Table 2.

The GRSOMO and GRSOMU algorithms

(i) Let $\mathrm{T}$ be the original unbalanced training set with $n+m$ samples, where $n>m$. And let $\mathbf{T}=\mathbf{P}\cup \mathbf{N}$, where $\mathrm{P}$ contains only the data in the minority class with $m$ samples and $\mathrm{N}$ contains only data in the majority class with $n$ samples

(ii) IF GRSOMO is desired THEN DO steps (iii)–(v)

(iii) Use GRSOM to generate new data from $\mathrm{P}$ for $n-m$ samples such that $\mathrm{P}$ is used as an input of the GRSOM function, i.e. GRSOM($\mathbf{X}$,$t_{\text{max}}$) where $\mathbf{X}\Leftarrow \mathrm{P}$. Then, the function will return the $n-m$ samples which are contained in the new grown data set ${\mathbf{X}}^{+}$, i.e. ${\mathbf{X}}^{+}\Leftarrow$ GRSOM($\mathbf{X}$,$t_{\text{max}}$). Note that, in the case of over-sampling approach, $t_{\text{max}}\Leftarrow n-m-N(t=0)$

(iv) ${\mathbf{P}}^{+}\Leftarrow {\mathbf{X}}^{+}$ and ${\mathbf{P}}^{++}\Leftarrow \mathbf{P}\cup {\mathbf{P}}^{+}$. Thus, the number of samples in the minority class can be adjusted from $m$ to $m+(n-m)=n$ samples which equals to the number of samples in the majority class

(v) Define the balanced training set as ${\mathbf{T}}^{+}\Leftarrow {\mathbf{P}}^{++}\cup \mathbf{N}$ and GO TO ix)

(vi) IF GRSOMU is desired THEN DO steps vii) to viii)

(vii) Use GRSOM to generate new data from $\mathbf{N}$ for $m$ samples in which $\mathbf{N}$ is used as an input of the GRSOM function, i.e. GRSOM($\mathbf{X}$) where $\mathbf{X}\Leftarrow \mathbf{N}$. Then, the function will return the new grown data set ${\mathbf{X}}^{+}$ with $m$ samples, i.e. $t_{\text{max}}\Leftarrow m-N(t=0)$, ${\mathbf{X}}^{+}\Leftarrow$ GRSOM($\mathbf{X}$, $t_{\text{max}}$)

(viii) ${\mathbf{N}}^{+}\Leftarrow {\mathbf{X}}^{+}$ and ${\mathbf{T}}^{+}\Leftarrow {\mathbf{N}}^{+}\cup \mathbf{P}$. Note that only the $m$ samples will be generated for the majority class which equals to original number of samples in the minority class. This leads to the balanced training set ${\mathbf{T}}^{+}$

(ix) Return ${\mathbf{T}}^{+}$

(x) END