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Multiplicative nonnegative graph embedding

In this paper, we study the problem of nonnegative graph embedding, originally investigated in [J. Yang et al., 2008] for reaping the benefits from both nonnegative data factorization and the specific purpose characterized by the intrinsic and penalty graphs. Our contributions are two-fold. On the one hand, we present a multiplicative iterative procedure for nonnegative graph embedding, which significantly reduces the computational cost compared with the iterative procedure in [14] involving the matrix inverse calculation of an M-matrix. On the other hand, the nonnegative graph embedding framework is expressed in a more general way by encoding each datum as a tensor of arbitrary order, which brings a group of byproducts, e.g., nonnegative discriminative tensor factorization algorithm, with admissible time and memory cost. Extensive experiments compared with the state-of-the-art algorithms on nonnegative data factorization, graph embedding, and tensor representation demonstrate the algorithmic properties in computation speed, sparsity, discriminating power, and robustness to realistic image occlusions.