Abstract
Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context.
Highlights
One key aspect of graph signal processing (GSP) is defining the graph connectivity. This can be done considering the natural interactions from the context where the graph signal is defined, it is desirable to develop formal statistical methods; that is, given a set of multivariate samples where every sample component is assigned to a node of the graph, the graph connectivity which best describes the implicit dependences between any two nodes can be learned
We can see that in the non-Gaussian cases (a) (b) and (c), partial correlation coefficient (PCC) cannot decrease the error with increased training set size
independent component analysis (ICA)-PCC methods improve on PCC after a sufficient number of training samples and maintain a decreased error for an increased training set size
Summary
The partial correlation coefficient (PCC) [1] is a classical concept that has relevance in a variety of statistical signal processing problems. One key aspect of GSP is defining the graph connectivity. This can be done considering the natural interactions from the context where the graph signal is defined (e.g., time or space proximity between two nodes), it is desirable to develop formal statistical methods; that is, given a set of multivariate samples where every sample component is assigned to a node of the graph, the graph connectivity which best describes the implicit dependences between any two nodes can be learned. Apart from this work, and to our knowledge, there have been no other attempts to consider non-Gaussian models in graph connectivity learning
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
