Abstract

Non-negative tensor factorization (NTF) has recently been proposed as sparse and efficient image representation (Wel ling and We- ber, Patt. Rec. Let., 2001). Until now, sparsity of the tensor factoriza- tion has been empirically observed in many cases, but there was no systematic way to control it. In this work, we show that a sparsity measure recently proposed for non-negative matrix factorization (Hoyer, J. Mach. Learn. Res., 2004) applies to NTF and allows precise control over sparseness of the resulting factorization. We devise an algorithm based on sequential conic programming and show improved performance over classical NTF codes on artificial and on real-world data sets.