Multiclassification: objectives and metrics


Name	Used for optimization	User-defined parameters	Formula and/or description
MultiClass	+	use_weights Default: true	Calculation principles $\text{[math]}$ $\text{[math]}$
MultiClassOneVsAll	+	use_weights Default: true	Calculation principles $\text{[math]}$ $\text{[math]}$
Precision	–	use_weights Default: true	This function is calculated separately for each class k numbered from 0 to M – 1. Calculation principles $\text{[math]}$
Recall	–	use_weights Default: true	This function is calculated separately for each class k numbered from 0 to M – 1. Calculation principles $\text{[math]}$
F1	–	use_weights Default: true	This function is calculated separately for each class k numbered from 0 to M – 1. Calculation principles $\text{[math]}$
TotalF1	–	use_weights Default: true	Calculation principles $\text{[math]}$ $\text{[math]}$ is the sum of the weights of the documents which correspond to the k class. If document weights are not specified $\text{[math]}$ stands for the number of times the k class, which corresponds to the i-th object, is found among the label values.
MCC	–	use_weights Default: true	Calculation principles This functions is defined in terms of a $\text{[math]}$ confusion matrix $\text{[math]}$ (where k is the number of classes): $\text{[math]}$ See the Wikipedia article for more details.
Accuracy	–	use_weights Default: true	Calculation principles $\text{[math]}$ $\text{[math]}$
HingeLoss	–	use_weights Default: true	See the Wikipedia article.
HammingLoss	–	use_weights Default: true	Calculation principles $\text{[math]}$
ZeroOneLoss	–	use_weights Default: true	Calculation principles $\text{[math]}$
Kappa	–	–	Calculation principles $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ is the weighted number of times class k is predicted by the model $\text{[math]}$ is the weighted number of times class k is set as the label for input objects
WKappa	–	–	Calculation principles See the formula on page 3 of the A note on the linearly weighted kappa coefficient for ordinal scales paper.


Name	Used for optimization	User-defined parameters	Formula and/or description
MultiClass	+	use_weights Default: true	Calculation principles $\text{[math]}$ $\text{[math]}$
MultiClassOneVsAll	+	use_weights Default: true	Calculation principles $\text{[math]}$ $\text{[math]}$
Precision	–	use_weights Default: true	This function is calculated separately for each class k numbered from 0 to M – 1. Calculation principles $\text{[math]}$
Recall	–	use_weights Default: true	This function is calculated separately for each class k numbered from 0 to M – 1. Calculation principles $\text{[math]}$
F1	–	use_weights Default: true	This function is calculated separately for each class k numbered from 0 to M – 1. Calculation principles $\text{[math]}$
TotalF1	–	use_weights Default: true	Calculation principles $\text{[math]}$ $\text{[math]}$ is the sum of the weights of the documents which correspond to the k class. If document weights are not specified $\text{[math]}$ stands for the number of times the k class, which corresponds to the i-th object, is found among the label values.
MCC	–	use_weights Default: true	Calculation principles This functions is defined in terms of a $\text{[math]}$ confusion matrix $\text{[math]}$ (where k is the number of classes): $\text{[math]}$ See the Wikipedia article for more details.
Accuracy	–	use_weights Default: true	Calculation principles $\text{[math]}$ $\text{[math]}$
HingeLoss	–	use_weights Default: true	See the Wikipedia article.
HammingLoss	–	use_weights Default: true	Calculation principles $\text{[math]}$
ZeroOneLoss	–	use_weights Default: true	Calculation principles $\text{[math]}$
Kappa	–	–	Calculation principles $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ is the weighted number of times class k is predicted by the model $\text{[math]}$ is the weighted number of times class k is set as the label for input objects
WKappa	–	–	Calculation principles See the formula on page 3 of the A note on the linearly weighted kappa coefficient for ordinal scales paper.