Popular understanding of ovo and ovr

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In reality, we often encounter multi classification learning tasks . Some binary classification algorithms can be directly extended to multi classification , But in more cases , We are based on some strategies , Use the binary classification algorithm to solve the multi classification problem . for example ：OvO、OvR.

OvO

Suppose the distribution of the training data set is shown in the figure below （ among A,B,C Represents the category of training data ）：

If you want to use logistic regression algorithm to solve this problem 3 Classification problem , have access to OvO.OvO(One Vs One) It is a strategy to use binary classification algorithm to solve multi classification problem . From the literal meaning, we can see that its core idea is one-on-one . So-called “ One ”, It refers to categories . and “ Yes ” It refers to the combination of two different categories from the training set to train multiple classifiers .

The rules of division are simple , It's a combination ($C_n^2$, among n Indicates the number of categories in the training set , In this case for 3). As shown in the figure below ( Each rectangle represents a division )：

Use these 3 Species division , The divided training set trains the binary classifier , You can get 3 A classifier . At this point, the training phase has been completed . As shown in the figure below ：

In the prediction phase , Just throw the test samples to those trained in the training stage 3 A classifier is used to predict , The final will be 3 The results predicted by classifiers are counted , The result with the highest number of votes is the predicted result . As shown in the figure below ：

OvR

Suppose the distribution of the training data set is shown in the figure below （ among A,B,C Represents the category of training data ）：

If you want to use logistic regression algorithm to solve this problem 3 Classification problem , have access to OvR.OvR(One Vs Rest) It is a strategy to use binary classification algorithm to solve multi classification problem . From the literal meaning, we can see that its core idea is A pair of surplus . A pair of surplus means to be right n When classifying samples by category , Take one sample as a class , Consider all the remaining types of samples as another class , In this way n A dichotomous question . So and OvO equally , It needs to be divided in the training stage .

The division is also very simple , As shown in the figure below ：

Use these 3 Species division , The divided training set trains the binary classifier , You can get 3 A classifier . At this point, the training phase has been completed . As shown in the figure below ：

In the prediction phase , Just throw the test samples to those trained in the training stage 3 A classifier is used to predict , Finally, choose the category with the highest probability as the final result . As shown in the figure below ：