@misc{yu2013largescale, abstract = {The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) the ability to tackle problems with a large number (say millions) of labels, and (b) the ability to handle data with missing labels. In this paper, we directly address both these problems by studying the multi-label problem in a generic empirical risk minimization (ERM) framework. Our framework, despite being simple, is surprisingly able to encompass several recent label-compression based methods which can be derived as special cases of our method. To optimize the ERM problem, we develop techniques that exploit the structure of specific loss functions - such as the squared loss function - to offer efficient algorithms. We further show that our learning framework admits formal excess risk bounds even in the presence of missing labels. Our risk bounds are tight and demonstrate better generalization performance for low-rank promoting trace-norm regularization when compared to (rank insensitive) Frobenius norm regularization. Finally, we present extensive empirical results on a variety of benchmark datasets and show that our methods perform significantly better than existing label compression based methods and can scale up to very large datasets such as the Wikipedia dataset.}, author = {Yu, Hsiang-Fu and Jain, Prateek and Kar, Purushottam and Dhillon, Inderjit S.}, interhash = {1252173520757338468a68e028494647}, intrahash = {716e5270c1dcb3a1e4eedf9934859021}, note = {cite arxiv:1307.5101}, title = {Large-scale Multi-label Learning with Missing Labels}, url = {http://arxiv.org/abs/1307.5101}, year = 2013 } @article{clauset-2004-70, author = {Clauset, Aaron and Newman, M. E. J. and Moore, Cristopher}, interhash = {2c68e3c981a00380692a3b0b661d7cfd}, intrahash = {0ea285bfc0f5a46ffec8a213e5133ba6}, journal = {Physical Review E}, pages = 066111, title = {Finding community structure in very large networks}, url = {http://www.citebase.org/abstract?id=oai:arXiv.org:cond-mat/0408187}, volume = 70, year = 2004 } @misc{citeulike:95936, abstract = {The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(m d log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in which case our algorithm runs in essentially linear time, O(n log^2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400,000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.}, author = {Clauset, Aaron and Newman, M. E. J. and Moore, Cristopher}, citeulike-article-id = {95936}, eprint = {cond-mat/0408187}, interhash = {2c68e3c981a00380692a3b0b661d7cfd}, intrahash = {f9a12630a6d31d576ea5222219a4cf0b}, month = {August}, priority = {0}, title = {Finding community structure in very large networks}, url = {http://arxiv.org/abs/cond-mat/0408187}, year = 2004 } @inproceedings{Ho98, address = {Granada}, author = {Hovy, E.H.}, booktitle = {Proc. 1st Intl. Conf. on Language Resources and Evaluation (LREC)}, interhash = {c8f274dc0380d76b5bb179152c47a959}, intrahash = {839e408657e0d8d6ca0b66fdae29063f}, isbn = {3-540-41066-X}, title = {Combining and Standardizing Large-Scale, Practical Ontologies for Machine Translation and Other Uses}, url = {http://www.isi.edu/natural-language/people/hovy/publications.html}, year = 1998 }