Bipartite graph partitioning and data clustering

Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, we propose a new data clustering method based on partitioning the underlying bipartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. We show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. We point out the connection of our clustering algorithm to correspondence analysis used in multivariate analysis. We also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, we apply our clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.Comment: Proceedings of ACM CIKM 2001, the Tenth International Conference on Information and Knowledge Management, 200

Understanding the white-light flare on 2012 March 9 : Evidence of a two-step magnetic reconnection

We attempt to understand the white-light flare (WLF) that was observed on 2012 March 9 with a newly constructed multi-wavelength solar telescope called the Optical and Near-infrared Solar Eruption Tracer (ONSET). We analyzed WLF observations in radio, H-alpha, white-light, ultraviolet, and X-ray bands. We also studied the magnetic configuration of the flare via the nonlinear force-free field (NLFFF) extrapolation and the vector magnetic field observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). Continuum emission enhancement clearly appeared at the 3600 angstrom and 4250 angstrom bands, with peak contrasts of 25% and 12%, respectively. The continuum emission enhancement closely coincided with the impulsive increase in the hard X-ray emission and a microwave type III burst at 03:40 UT. We find that the WLF appeared at one end of either the sheared or twisted field lines or both. There was also a long-lasting phase in the H-alpha and soft X-ray bands after the white-light emission peak. In particular, a second, yet stronger, peak appeared at 03:56 UT in the microwave band. This event shows clear evidence that the white-light emission was caused by energetic particles bombarding the lower solar atmosphere. A two-step magnetic reconnection scenario is proposed to explain the entire process of flare evolution, i.e., the first-step magnetic reconnection between the field lines that are highly sheared or twisted or both, and the second-step one in the current sheet, which is stretched by the erupting flux rope. The WLF is supposed to be triggered in the first-step magnetic reconnection at a relatively low altitude.Comment: 4 pages, 4 figures, published in A&A Lette