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What is Matthews Correlation Coefficient mean?
The Matthews correlation coefficient (MCC) or phi coefficient is used in machine learning as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975. The MCC is defined identically to Pearson's phi coefficient, introduced by Karl Pearson, also known as the Yule phi coefficient from its introduction by Udny Yule in 1912. Despite these antecedents which predate Matthews's use by several decades, the term MCC is widely used in the field of bioinformatics and machine learning.
The coefficient takes into account true and false positives and negatives and is generally regarded as a balanced measure which can be used even if the classes are of very different sizes. The MCC is in essence a correlation coefficient between the observed and predicted binary classifications; it returns a value between −1 and +1. A coefficient of +1 represents a perfect prediction, 0 no better than random prediction and −1 indicates total disagreement between prediction and observation. However, if MCC equals neither −1, 0, or +1, it is not a reliable indicator of how similar a predictor is to random guessing because MCC is dependent on the dataset. MCC is closely related to the chi-square statistic for a 2×2 contingency table
| MCC | = χ 2 n {\displaystyle |{\text{MCC}}|={\sqrt {\frac {\chi ^{2}}{n}}}}where n is the total number of observations.
While there is no perfect way of describing the confusion matrix of true and false positives and negatives by a single number, the Matthews correlation coefficient is generally regarded as being one of the best such measures. Other measures, such as the proportion of correct predictions (also termed accuracy), are not useful when the two classes are of very different sizes. For example, assigning every object to the larger set achieves a high proportion of correct predictions, but is not generally a useful classification.
The MCC can be calculated directly from the confusion matrix using the formula:
MCC = T P × T N − F P × F N ( referencePosted on 04 Nov 2024, this text provides information on Miscellaneous in Maths related to Maths. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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