查看“模板:Confusion matrix terms”的源代码

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|+ Terminology and derivations<br/>from a [[confusion matrix]]
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; condition positive (P): the number of real positive cases in the data
; condition negative (N): the number of real negative cases in the data
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; true positive (TP): A test result that correctly indicates the presence of a condition or characteristic
; true negative (TN): A test result that correctly indicates the absence of a condition or characteristic
; false positive (FP), Type I error: A test result which wrongly indicates that a particular condition or attribute is present
; false negative (FN), Type II error: A test result which wrongly indicates that a particular condition or attribute is absent
----
; [[sensitivity (test)|sensitivity]], [[Precision_and_recall#Recall|recall]], [[hit rate]], or [[sensitivity (test)|true positive rate]] (TPR): <math>\mathrm{TPR} = \frac {\mathrm{TP}} {\mathrm{P}} = \frac {\mathrm{TP}} {\mathrm{TP}+\mathrm{FN}}= 1 - \mathrm{FNR}</math>
; [[Specificity (tests)|specificity]], [[Specificity (tests)|selectivity]] or [[Specificity (tests)|true negative rate]] (TNR): <math>\mathrm{TNR} = \frac {\mathrm{TN}} {\mathrm{N}} = \frac {\mathrm{TN}} {\mathrm{TN} + \mathrm{FP}} = 1 - \mathrm{FPR}</math>
; [[Precision_and_recall#Precision|precision]] or [[positive predictive value]] (PPV): <math>\mathrm{PPV} = \frac {\mathrm{TP}} {\mathrm{TP} + \mathrm{FP}} = 1 - \mathrm{FDR}</math>
; [[negative predictive value]] (NPV): <math>\mathrm{NPV} = \frac {\mathrm{TN}} {\mathrm{TN} + \mathrm{FN}} = 1 - \mathrm{FOR}</math>
; miss rate or [[Type I and type II errors#False positive and false negative rates|false negative rate]] (FNR): <math>\mathrm{FNR} = \frac {\mathrm{FN}} {\mathrm{P}} = \frac {\mathrm{FN}} {\mathrm{FN} + \mathrm{TP}} = 1 - \mathrm{TPR} </math>
; [[False positive rate|fall-out]] or [[False positive rate|false positive rate]] (FPR): <math>\mathrm{FPR} = \frac {\mathrm{FP}} {\mathrm{N}} = \frac {\mathrm{FP}} {\mathrm{FP} + \mathrm{TN}} = 1 - \mathrm{TNR}</math>
; [[false discovery rate]] (FDR): <math>\mathrm{FDR} = \frac {\mathrm{FP}} {\mathrm{FP} + \mathrm{TP}} = 1 - \mathrm{PPV} </math>
; [[Positive and negative predictive values|false omission rate]] (FOR): <math>\mathrm{FOR} = \frac {\mathrm{FN}} {\mathrm{FN} + \mathrm{TN}} = 1 - \mathrm{NPV} </math>
; [[Positive likelihood ratio]] (LR+): <math>\mathrm{LR+} = \frac {\mathrm{TPR}} {\mathrm{FPR}} </math>
; [[Negative likelihood ratio]] (LR-): <math>\mathrm{LR-} = \frac {\mathrm{FNR}} {\mathrm{TNR}} </math>
; [[prevalence threshold]] (PT): <math>\mathrm{PT}= \frac{\sqrt{\mathrm{FPR}}}{\sqrt{\mathrm{TPR}} + \sqrt{\mathrm{FPR}}} </math>
; threat score (TS) or critical success index (CSI): <math>\mathrm{TS} = \frac{\mathrm{TP}}{\mathrm{TP} + \mathrm{FN} + \mathrm{FP}}</math>
----
; [[Prevalence]]: <math> \frac {\mathrm{P}} {\mathrm{P} + \mathrm{N}} </math>
; [[accuracy]] (ACC): <math>\mathrm{ACC} = \frac {\mathrm{TP} + \mathrm{TN}} {\mathrm{P} + \mathrm{N}} = \frac {\mathrm{TP} + \mathrm{TN}} {\mathrm{TP} + \mathrm{TN} + \mathrm{FP} + \mathrm{FN}} </math>
; balanced accuracy (BA): <math>\mathrm{BA} = \frac {\mathrm{TPR} + \mathrm{TNR}}{2} </math>
; [[F1 score]]: is the [[Harmonic mean#Harmonic mean of two numbers|harmonic mean]] of [[Information retrieval#Precision|precision]] and [[sensitivity (test)|sensitivity]]: <math>\mathrm{F}_1 = 2 \times \frac {\mathrm{PPV} \times \mathrm{TPR}} {\mathrm{PPV} + \mathrm{TPR}} = \frac {2 \mathrm{TP}} {2 \mathrm{TP} + \mathrm{FP} + \mathrm{FN}}</math>
; [[phi coefficient]] (φ or r<sub>φ</sub>) or [[Matthews correlation coefficient]] (MCC): <math> \mathrm{MCC} = \frac{ \mathrm{TP} \times \mathrm{TN} - \mathrm{FP} \times \mathrm{FN} } {\sqrt{ (\mathrm{TP}+\mathrm{FP}) ( \mathrm{TP} + \mathrm{FN} ) ( \mathrm{TN} + \mathrm{FP} ) ( \mathrm{TN} + \mathrm{FN} ) } }</math>
