## Table of contents

- Overview
- Installation
- Usage
- Document
- Try PyCM in Your Browser
- Issues & Bug Reports
- Todo
- Outputs
- Dependencies
- Contribution
- References
- Cite
- Authors
- License
- Donate
- 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 an accurate evaluation of large variety of classifiers.

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## Installation

### Source code

- Download Version 2.0 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==2.0`

or`pip3 install pycm==2.0`

(Need root access)

### Conda

- Check Conda Managing Package
`conda install -c sepandhaghighi pycm`

(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
Pearson C 0.59568
Phi-Squared 0.55
RCI 0.34947
RR 4.0
Reference Entropy 1.5
Response Entropy 1.48336
SOA1(Landis & Koch) Fair
SOA2(Fleiss) Poor
SOA3(Altman) Fair
SOA4(Cicchetti) Poor
Scott PI 0.34426
Standard Error 0.14232
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
AM(Difference between automatic and manual classification) 2 -1 -1
AUC(Area under the roc curve) 0.88889 0.61111 0.58333
AUCI(AUC value interpretation) Very Good Fair Poor
BCD(Bray-Curtis dissimilarity) 0.08333 0.04167 0.04167
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
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) 0.65217 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
GI(Gini index) 0.77778 0.22222 0.16667
GM(G-mean geometric mean of specificity and sensitivity) 0.88192 0.54433 0.57735
IBA(Index of balanced accuracy) 0.95062 0.13169 0.27778
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) 0.6 0.3 0.17143
N(Condition negative) 9 9 6
NLR(Negative likelihood ratio) 0.0 0.75 0.75
NPV(Negative predictive value) 1.0 0.8 0.57143
OP(Optimized precision) 0.70833 0.29545 0.44048
P(Condition positive or support) 3 3 6
PLR(Positive likelihood ratio) 4.5 3.0 1.5
PLRI(Positive likelihood ratio interpretation) Poor Poor Poor
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
Y(Youden index) 0.77778 0.22222 0.16667
dInd(Distance index) 0.22222 0.67586 0.60093
sInd(Similarity index) 0.84287 0.52209 0.57508
>>> 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.print_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
Pearson C 0.43853
Phi-Squared 0.2381
RCI 0.20871
RR 4.0
Reference Entropy 0.95443
Response Entropy 0.54356
SOA1(Landis & Koch) Fair
SOA2(Fleiss) Poor
SOA3(Altman) Fair
SOA4(Cicchetti) Poor
Scott PI 0.33333
Standard Error 0.15309
TPR Macro 0.66667
TPR Micro 0.75
Zero-one Loss 2
Class Statistics :
Classes Class1 Class2
ACC(Accuracy) 0.75 0.75
AM(Difference between automatic and manual classification) -2 2
AUC(Area under the roc curve) 0.66667 0.66667
AUCI(AUC value interpretation) Fair Fair
BCD(Bray-Curtis dissimilarity) 0.125 0.125
BM(Informedness or bookmaker informedness) 0.33333 0.33333
CEN(Confusion entropy) 0.5 0.43083
DOR(Diagnostic odds ratio) None None
DP(Discriminant power) None None
DPI(Discriminant power interpretation) 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
GI(Gini index) 0.33333 0.33333
GM(G-mean geometric mean of specificity and sensitivity) 0.57735 0.57735
IBA(Index of balanced accuracy) 0.11111 0.55556
IS(Information score) 1.41504 0.19265
J(Jaccard index) 0.33333 0.71429
LS(Lift score) 2.66667 1.14286
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
NLR(Negative likelihood ratio) 0.66667 0.0
NPV(Negative predictive value) 0.71429 1.0
OP(Optimized precision) 0.25 0.25
P(Condition positive or support) 3 5
PLR(Positive likelihood ratio) None 1.5
PLRI(Positive likelihood ratio interpretation) None Poor
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
Y(Youden index) 0.33333 0.33333
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.print_matrix()
Predict Class1 Class2
Actual
Class1 1 2
Class2 0 5
```

`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'])
```

### 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)

### Parameter recommender

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.

```
>>> 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']
```

### Comapre

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.

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

### Acceptable data types

#### ConfusionMatrix

`actual_vector`

: python`list`

or numpy`array`

of any stringable objects`predict_vector`

: python`list`

or numpy`array`

of any stringable objects`matrix`

:`dict`

`digit`

:`int`

`threshold`

:`FunctionType (function or lambda)`

`file`

:`File object`

`sample_weight`

: python`list`

or numpy`array`

of numbers`transpose`

:`bool`

- Run
`help(ConfusionMatrix)`

for`ConfusionMatrix`

object details

#### Compare

`cm_dict`

: python`dict`

of`ConfusionMatrix`

object (`str`

:`ConfusionMatrix`

)`by_class`

:`bool`

`weight`

: python`dict`

of class weights (`class_name`

:`float`

)`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 service! Try it out now! :

- Check
`Examples`

in`Document`

folder

## Issues & bug reports

Just fill an issue and describe it. We'll check it ASAP! or send an email to info@pycm.ir.

- Please complete the issue template

## Todo

Moved here

## Outputs

## Dependencies

## Contribution

Moved here

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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.

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## 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} }

Download PyCM.bib

JOSS | |

Zenodo | |

Researchgate |

## License

## Donate to our project

If you do like our project and we hope that you do, can you please support us? Our project is not and is never going to be working for profit. We need the money just so we can continue doing what we do ;-) .