781 research outputs found
Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting
In this work, we introduce a highly efficient algorithm to address the
nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix
factorization (NMF) with an additional underapproximation constraint. NMU
results are interesting as, compared to traditional NMF, they present
additional sparsity and part-based behavior, explaining unique data features.
To show these features in practice, we first present an application to the
analysis of climate data. We then present an NMU-based algorithm to robustly
fit multiple parametric models to a dataset. The proposed approach delivers
state-of-the-art results for the estimation of multiple fundamental matrices
and homographies, outperforming other alternatives in the literature and
exemplifying the use of efficient NMU computations
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
Probabilistic Archetypal Analysis
Archetypal analysis represents a set of observations as convex combinations
of pure patterns, or archetypes. The original geometric formulation of finding
archetypes by approximating the convex hull of the observations assumes them to
be real valued. This, unfortunately, is not compatible with many practical
situations. In this paper we revisit archetypal analysis from the basic
principles, and propose a probabilistic framework that accommodates other
observation types such as integers, binary, and probability vectors. We
corroborate the proposed methodology with convincing real-world applications on
finding archetypal winter tourists based on binary survey data, archetypal
disaster-affected countries based on disaster count data, and document
archetypes based on term-frequency data. We also present an appropriate
visualization tool to summarize archetypal analysis solution better.Comment: 24 pages; added literature review and visualizatio
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