappa_se_calc function renamed to kappa_SE_calc
• se_calc function modified and renamed to SE_calc
• CI/SE functions moved to pycm_ci.py
• Minor bug in save_html method fixed

2.4 - 2019-07-31

Added

• Tversky index (TI)
• Area under the PR curve (AUPR)
• FUNDING.yml

Changed

• AUC_calc function modified
• Document modified
• summary parameter added to save_html,save_stat,save_csv and stat methods
• sample_weight bug in numpy array format fixed
• Inputs manipulation bug fixed
• Test system modified
• Warning system modified
• alt_link parameter added to save_html method and online_help function
• Compare class tests moved to compare_test.py
• Warning tests moved to warning_test.py

2.3 - 2019-06-27

Added

• Adjusted F-score (AGF)
• Overlap coefficient (OC)
• Otsuka-Ochiai coefficient (OOC)

Changed

• save_stat and save_vector parameters added to save_obj method
• Document modified
• README.md modified
• Parameters recommendation for imbalance dataset modified
• Minor bug in Compare class fixed
• pycm_help function modified
• Benchmarks color modified

2.2 - 2019-05-30

Added

• Negative likelihood ratio interpretation (NLRI)
• Cramer's benchmark (SOA5)
• Matthews correlation coefficient interpretation (MCCI)
• Matthews's benchmark (SOA6)
• F1 macro
• F1 micro
• Accuracy macro

Changed

• Compare class score calculation modified
• Parameters recommendation for multi-class dataset modified
• Parameters recommendation for imbalance dataset modified
• README.md modified
• Document modified
• Logo updated

2.1 - 2019-05-06

Added

• Adjusted geometric mean (AGM)
• Yule's Q (Q)
• Compare class and parameters recommendation system block diagrams

Changed

• Document links bug fixed
• Document modified

2.0 - 2019-04-15

Added

• G-Mean (GM)
• Index of balanced accuracy (IBA)
• Optimized precision (OP)
• Pearson's C (C)
• Compare class
• Parameters recommendation warning
• ConfusionMatrix equal method

Changed

• Document modified
• stat_print function bug fixed
• table_print function bug fixed
• Beta parameter renamed to beta (F_calc function & F_beta method)
• Parameters recommendation for imbalance dataset modified
• normalize parameter added to save_html method
• pycm_func.py splitted into pycm_class_func.py and pycm_overall_func.py
• vector_filter,vector_check,class_check and matrix_check functions moved to pycm_util.py
• RACC_calc and RACCU_calc functions exception handler modified
• Docstrings modified

1.9 - 2019-02-25

Added

• Automatic/Manual (AM)
• Bray-Curtis dissimilarity (BCD)
• CODE_OF_CONDUCT.md
• ISSUE_TEMPLATE.md
• PULL_REQUEST_TEMPLATE.md
• CONTRIBUTING.md
• X11 color names support for save_html method
• Parameters recommendation system
• Warning message for high dimension matrix print
• Interactive notebooks section (binder)

Changed

• save_matrix and normalize parameters added to save_csv method
• README.md modified
• Document modified
• ConfusionMatrix.__init__ optimized
• Document and examples output files moved to different folders
• Test system modified
• relabel method bug fixed

1.8 - 2019-01-05

Added

• Lift score (LS)
• version_check.py

Changed

• color parameter added to save_html method
• Error messages modified
• Document modified
• Website changed to http://www.pycm.ir
• Interpretation functions moved to pycm_interpret.py
• Utility functions moved to pycm_util.py
• Unnecessary else and elif removed
• == changed to is

1.7 - 2018-12-18

Added

• Gini index (GI)
• Example-7
• pycm_profile.py

Changed

• class_name parameter added to stat,save_stat,save_csv and save_html methods
• overall_param and class_param parameters empty list bug fixed
• matrix_params_calc, matrix_params_from_table and vector_filter functions optimized
• overall_MCC_calc, CEN_misclassification_calc and convex_combination functions optimized
• Document modified

1.6 - 2018-12-06

Added

• AUC value interpretation (AUCI)
• Example-6
• Anaconda cloud package

Changed

• overall_param and class_param parameters added to stat,save_stat and save_html methods
• class_param parameter added to save_csv method
• _ removed from overall statistics names
• README.md modified
• Document modified

1.5 - 2018-11-26

Added

• Relative classifier information (RCI)
• Discriminator power (DP)
• Youden's index (Y)
• Discriminant power interpretation (DPI)
• Positive likelihood ratio interpretation (PLRI)
• __len__ method
• relabel method
• __class_stat_init__ function
• __overall_stat_init__ function
• matrix attribute as dict
• normalized_matrix attribute as dict
• normalized_table attribute as dict

