The analysis of convergence and its application is shown for the Active Sampling-at-the-Boundary method applied to multidimensional space using orthogonal pillar vectors. Active learning method facilitates identifying an optimal decision boundary for pattern classification in machine learning. The result of this method is compared with the standard active learning method that uses random sampling on the decision boundary hyperplane. The comparison is done through simulation and application to the real-world data from the UCI benchmark data set. The boundary is modeled as a nonseparable linear decision hyperplane in multidimensional space with a stochastic oracle.