3,680 research outputs found
Statistical Traffic State Analysis in Large-scale Transportation Networks Using Locality-Preserving Non-negative Matrix Factorization
Statistical traffic data analysis is a hot topic in traffic management and
control. In this field, current research progresses focus on analyzing traffic
flows of individual links or local regions in a transportation network. Less
attention are paid to the global view of traffic states over the entire
network, which is important for modeling large-scale traffic scenes. Our aim is
precisely to propose a new methodology for extracting spatio-temporal traffic
patterns, ultimately for modeling large-scale traffic dynamics, and long-term
traffic forecasting. We attack this issue by utilizing Locality-Preserving
Non-negative Matrix Factorization (LPNMF) to derive low-dimensional
representation of network-level traffic states. Clustering is performed on the
compact LPNMF projections to unveil typical spatial patterns and temporal
dynamics of network-level traffic states. We have tested the proposed method on
simulated traffic data generated for a large-scale road network, and reported
experimental results validate the ability of our approach for extracting
meaningful large-scale space-time traffic patterns. Furthermore, the derived
clustering results provide an intuitive understanding of spatial-temporal
characteristics of traffic flows in the large-scale network, and a basis for
potential long-term forecasting.Comment: IET Intelligent Transport Systems (2013
Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables
Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety
of engineering and scientific fields. Dynamic mode decomposition (DMD), which
is a numerical algorithm for the spectral analysis of Koopman operators, has
been attracting attention as a way of obtaining global modal descriptions of
NLDSs without requiring explicit prior knowledge. However, since existing DMD
algorithms are in principle formulated based on the concatenation of scalar
observables, it is not directly applicable to data with dependent structures
among observables, which take, for example, the form of a sequence of graphs.
In this paper, we formulate Koopman spectral analysis for NLDSs with structures
among observables and propose an estimation algorithm for this problem. This
method can extract and visualize the underlying low-dimensional global dynamics
of NLDSs with structures among observables from data, which can be useful in
understanding the underlying dynamics of such NLDSs. To this end, we first
formulate the problem of estimating spectra of the Koopman operator defined in
vector-valued reproducing kernel Hilbert spaces, and then develop an estimation
procedure for this problem by reformulating tensor-based DMD. As a special case
of our method, we propose the method named as Graph DMD, which is a numerical
algorithm for Koopman spectral analysis of graph dynamical systems, using a
sequence of adjacency matrices. We investigate the empirical performance of our
method by using synthetic and real-world data.Comment: 34 pages with 4 figures, Published in Neural Networks, 201
LMI based Stability and Stabilization of Second-order Linear Repetitive Processes
This paper develops new results on the stability and control of a class of linear repetitive processes described by a second-order matrix discrete or differential equation. These are developed by transformation of the secondorder dynamics to those of an equivalent first-order descriptor state-space model, thus avoiding the need to invert a possibly ill-conditioned leading coefficient matrix in the original model
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