Computing the volume of a high-dimensional semi-unsupervised hierarchical copula

References

• Calinski , R. and Harabasz , J. 1974 . A dendrite method for cluster analysis . Commun. Statist. , 3 : 1 – 27 .
   Google Scholar
• Cherubini , U. and Romagnoli , S. 2009 . Computing the volume of n-dimensional copulas . Appl. Math. Finan. , 16 ( 4 ) : 307 – 314 .
   Google Scholar
• Cherubini , U. , Luciano , E. and Vecchiato , W. 2004 . Copula Methods in Finance , Chichester, , UK : Wiley Finance Series .
   Google Scholar
• Cifuentes , A. and O'Connor , G. 1996 . “ The binomial expansion method applied to CBO/CLO analysis ” . Moody's special report
   Google Scholar
• Cifuentes , A. , Efrat , I. , Glouck , J. and Murphy , E. 1999 . “ Buying and selling credit risk: a perspective on credit-linked obligations ” . In Credit Derivatives: Application for Risk management, Investment and Portfolio Optimization , 112 – 123 . London : Risk Books .
   Google Scholar
• Duffie , D. and Gârleanu , N. 2001 . Risk and valuation of collateralized debt obligations . Finan. Anal. J. , 57 ( 1 ) : 41 – 59 .
   Web of Science ®Google Scholar
• Embrechts , P. , Lindskog , F. and McNeil , A. 2003 . “ Modeling dependence with copulas and applications to risk management ” . In Handbook of Heavy Tailed Distributions in Finance , Edited by: Rachev , S. T. Amsterdam : Elsevier/North-Holland .
   Google Scholar
• Francois , D. , Wertz , V. and Verleysen , M. Non-Euclidean metrics for similarity search in noisy datasets . Proc. European Symposium on Artificial Neural Networks, ESANN 2005 .
   Google Scholar
• Hartigan , J. 1985 . Statistical theory in clustering . J. Class. , 2 ( 1 ) : 63 – 76 .
   Web of Science ®Google Scholar
• Joe , H. 1997 . Multivariate Models and Dependence Concepts , London : Chapman & Hall .
   Google Scholar
• Kohonen , T. and Honkela , T. 2007 . Kohonen network . Scholarpedia , 2 ( 1 ) : 1568
   Google Scholar
• Krzanowski , W. and Lai , Y. 1985 . A criterion for determining the number of groups in a dataset using sum of squares clustering . Biometrics , 44 : 23 – 34 .
   Web of Science ®Google Scholar
• Mc Neil , A. J. , Frey , R. and Embrechts , P. 2005 . Quantitative Risk Management: Concept, Techniques and Tools , Princeton, NJ : Princeton University Press .
   Google Scholar
• Muhr , M. and Granitzer , M. Automatic cluster number selection using split and merge K-means approach . 20th International Workshop on Database and Expert systems application . pp. 363 – 367 . Silver Spring, MD : IEEE .
   Google Scholar
• Nelsen , R. 2006 . Introduction to Copulas , Heidelberg : Springer .
   Google Scholar
• Pelleg , D. and Moore , A. X-means: Extending K-means with efficient estimation of the number of clusters . Proc. 17th International Conf. on Machine Learning . pp. 727 – 734 . San Francisco, CA : Morgan Kaufmann .
   Google Scholar
• Rouvinez , C. 2004 . “ Diversity scoring for market value CDOs ” . In Risk Annual: The Technical Papers of The Cutting Edge Section Of Risk , 514 – 516 . London : Risk Books .
   Google Scholar
• Savu , C. and Trede , M. 2006 . “ Hierarchical Archimedean Copulas ” . In International Conference on High Frequency Finance Konsstanz, , Germany May
   Google Scholar
• Schönbucher , P. J. 2003 . Taken to the limit: simple and not-so-simple loan loss distributions . Wilmott Magazine , 1 : 63 – 72 .
   Google Scholar
• Schorin , C. and Weinrich , S. 1998 . Collateralized debt obligation handbook , Morgan Stanley Dean Witter . Working paper
   Google Scholar
• Su , M. C. and Chou , C. H. 2001 . A modified version of the K-means algorithm with a distance based on cluster symmetry . IEEE Tran. Pattern Anal. Mach. Intell. , 23 ( 6 ) : 674 – 680 .
   Google Scholar
• Wang , L. , Bo , L. and Jiao , L. 2006 . “ A modified K-means clustering with a density-sensitive distance metric ” . 544 – 551 . Rough Sets and Knowledge Technology, Lecture notes in Computer Science, Vol. 4062
   Google Scholar
• Xing , E. P. , Ng , A. Y. , Jordan , M. I. and Russell , S. Distance metric learning, with application to clustering with side-information . Advances in Neural Information Processing System 2003 . Whistler, British Columbia, Canada. pp. 505 – 512 .
   Google Scholar