; [[Fowlkes–Mallows index]] (FM): <math> \mathrm{FM} = \mathrm{\sqrt{\frac {TP}{TP+FP} \times \frac{TP}{TP+FN}} = \sqrt{ PPV \times TPR }}</math>
; [[informedness]] or bookmaker informedness (BM): <math> \mathrm{BM} = \mathrm{TPR} + \mathrm{TNR} - 1</math>
; [[markedness]] (MK) or deltaP (Δp): <math> \mathrm{MK} = \mathrm{PPV} + \mathrm{NPV} - 1</math>
; [[Diagnostic odds ratio]] (DOR): <math> \mathrm{DOR} = \frac {\mathrm{LR+}} {\mathrm{LR-}} </math>

<span style="font-size:90%;">''Sources:'' Fawcett (2006),<ref>{{cite journal |last=Fawcett |first=Tom |title=An Introduction to ROC Analysis |journal=Pattern Recognition Letters |date=2006 |volume=27 |issue=8 |pages=861–874 |doi=10.1016/j.patrec.2005.10.010 |bibcode=2006PaReL..27..861F |s2cid=2027090 |url=http://people.inf.elte.hu/kiss/11dwhdm/roc.pdf}}</ref> Piryonesi and El-Diraby (2020),<ref>{{Cite journal|last1=Piryonesi S. Madeh|last2=El-Diraby Tamer E.|date=2020-03-01|title=Data Analytics in Asset Management: Cost-Effective Prediction of the Pavement Condition Index|journal=Journal of Infrastructure Systems|volume=26|issue=1|pages=04019036|doi=10.1061/(ASCE)IS.1943-555X.0000512|s2cid=213782055 }}</ref>
Powers (2011),<ref>{{cite journal |first=David M. W. |last=Powers |date=2011 |title=Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation |journal=Journal of Machine Learning Technologies |volume=2 |issue=1 |pages=37–63 |url=https://www.researchgate.net/publication/228529307}}</ref> Ting (2011),<ref>{{cite book |last=Ting |first=Kai Ming |editor2-first=Geoffrey I. |editor2-last=Webb |editor1-first=Claude |editor1-last=Sammut |title=Encyclopedia of machine learning |date=2011 |publisher=Springer |doi=10.1007/978-0-387-30164-8 |isbn=978-0-387-30164-8 }}</ref> CAWCR,<ref>{{cite web |url=https://www.cawcr.gov.au/projects/verification/ |title=WWRP/WGNE Joint Working Group on Forecast Verification Research |last1=Brooks |first1=Harold |last2=Brown |first2=Barb |last3=Ebert |first3=Beth |last4=Ferro |first4=Chris |last5=Jolliffe |first5=Ian |last6=Koh |first6=Tieh-Yong |last7=Roebber |first7=Paul |last8=Stephenson |first8=David |date=2015-01-26|website=Collaboration for Australian Weather and Climate Research|publisher=World Meteorological Organisation|access-date=2019-07-17}}</ref> {{Nowrap|D. Chicco & G. Jurman (2020, 2021, 2023)}},<ref>{{cite journal |author=Chicco D. |author2=Jurman G. |title = The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation |journal = BMC Genomics |volume = 21 |issue = 1 |date = January 2020 |page = 6-1–6-13 |pmid = 31898477 |doi = 10.1186/s12864-019-6413-7 |pmc = 6941312 |doi-access=free }}</ref><ref>{{cite journal |author=Chicco D. |author2=Toetsch N. |author3=Jurman G. |title = The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation |journal = BioData Mining |volume = 14 |issue = 13 |date = February 2021 |page = 13 |pmid = 33541410 | pmc = 7863449 |doi = 10.1186/s13040-021-00244-z |doi-access=free }}</ref><ref>{{cite journal |author = Chicco D. |author2 = Jurman G. | title = The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification | journal = BioData Mining | date = 2023 | volume = 16 | issue = 1 |page = 4 | doi = 10.1186/s13040-023-00322-4  |pmid = 36800973 | pmc = 9938573 |doi-access = free}}</ref>  Tharwat (2018).<ref>{{cite journal |author = Tharwat A. |title = Classification assessment methods |journal = Applied Computing and Informatics |date = August 2018 |volume = 17 |pages = 168–192 |doi = 10.1016/j.aci.2018.08.003 |doi-access = free }}</ref> Balayla (2020)<ref>{{cite journal |last=Balayla |first=Jacques |title=Prevalence threshold (ϕe) and the geometry of screening curves |journal=PLOS ONE |date=2020 |volume=15 |issue=10 |pages=e0240215 |doi=10.1371/journal.pone.0240215 |pmid=33027310 |pmc=7540853 |arxiv=2006.00398 |bibcode=2020PLoSO..1540215B |doi-access=free }}</ref></span>
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