This paper introduced a multi-class support vector machine through probabilistic constraints based on a geometric structure in which the inputs are random variables. In previous works, the inputs are restricted to bounded distribution functions, which sometimes do not respond. Here, we presented a modified model in which the input data set comes from unbounded distribution functions. The variables considered in the two states were from known and unknown populations. With statistical methods, we released the constraints of the primal problem from the probabilistic state and turned constraints into a linear combination of parameters of random variables. We used the bootstrap resampling, and then moment methods to sample and estimate model parameters, respectively. Simulation through statistical tools shows excellent performance. The obtained experimental results confirmed that our proposed model performs significantly better and is more effective regarding statistical indices in sampling, reducing error rate, and classification accuracy, compared to previous multi-class support vector machines based on geometric structure.

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