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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 the tensor factorization 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.

We present a protein fold recognition method, MANIFOLD, which uses the similarity between target and template proteins in predicted secondary structure, sequence and enzyme code to predict the fold of the target protein. We developed a non-linear ranking scheme in order to combine the scores of the three different similarity measures used. For a difficult test set of proteins with very little sequence similarity, the program predicts the fold class correctly in 34% of cases. This is an over twofold increase in accuracy compared with sequence-based methods such as PSI-BLAST or GenTHREADER, which score 13-14% correct first hits for the same test set. The functional similarity term increases the prediction accuracy by up to 3% compared with using the combination of secondary structure similarity and PSI-BLAST alone. We argue that using functional and secondary structure information can increase the fold recognition beyond sequence similarity.

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