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This paper presents a reduced kernel-based classification model for multi-category discrimination of sets or objects. The proposed model is based on the Tikhonov regularization scheme. This approach extends Mangasarian reduced support vector machine (RSVM) model in a least square framework for the case of multi-categorical discrimination. The dimension reduction of the kernel matrix is achieved by selecting random subsets of the training set. Advantages of this formulation include explicit expressions for the classification weights of the classifier(s), its ability to incorporate several classes in a single optimization problem, and computational tractability in providing the optimal classification weights for multi-categorical separation. Computational results are also provided for two-phase flow data.