RPCL-based local PCA algorithm

Mining local structure is important in data analysis. Gaussian mixture is able to describe local structure through covariance matrices, but when used on high-dimensional data, specifying such a large number of d(d+1)/2 free elements in each covariance matrix is difficult. By constraining the covariance matrix in decomposed orthonormal form, we propose a Local PCA algorithm to tackle this problem with the help of RPCL (Rival Penalized Competitive Learning), which can automatically determine the number of local structures.