Non-negative matrix factorization (NMF) provides the advantage of parts-based data representation through additive only combinations. It has been widely adopted in areas like item recommending, text mining, data clustering, speech denoising, etc. In this paper, we provide an algorithm that allows the factorization to have linear or approximately linear constraints with respect to each factor. We prove that if the constraint function is linear, algorithms within our multiplicative framework will converge. This theory supports a large variety of equality and inequality constraints, and can facilitate application of NMF to a much larger domain. Taking the recommender system as an example, we demonstrate how a specialized weighted and constrained NMF algorithm can be developed to fit exactly for the problem, and the tests justify that our constraints improve the performance for both weighted and unweighted NMF algorithms under several different metrics. In particular, on the Movie lens data with 94% of items, the Constrained NMF improves recall rate 3% compared to SVD50 and 45% compared to SVD150, which were reported as the best two in the top-N metric.

A web-based system is developed for the analysis and prediction of tropical cyclones, particularly their landfalls and recurvatures. To facilitate accessibility to the system, its development is based on Google Maps application programming interface (API), Java and client/server architecture. In addition to the construction of a powerful query system for the multi-source, multi-scale and multi-level tropical cyclone database, data mining approach and dynamic modelling approach have been implemented and integrated for effective and efficient analysis, prediction and visualization of tropical cyclone movements. The system can be accessed worldwide by researchers, professionals and the general public. It is thus a powerful system for research, real-life application and knowledge dissemination. Its extensibility and user-friendliness pave the road for further development and enable more in-depth analysis and real-time operation.