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Mean Vector Component Analysis for Visualization and Clustering of Nonnegative Data

Mean vector component analysis (MVCA) is introduced as a new method for visualization and clustering of nonnegative 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 it is shown to capture clustering structure. MVCA corresponds to certain uncentered 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 sometimes considerably improved clustering results for nonnegative data, compared with PCA.