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This talk introduces a new statistical model based on a permanent process for supervised and unsupervised classification problems. Unlike many research works in the literature, the proposed model assumes only exchangeability instead of independence on observations. Regardless of the number of classes or the dimension of the feature variables, the model may require only 2-3 parameters for fitting the covariance structure. It works well even if the class occupies non-convex, disjoint regions, or regions overlapped with other classes in the feature space. The application to DNA microarray analysis indicates that the proposed model is more capable of handling high-dimensional data. It can employ more feature variables in an efficient way and reduce the prediction error significantly. This is critical when the true classification relies on non-reducible high-dimensional features.