We exploit the biconvex nature of the Euclidean non-negative matrix factorization (NMF) optimization problem to derive optimization schemes based on sequential quadratic and secon...
Non-negative tensor factorization (NTF) has recently been proposed as sparse and efficient image representation (Welling and Weber, Patt. Rec. Let., 2001). Until now, sparsity of t...
Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statisti...
Julien Mairal, Francis Bach, Jean Ponce, Guillermo...
We interpret non-negative matrix factorization geometrically, as the problem of finding a simplicial cone which contains a cloud of data points and which is contained in the posi...
We derive algorithms for finding a nonnegative n-dimensional tensor factorization (n-NTF) which includes the non-negative matrix factorization (NMF) as a particular case when n = ...