Mining local structure is important in data analysis. Gaussian mixture is able to describe local structure through the covariance matrices, but when used on high dimensional data, fitly specifying such a large number of d(d + 1)=2 free elements in each covariance matrix is difficult. In this paper, by constraining the covariance matrix in decomposed orthonormal form, we propos a Local PCA algorithm to tackle this problem in help of RPCL competitive learning, which can automatically determine the number of local structure.