Changed

• README.md modified
• Document modified
• LR+ renamed to PLR
• LR- renamed to NLR
• normalized_matrix method renamed to print_normalized_matrix
• matrix method renamed to print_matrix
• entropy_calc fixed
• cross_entropy_calc fixed
• conditional_entropy_calc fixed
• print_table bug for large numbers fixed
• JSON key bug in save_obj fixed
• transpose bug in save_obj fixed
• Python 3.7 added to .travis.yaml and appveyor.yml

1.4 - 2018-11-12

Added

• Area under curve (AUC)
• AUNU
• AUNP
• Class balance accuracy (CBA)
• Global performance index (RR)
• Overall MCC
• Distance index (dInd)
• Similarity index (sInd)
• one_vs_all
• dev-requirements.txt

Changed

• README.md modified
• Document modified
• save_stat modified
• requirements.txt modified

1.3 - 2018-10-10

Added

• Confusion entropy (CEN)
• Overall confusion entropy (Overall CEN)
• Modified confusion entropy (MCEN)
• Overall modified confusion entropy (Overall MCEN)
• Information score (IS)

Changed

• README.md modified

1.2 - 2018-10-01

Added

• No information rate (NIR)
• P-Value
• sample_weight
• transpose

Changed

• README.md modified
• Key error in some parameters fixed
• OSX env added to .travis.yml

1.1 - 2018-09-08

Added

• Zero-one loss
• Support
• online_help function

Changed

• README.md modified
• html_table function modified
• table_print function modified
• normalized_table_print function modified

1.0 - 2018-08-30

Added

• Hamming loss

Changed

• README.md modified

0.9.5 - 2018-07-08

Added

• Obj load
• Obj save
• Example-4

Changed

• README.md modified
• Block diagram updated

0.9 - 2018-06-28

Added

• Activation threshold
• Example-3
• Jaccard index
• Overall Jaccard index

Changed

• README.md modified
• setup.py modified

0.8.6 - 2018-05-31

Added

• Example section in document
• Python 2.7 CI
• JOSS paper pdf

Changed

• Cite section
• ConfusionMatrix docstring
• round function changed to numpy.around
• README.md modified

0.8.5 - 2018-05-21

Added

• Example-1 (Comparison of three different classifiers)
• Example-2 (How to plot via matplotlib)
• JOSS paper
• ConfusionMatrix docstring

Changed

• Table size in HTML report
• Test system
• README.md modified

0.8.1 - 2018-03-22

Added

• Goodman and Kruskal's lambda B
• Goodman and Kruskal's lambda A
• Cross entropy
• Conditional entropy
• Joint entropy
• Reference entropy
• Response entropy
• Kullback-Liebler divergence
• Direct ConfusionMatrix
• Kappa unbiased
• Kappa no prevalence
• Random accuracy unbiased
• pycmVectorError class
• pycmMatrixError class
• Mutual information
• Support numpy arrays

Changed

• Notebook file updated

Removed

• pycmError class

0.7 - 2018-02-26

Added

• Cramer's V
• 95% confidence interval
• Chi-Squared
• Phi-Squared
• Chi-Squared DF
• Standard error
• Kappa standard error
• Kappa 95% confidence interval
• Cicchetti benchmark

Changed

• Overall statistics color in HTML report
• Parameters description link in HTML report

0.6 - 2018-02-21

Added

• CSV report
• Changelog
• Output files
• digit parameter to ConfusionMatrix object

Changed

• Confusion matrix color in HTML report
• Parameters description link in HTML report
• Capitalize descriptions

0.5 - 2018-02-17

Added

• Scott's pi
• Gwet's AC1
• Bennett S score
• HTML report

0.4 - 2018-02-05

Added

• TPR micro/macro
• PPV micro/macro
• Overall RACC
• Error rate (ERR)
• FBeta score
• F0.5
• F2
• Fleiss benchmark
• Altman benchmark
• Output file(.pycm)

Changed

• Class with zero item
• Normalized matrix

Removed

• Kappa and SOA for each class

0.3 - 2018-01-27

Added

• Kappa
• Random accuracy
• Landis and Koch benchmark
• overall_stat

0.2 - 2018-01-24

Added

• Population
• Condition positive
• Condition negative
• Test outcome positive
• Test outcome negative
• Prevalence
• G-measure
• Matrix method
• Normalized matrix method
• Params method

Changed

• statistic_result to class_stat
• params to stat

0.1 - 2018-01-22

Added

• ACC
• BM
• DOR
• F1-Score
• FDR
• FNR
• FOR
• FPR
• LR+
• LR-
• MCC
• MK
• NPV
• PPV
• TNR
• TPR
• documents and README.md