模板:Confusion matrix terms

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{{{CRITERION}}}

Terminology and derivations
from a confusion matrix
condition positive (P) the number of real positive cases in the data condition negative (N) the number of real negative cases in the data 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, recall, hit rate, or true positive rate (TPR) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{TPR} = \frac {\mathrm{TP}} {\mathrm{P}} = \frac {\mathrm{TP}} {\mathrm{TP}+\mathrm{FN}}= 1 - \mathrm{FNR}} specificity, selectivity or true negative rate (TNR) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{TNR} = \frac {\mathrm{TN}} {\mathrm{N}} = \frac {\mathrm{TN}} {\mathrm{TN} + \mathrm{FP}} = 1 - \mathrm{FPR}} precision or positive predictive value (PPV) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{PPV} = \frac {\mathrm{TP}} {\mathrm{TP} + \mathrm{FP}} = 1 - \mathrm{FDR}} negative predictive value (NPV) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{NPV} = \frac {\mathrm{TN}} {\mathrm{TN} + \mathrm{FN}} = 1 - \mathrm{FOR}} miss rate or false negative rate (FNR) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{FNR} = \frac {\mathrm{FN}} {\mathrm{P}} = \frac {\mathrm{FN}} {\mathrm{FN} + \mathrm{TP}} = 1 - \mathrm{TPR} } fall-out or false positive rate (FPR) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{FPR} = \frac {\mathrm{FP}} {\mathrm{N}} = \frac {\mathrm{FP}} {\mathrm{FP} + \mathrm{TN}} = 1 - \mathrm{TNR}} false discovery rate (FDR) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{FDR} = \frac {\mathrm{FP}} {\mathrm{FP} + \mathrm{TP}} = 1 - \mathrm{PPV} } false omission rate (FOR) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{FOR} = \frac {\mathrm{FN}} {\mathrm{FN} + \mathrm{TN}} = 1 - \mathrm{NPV} } Positive likelihood ratio (LR+) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{LR+} = \frac {\mathrm{TPR}} {\mathrm{FPR}} } Negative likelihood ratio (LR-) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{LR-} = \frac {\mathrm{FNR}} {\mathrm{TNR}} } prevalence threshold (PT) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{PT}= \frac{\sqrt{\mathrm{FPR}}}{\sqrt{\mathrm{TPR}} + \sqrt{\mathrm{FPR}}} } threat score (TS) or critical success index (CSI) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{TS} = \frac{\mathrm{TP}}{\mathrm{TP} + \mathrm{FN} + \mathrm{FP}}} Prevalence 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \frac {\mathrm{P}} {\mathrm{P} + \mathrm{N}} } accuracy (ACC) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{ACC} = \frac {\mathrm{TP} + \mathrm{TN}} {\mathrm{P} + \mathrm{N}} = \frac {\mathrm{TP} + \mathrm{TN}} {\mathrm{TP} + \mathrm{TN} + \mathrm{FP} + \mathrm{FN}} } balanced accuracy (BA) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{BA} = \frac {\mathrm{TPR} + \mathrm{TNR}}{2} } F1 score is the harmonic mean of precision and sensitivity: 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \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}}} phi coefficient (φ or r_φ) or Matthews correlation coefficient (MCC) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \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} ) } }} Fowlkes–Mallows index (FM) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{FM} = \mathrm{\sqrt{\frac {TP}{TP+FP} \times \frac{TP}{TP+FN}} = \sqrt{ PPV \times TPR }}} informedness or bookmaker informedness (BM) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{BM} = \mathrm{TPR} + \mathrm{TNR} - 1} markedness (MK) or deltaP (Δp) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{MK} = \mathrm{PPV} + \mathrm{NPV} - 1} Diagnostic odds ratio (DOR) 解析失败 (SVG（MathML可通过浏览器插件启用）：从服务器“https://wikimedia.org/api/rest_v1/”返回无效的响应（“Math extension cannot connect to Restbase.”）：): {\displaystyle \mathrm{DOR} = \frac {\mathrm{LR+}} {\mathrm{LR-}} } Sources: Fawcett (2006),^[1] Piryonesi and El-Diraby (2020),^[2] Powers (2011),^[3] Ting (2011),^[4] CAWCR,^[5] D. Chicco & G. Jurman (2020, 2021, 2023),^[6]^[7]^[8] Tharwat (2018).^[9] Balayla (2020)^[10]

