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In this paper, the normal mixture model subjected to general linear restrictionfor component-means based on linear regression is proposed, and its tting methodby EM algorithm and Lagrange multiplier is provided. This model is applied togene clustering of microarray expression data, which demonstrates it has very goodperformances for real data set. This model also allows to obtain the clusters that ananalyst wants to nd out in the fashion that the hypothesis for component-meansis represented by the design matrices and the linear restriction matrices.