Local representation of faces through extended NMF

Presented is an extension of the non-negative matrix factorisation (NMF) by imposing an orthogonality constraint on the basis matrix and controlling the sparseness of the coefficient matrix for robust learning of compact local part-based representation of face images. The extended NMF is solved by a projected gradient algorithm with a data-driven initialisation scheme. In addition, an indicator is proposed to objectively measure the locality and compactness of local part-based representation and to quantitatively evaluate the efficiency of the extended NMF. Experimental results on benchmark face databases show that the proposed extended NMF is much more effective in learning local part-based representation and more tolerant to the variations, especially misalignment, of the training samples than conventional NMF and its major extensions.