↑ Fawcett, Tom (2006). "An Introduction to ROC Analysis" (PDF). Pattern Recognition Letters. 27 (8): 861–874. Bibcode:2006PaReL..27..861F. doi:10.1016/j.patrec.2005.10.010. S2CID 2027090.
↑ Piryonesi S. Madeh; El-Diraby Tamer E. (2020-03-01). "Data Analytics in Asset Management: Cost-Effective Prediction of the Pavement Condition Index". Journal of Infrastructure Systems. 26 (1): 04019036. doi:10.1061/(ASCE)IS.1943-555X.0000512. S2CID 213782055.
↑ Powers, David M. W. (2011). "Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation". Journal of Machine Learning Technologies. 2 (1): 37–63.
↑ Ting, Kai Ming (2011). Sammut, Claude; Webb, Geoffrey I. (eds.). Encyclopedia of machine learning. Springer. doi:10.1007/978-0-387-30164-8. ISBN 978-0-387-30164-8.
↑ Brooks, Harold; Brown, Barb; Ebert, Beth; Ferro, Chris; Jolliffe, Ian; Koh, Tieh-Yong; Roebber, Paul; Stephenson, David (2015-01-26). "WWRP/WGNE Joint Working Group on Forecast Verification Research". Collaboration for Australian Weather and Climate Research. World Meteorological Organisation. Retrieved 2019-07-17.
↑ Chicco D.; Jurman G. (January 2020). "The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation". BMC Genomics. 21 (1): 6-1–6-13. doi:10.1186/s12864-019-6413-7. PMC 6941312. PMID 31898477.
↑ Chicco D.; Toetsch N.; Jurman G. (February 2021). "The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation". BioData Mining. 14 (13): 13. doi:10.1186/s13040-021-00244-z. PMC 7863449. PMID 33541410.
↑ Chicco D.; Jurman G. (2023). "The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification". BioData Mining. 16 (1): 4. doi:10.1186/s13040-023-00322-4. PMC 9938573. PMID 36800973.
↑ Tharwat A. (August 2018). "Classification assessment methods". Applied Computing and Informatics. 17: 168–192. doi:10.1016/j.aci.2018.08.003.
↑ Balayla, Jacques (2020). "Prevalence threshold (ϕe) and the geometry of screening curves". PLOS ONE. 15 (10): e0240215. arXiv:2006.00398. Bibcode:2020PLoSO..1540215B. doi:10.1371/journal.pone.0240215. PMC 7540853. PMID 33027310.

[1] Fawcett, Tom (2006). "An Introduction to ROC Analysis" (PDF). Pattern Recognition Letters. 27 (8): 861–874. Bibcode:2006PaReL..27..861F. doi:10.1016/j.patrec.2005.10.010. S2CID 2027090.

[2] Piryonesi S. Madeh; El-Diraby Tamer E. (2020-03-01). "Data Analytics in Asset Management: Cost-Effective Prediction of the Pavement Condition Index". Journal of Infrastructure Systems. 26 (1): 04019036. doi:10.1061/(ASCE)IS.1943-555X.0000512. S2CID 213782055.

[3] Powers, David M. W. (2011). "Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation". Journal of Machine Learning Technologies. 2 (1): 37–63.

[4] Ting, Kai Ming (2011). Sammut, Claude; Webb, Geoffrey I. (eds.). Encyclopedia of machine learning. Springer. doi:10.1007/978-0-387-30164-8. ISBN 978-0-387-30164-8.

[5] Brooks, Harold; Brown, Barb; Ebert, Beth; Ferro, Chris; Jolliffe, Ian; Koh, Tieh-Yong; Roebber, Paul; Stephenson, David (2015-01-26). "WWRP/WGNE Joint Working Group on Forecast Verification Research". Collaboration for Australian Weather and Climate Research. World Meteorological Organisation. Retrieved 2019-07-17.

[6] Chicco D.; Jurman G. (January 2020). "The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation". BMC Genomics. 21 (1): 6-1–6-13. doi:10.1186/s12864-019-6413-7. PMC 6941312. PMID 31898477.

[7] Chicco D.; Toetsch N.; Jurman G. (February 2021). "The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation". BioData Mining. 14 (13): 13. doi:10.1186/s13040-021-00244-z. PMC 7863449. PMID 33541410.

[8] Chicco D.; Jurman G. (2023). "The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification". BioData Mining. 16 (1): 4. doi:10.1186/s13040-023-00322-4. PMC 9938573. PMID 36800973.

[9] Tharwat A. (August 2018). "Classification assessment methods". Applied Computing and Informatics. 17: 168–192. doi:10.1016/j.aci.2018.08.003.

[10] Balayla, Jacques (2020). "Prevalence threshold (ϕe) and the geometry of screening curves". PLOS ONE. 15 (10): e0240215. arXiv:2006.00398. Bibcode:2020PLoSO..1540215B. doi:10.1371/journal.pone.0240215. PMC 7540853. PMID 33027310.

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