scholarly journals Intrinsic Wavelet Regression for Curves of Hermitian Positive Definite Matrices

Author(s):  
Joris Chau ◽  
Rainer von Sachs
2011 ◽  
Vol 435 (2) ◽  
pp. 307-322 ◽  
Author(s):  
Hosoo Lee ◽  
Yongdo Lim ◽  
Takeaki Yamazaki

Author(s):  
David Barber

Finding clusters of well-connected nodes in a graph is a problem common to many domains, including social networks, the Internet and bioinformatics. From a computational viewpoint, finding these clusters or graph communities is a difficult problem. We use a clique matrix decomposition based on a statistical description that encourages clusters to be well connected and few in number. The formal intractability of inferring the clusters is addressed using a variational approximation inspired by mean-field theories in statistical mechanics. Clique matrices also play a natural role in parametrizing positive definite matrices under zero constraints on elements of the matrix. We show that clique matrices can parametrize all positive definite matrices restricted according to a decomposable graph and form a structured factor analysis approximation in the non-decomposable case. Extensions to conjugate Bayesian covariance priors and more general non-Gaussian independence models are briefly discussed.


2009 ◽  
Vol 3 (2) ◽  
pp. 64-76 ◽  
Author(s):  
Masatoshi Ito ◽  
Yuki Seo ◽  
Takeaki Yamazaki ◽  
Masahiro Yanagida

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