Image patch analysis of sunspots and active regions. II. Clustering via matrix factorization

Separating active regions that are quiet from potentially eruptive ones is a key issue in Space Weather applications. Traditional classification schemes such as Mount Wilson and McIntosh have been effective in relating an active region large scale magnetic configuration to its ability to produce eruptive events. However, their qualitative nature prevents systematic studies of an active region's evolution for example. We introduce a new clustering of active regions that is based on the local geometry observed in Line of Sight magnetogram and continuum images. We use a reduced-dimension representation of an active region that is obtained by factoring the corresponding data matrix comprised of local image patches. Two factorizations can be compared via the definition of appropriate metrics on the resulting factors. The distances obtained from these metrics are then used to cluster the active regions. We find that these metrics result in natural clusterings of active regions. The clusterings are related to large scale descriptors of an active region such as its size, its local magnetic field distribution, and its complexity as measured by the Mount Wilson classification scheme. We also find that including data focused on the neutral line of an active region can result in an increased correspondence between our clustering results and other active region descriptors such as the Mount Wilson classifications and the $R$ value. We provide some recommendations for which metrics, matrix factorization techniques, and regions of interest to use to study active regions.Comment: Accepted for publication in the Journal of Space Weather and Space Climate (SWSC). 33 pages, 12 figure

A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and Optimality

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points of the nonconvex SymNMF problem. Furthermore, it achieves a global sublinear convergence rate. We also show that the algorithm can be efficiently implemented in parallel. Further, sufficient conditions are provided which guarantee the global and local optimality of the obtained solutions. Extensive numerical results performed on both synthetic and real data sets suggest that the proposed algorithm converges quickly to a local minimum solution.Comment: IEEE Transactions on Signal Processing (to appear

Online Unsupervised Multi-view Feature Selection

In the era of big data, it is becoming common to have data with multiple modalities or coming from multiple sources, known as "multi-view data". Multi-view data are usually unlabeled and come from high-dimensional spaces (such as language vocabularies), unsupervised multi-view feature selection is crucial to many applications. However, it is nontrivial due to the following challenges. First, there are too many instances or the feature dimensionality is too large. Thus, the data may not fit in memory. How to select useful features with limited memory space? Second, how to select features from streaming data and handles the concept drift? Third, how to leverage the consistent and complementary information from different views to improve the feature selection in the situation when the data are too big or come in as streams? To the best of our knowledge, none of the previous works can solve all the challenges simultaneously. In this paper, we propose an Online unsupervised Multi-View Feature Selection, OMVFS, which deals with large-scale/streaming multi-view data in an online fashion. OMVFS embeds unsupervised feature selection into a clustering algorithm via NMF with sparse learning. It further incorporates the graph regularization to preserve the local structure information and help select discriminative features. Instead of storing all the historical data, OMVFS processes the multi-view data chunk by chunk and aggregates all the necessary information into several small matrices. By using the buffering technique, the proposed OMVFS can reduce the computational and storage cost while taking advantage of the structure information. Furthermore, OMVFS can capture the concept drifts in the data streams. Extensive experiments on four real-world datasets show the effectiveness and efficiency of the proposed OMVFS method. More importantly, OMVFS is about 100 times faster than the off-line methods