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Quadratic pencils arising from applications are often inherently structured. Factors contributing to the structure include the connectivity of elements within the underlying physical system and the mandatory nonnegativity of physical parameters. For physical feasibility, structural constraints must be respected. Consequently, they impose additional… (More)

In various applications, data in multi-dimensional space are normalized to unit length. This paper considers the problem of best fitting given points on the m-dimensional unit sphere S m−1 by k-dimensional great circles with k much less than m. The task is cast as an algebraically constrained low-rank matrix approximation problem. Using the fidelity of the… (More)

We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by non-negative matrix factorizations. Non-negative matrix factoriza-tion represents an emerging example of subspace methods which is able to extract interpretable parts from a set of template image objects and then to… (More)

Nonnegative matrix factorizations (NMF) have recently assumed an important role in several fields, such as pattern recognition, automated image exploitation, data clustering and so on. They represent a peculiar tool adopted to obtain a reduced representation of multivariate data by using additive components only, in order to learn parts-based… (More)