Nonnegative Tensor Co-Factorization and Its Unified Solution.

In this paper, we present a new joint factorization algorithm, called Nonnegative Tensor Co-Factorization (NTCoF). The key idea is to simultaneously factorize multiple visual features of the same data into nonnegative dimensionality-reduced representations, and meanwhile, to maximize the correlations of the low-dimensional representations. The data is generally encoded as tensors of arbitrary order, rather than vectors, to preserve the original data structures. NTCoF provides a simple and efficient way to fuse multiple complementary features for enhancing the discriminative power of the desired rank-reduced representations under the nonnegative constraints. We formulate the related objectives with a block-wise quadratic nonnegative function. To optimize, a unified convergence provable solution is developed. This solution is applicable for any nonnegative optimization problems with block-wise quadratic objective functions, and thus offer an unified platform based on which specific solution can be directly derived by skipping over tedious proof about algorithmic convergence. We apply the proposed algorithm and solution on three image tasks, face recognition, multi-class image categorization and multi-label image annotation. Results with comparisons on public challenging datasets show that the proposed algorithm can outperform both the traditional nonnegative methods and the popular feature combination methods.