Algorithm 1 Geometrical Divide (GD)

dataParticles: list of data particles

featureVectors: list of data particle’s feature vectors $F=\left[f_1,f_2\right]$

newDataParticles: list of data particles created by divide

$N_{min}$: size of the smallest class

$d$$:d\in {\mathbb{N}}_{+}$$\mathbf{AND}{log}_2{N}_{min}<d$

FOR$i=2$; $i\le d$

$\mathbf{FOREACH}P\in \mathbf{d}\mathbf{a}\mathbf{t}\mathbf{a}\mathbf{P}\mathbf{a}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{c}\mathbf{l}\mathbf{e}\mathbf{s}$ DO

${\mathsf{\mu }}_P\leftarrow$ $\mathrm{centroid}\left(P\right)$          $//\mathsf{\mu }=\left[{\mu }_1,{\mu }_2\right]$

$C_P\leftarrow$ $\mathrm{geometricCentroid}\left(P\right)$   $//C=\left[c_1,c_2\right]$ dataParticle1 = List()           // create two empty lists dataParticle1

dataParticle2 = List()          // and dataParticle2 for new data particles

$\mathbf{FOREACH}F\in \mathbf{f}\mathbf{e}\mathbf{a}\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{e}\mathbf{V}\mathbf{e}\mathbf{c}\mathbf{t}\mathbf{o}\mathbf{r}\mathbf{s}$ DO

$\mathbf{IF}\left(f_2-{\mu }_2\right)\left(c_1-{\mu }_1\right)-\left(c_2-{\mu }_2\right)\left(f_1-{\mu }_1\right)>0$ THEN

$\mathrm{dataParticle}1\leftarrow$ $\mathrm{add}\left(\mathrm{returnParticle}\right(F\left)\right)$

ELSE $\mathrm{dataParticle}2\leftarrow$ $\mathrm{add}\left(\mathrm{returnParticle}\right(F\left)\right)$

END IF

END FOREACH

$\mathrm{newDataParticles}\leftarrow$ add(dataParticle1) $\mathrm{newDataParticles}\leftarrow$ add(dataParticle2)

END FOREACH

$\mathrm{dataParticles}\leftarrow$ newDataParticles

$\mathrm{newDataParticles}\leftarrow$ clear()

END FOR