Keynote Plenary

A generic principle is presented for forming multiplicative update rules, which integrate an orthonormality constraint into nonnegative learning. The principle, called Orthogonal Nonnegative Learning (ONL), is rigorously derived from the Lagrangian technique. As an example, the proposed method is applied for transforming Nonnegative Matrix Factorization and its variants into their orthogonal versions. Also, an on-line positive PCA rule is derived.

In general, such orthogonal nonnegative learning can give very useful approximative solutions for problems involving non-vectorial data, for example, binary solutions. Combinatorial optimization is replaced by continuous-space gradient optimization which is often computationally lighter.

It is shown how the multiplicative update rules obtained by using the proposed ONL principle can find a nonnegative and highly orthogonal matrix for an approximated graph partitioning problem. The empirical results on various graphs indicate that our nonnegative learning algorithms not only outperform those without the orthogonality condition, but also surpass some other existing partitioning approaches.

Erkki Oja received the Dr.Sc. degree from Helsinki University of Technology in 1977. He is Director of the Adaptive Informatics Research Centre and Professor of Computer Science at the Department of Information and Computer Science, Helsinki University of Technology, Finland. He has been research associate at Brown University, Providence, RI, and visiting professor at the Tokyo Institute of Technology, Japan. He is the author or coauthor of about 300 articles and book chapters on pattern recognition, computer vision, and neural computing, and three books: "Subspace Methods of Pattern Recognition" (New York: Research Studies Press and Wiley, 1983), which has been translated into Chinese and Japanese; "Kohonen Maps" (Amsterdam, The Netherlands: Elsevier, 1999), and "Independent Component Analysis" (New York: Wiley, 2001; also translated into Chinese and Japanese). His research interests are in the study of principal component and independent component analysis, self-organization, statistical pattern recognition, and machine learning.

Prof. Oja is a member of the Finnish Academy of Sciences, Founding Fellow of the International Association of Pattern Recognition (IAPR), Fellow of the IEEE, Past President of the European Neural Network Society (ENNS), and Fellow of the International Neural Network Society (INNS). He is a member of the editorial boards of several journals and has been in the program committees of several recent conferences including the International Conference on Artificial Neural Networks (ICANN), International Joint Conference on Neural Networks (IJCNN), and Neural Information Processing Systems (NIPS). He holds an honorary doctorate from Uppsala University, Sweden, and was the recipient of the 2006 IEEE Computational Intelligence Society Neural Networks Pioneer Award.