so , the prediction of liquefaction potential of soil due to an earthquake is an important step for earthquake hazard mitigation . there are various techniques available for the determination of liquefaction potential of soil in the literature [ 113 ] researchers used artificial intelligence ( ai ) techniques for the prediction of liquefaction susceptibility of soil [ 1425 ] . this article adopts cone penetration test ( cpt ) based minimax probability machine ( mpm ) for the prediction of seismic liquefaction potential of soil . many cpt tests were conducted after the earthquake . two models ( model i and model ii ) model i adopts cone resistance ( qc ) and cyclic stress ratio ( csr ) as input variables . qc and peck ground acceleration ( pga ) have been used as inputs of the model ii . in mpm , it is assumed that positive definite covariance matrices exist in each of the two classes . in mpm , the probability of misclassification of future data is minimized . in mpm , following optimal hyperplane is used for separating the two classes of points.(1)atz = ba , zrn;br in mpm , the following optimization problem is constructed : ( 2)max,b , a0constraint : infpr{atxb}infpr{atyb}where  is called the worst - case accuracy . the above optimization problem ( 2 ) so , it takes the following form.(3)max,aconstraint :- b+atxatxa - b - atyatya the optimization problem ( 3 ) is written in the following form : minaatya+atxa(4)subjected to : at(x - y)=1the above optimization problem ( 4 ) is solved by convex programming technique . to develop the above mpm , non - liquefied sites are denoted by + 1 and liquefied sites are denoted by 1 . in mpm , training dataset is adopted to develop the model and a testing is employed to verify the developed mpm . this study adopts radial basis function k(xi , x)=exp-(xi - x)(xi - x)t22 ( where  is width of radial basis function ) as kernel function for developing the mpm . the success of mpm depends on the choice of proper value of . this study adopts trial and error approach for the determination of the design value of . training and testing performance have been determined by using the following equation.(5)training / testing performance(%)=no of data predicted accurately by mpmtotal data100fig . 1 shows the effect of  on training performance ( % ) for model i. it is observed from fig . 1 that the developed mpm gives best training performance at   =  0.19 for model i. the developed mpm gives 100% training performance . tables 1 and 2 illustrate the performance of mpm for training and testing dataset respectively . 2 that the best training performance has been achieved at   =  0.13 . the performance of mpm for training and testing dataset has been depicted in tables 1 and 2 , respectively . 3 plots the results of model ii . the generalization capability of developed model ii has been examined by the global datasets . these global datasets consists information about liquefiable and non - liquefiable soil of five earthquakes . two models ( model i and model ii ) have been tried to get best performance . this study shows that the developed mpm can predict liquefaction potential of soil based on qc and pga . geotechnical engineers can use the developed charts for the determination of seismic liquefaction potential of soil .
the evaluation of liquefaction potential of soil due to an earthquake is an important step in geosciences . 
 this article examines the capability of minimax probability machine ( mpm ) for the prediction of seismic liquefaction potential of soil based on the cone penetration test ( cpt ) data . 
 the dataset has been taken from chi  chi earthquake . 
 mpm is developed based on the use of hyperplanes . 
 it has been adopted as a classification tool . 
 this article uses two models ( model i and model ii ) . 
 model i employs cone resistance ( qc ) and cyclic stress ratio ( csr ) as input variables . 
 qc and peak ground acceleration ( pga ) have been taken as inputs for model ii . 
 the developed mpm gives 100% accuracy . 
 the results show that the developed mpm can predict liquefaction potential of soil based on qc and pga .