Mean vector component analysis: A new approach to un-centered PCA for non-negative data

Mean vector component analysis (MVCA) is here introduced as a new method for dimensionality reduction of non-negative data. The method is based on dimensionality reduction by preserving the squared length, and implicitly also the direction, of the mean vector of the original data. The optimal mean vector preserving basis is obtained from the spectral decomposition of the inner-product matrix, and is shown to capture clustering structure. MVCA corresponds to certain un-centered principal component analysis (PCA) axes. Unlike traditional PCA, these axes are in general not corresponding to the top eigenvalues. MVCA is shown to produce different visualizations and some times considerably improved clustering results for non-negative data, compared to PCA.