Confusion matrix

Table layout for visualizing performance; also called an error matrix / From Wikipedia, the free encyclopedia

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In the field of machine learning and specifically the problem of statistical classification, a confusion matrix, also known as error matrix,[11] is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one; in unsupervised learning it is usually called a matching matrix.

Table info: ...
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)
specificity, selectivity or true negative rate (TNR)
precision or positive predictive value (PPV)
negative predictive value (NPV)
miss rate or false negative rate (FNR)
fall-out or false positive rate (FPR)
false discovery rate (FDR)
false omission rate (FOR)
Positive likelihood ratio (LR+)
Negative likelihood ratio (LR-)
prevalence threshold (PT)
threat score (TS) or critical success index (CSI)

accuracy (ACC)
balanced accuracy (BA)
F1 score
is the harmonic mean of precision and sensitivity:
phi coefficient (φ or rφ) or Matthews correlation coefficient (MCC)
Fowlkes–Mallows index (FM)
informedness or bookmaker informedness (BM)
markedness (MK) or deltaP (Δp)
Diagnostic odds ratio (DOR)

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]


Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa both variants are found in the literature.[12] The name stems from the fact that it makes it easy to see whether the system is confusing two classes (i.e. commonly mislabeling one as another).

It is a special kind of contingency table, with two dimensions ("actual" and "predicted"), and identical sets of "classes" in both dimensions (each combination of dimension and class is a variable in the contingency table).