Paper Info
Title
The alignment distance on Spaces of Linear Dynamical Systems
Abstract
We introduce a family of group action induced distances on spaces of Linear Dynamical Systems (LDSs) of fixed size and order. The distance between two LDSs is computed by finding the change of basis that best aligns the state-space realizations of the two LDSs, hence the name alignment distance. This distance can be computed efficiently, hence it is particularly suitable for applications in modern dynamic data analysis (e.g., video sequence classification and clustering), where a large number of high-dimensional LDSs may need to be compared. Based on the alignment distance, we also define a notion of average between LDSs of the same size and order with the property that the order and in some cases stability are naturally preserved. Various extensions to the basic notion of alignment distance are also proposed.
Year
DOI
Venue
2013
10.1109/CDC.2013.6760039
Decision and Control
Keywords
Field
DocType
data analysis,linear systems,stability,state-space methods,time-varying systems,alignment distance,dynamic data analysis,group action induced distances,high-dimensional LDSs,linear dynamical systems spaces,stability,state-space realizations
Linear dynamical system,Linear system,Control theory,Computer science,Change of basis,Dynamic data,Cluster analysis
Conference
ISSN
ISBN
Citations 
0743-1546
978-1-4673-5714-2
6
PageRank 
References 
Authors
0.57
6
2
Name
Order
Citations
PageRank
Bijan Afsari113710.27
rene victor valqui vidal25331260.14