In depth understanding of machine learning - unbalanced learning: sample sampling technology - [adasyn sampling method of manual sampling technology]

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And Borderline-SMOTE The algorithm is similar ,ADASYN（Adaptive Synthetic Sampling） The algorithm is also an improved SMOTE Algorithm . The algorithm is based on 2008 in , The main idea is to make full use of the density distribution information of samples to determine the frequency of each minority sample as the main sample , Synthesize more training data for a few difficult category samples , So as to correct the negative effects caused by the unbalanced distribution of categories as much as possible .

ADASYN The algorithm first needs to determine the number of new minority samples to be generated , namely $N^{+}\times \text{SR}$, Then in the original training set $S$ Find each minority sample on $x_i^{+},i=1,2,\cdots ,N^{+}$ Of $K$ a near neighbor , among , The first $i$ The number of nearest neighbors of the majority classes of the minority class samples is recorded as $N_i^{\text{major}}$, Then the proportion parameters of each minority sample can be determined by the following formula ${\Gamma }_i$：
$${\Gamma }_i=\frac{N_i^{\text{major}}}{Z\times K}$$

among ,$Z$ Is the standardization factor , To guarantee $\sum {\Gamma }_i=1$. After the proportion parameter is determined , The frequency that each minority sample is selected as the main sample can be determined by the following formula ：
$$g_i={\Gamma }_i\times N^{+}\times \text{SR}$$

It is not difficult to see from the above formula , And Borderline-SMOTE The algorithm is similar ,ADASYN The algorithm pays more attention to a few samples located near the decision boundary , They are selected as the main samples much more frequently than those located in a few decision-making areas . Of course , This will further amplify the propagation intensity of a few types of noise information ,ADASYN The specific flow of the algorithm is as follows ：

ADASYN Sampling method
Input ： Training set $S=\{(x_i,y_i),i=1,2,\cdots ,N,y_i\in \{+,-\}\}$; Number of samples of most classes $N^{-}$, Number of samples of a few classes $N^{+}$, among $N^{-}+N^{+}=N$; Unbalance ratio $\text{IR}=\frac{N^{-}}{N^{+}}$; Sampling rate $\text{SR}$; Proximity parameter $K$
Output ： Training set after oversampling $S=\{(x_i,y_i),i=1,2,\cdots ,N+N^{+}\times \text{SR},y_i\in \{+,-\}\}$
( 1 ) From the training set $S$ Take out all the samples of majority and minority classes , Make up the training sample set of most classes $S^{-}$ And a few training sample sets $S^{+}$
( 2 ) Set the newly generated sample set $S^{\text{New}}$ It's empty +
( 3 ) for$i=1:N^{+}$
( 4 ) \quad stay $S^{+}$ Find the corresponding sample in $x_i$
( 5 ) \quad stay $S$ Find $x_i$ Of $K$ a near neighbor , Record that the number of nearest neighbors of most classes is $N^{\text{major}}$
( 6 ) \quad Calculate its scale parameters ：${\Gamma }_i=\frac{N_i^{\text{major}}}{Z\times K}$
( 7 ) \quad Calculate the main sample frequency ：$g_i={\Gamma }_i\times N^{+}\times \text{SR}$
( 8 ) for$i=1:N^{+}$
( 9 ) \quad stay $S^{+}$ Select a main sample randomly $x_i$
(10) \quad for$i=1:g_i$
(11) \qquad call SMOTE Algorithm generates master samples $x_i$ A new sample of $x_i^{\text{new}}$
(12) \qquad add to $x_i^{\text{new}}$ to $S^{\text{New}}$：$S^{\text{New}}=S^{\text{New}}\cup x_i^{\text{new}}$
(13) return Training set after oversampling $S^{\prime }=S^{-}\cup S^{\text{New}}$