71 research outputs found
On the notion of weak isometry for finite metric spaces
No full textFinite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing rescaling of the distance functions. In this paper, we analyse some of the possible complete and incomplete invariants for weak isometry and we introduce a dissimilarity measure that asses how far two spaces are from being weakly isometric. Furthermore, we compare these ideas with the theory of persistent homology, to study how the two are related
Comparing point clouds
No full textMemoli, Facundo; Sapiro, Guillermo. (2004). Comparing point clouds. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4032
A theoretical and computational framework for isometry invariant recognition of point cloud data
No full textMemoli, Facundo; Sapiro, Guillermo. (2004). A theoretical and computational framework for isometry invariant recognition of point cloud data. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4035
Meshless geometric subdivision
No full textMoenning, Carsten; Memoli, Facundo; Sapiro, Guillermo. (2004). Meshless geometric subdivision. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4031
Brain and surface warping via minimizing Lipschitz extensions
No full textMemoli, Facundo; Sapiro, Guillermo; Thompson, Paul. (2005). Brain and surface warping via minimizing Lipschitz extensions. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4214
Distance functions and geodesics on point clouds
No full textA new paradigm for computing intrinsic distance functions and geodesics on sub-manifolds of Rd given by point clouds is introduced in this paper. The basic idea is that, as shown here, intrinsic distance functions and geodesics on general co-dimension sub-manifolds of Rd can be accurately approximated by extrinsic Euclidean ones computed inside a thin offset band surrounding the manifold...Memoli, Facundo; Sapiro, Guillermo. (2003). Distance functions and geodesics on point clouds. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3924
Interleaving by Parts: Join Decompositions of Interleavings and Join-Assemblage of Geodesics
No full textMetrics of interest in topological data analysis (TDA) are often explicitly or implicitly in the form of an interleaving distance d(I )between poset maps (i.e. order-preserving maps), e.g. the Gromov-Hausdorff distance between metric spaces can be reformulated in this way. We propose a representation of a poset map F : P ? Q as a join (i.e. supremum) V-b?B F-b of simpler poset maps F-b (for a join dense subset B ? Q) which in turn yields a decomposition of dI into a product metric. The decomposition of d(I) is simple, but its ramifications are manifold: (1) We can construct a geodesic path between any poset maps F and G with d(I)(F, G) < 8 by assembling geodesics between all F(b)s and G(b)s via the join operation. This construction generalizes at least three constructions of geodesic paths that have appeared in the literature. (2) We can extend the Gromov-Hausdorff distance to a distance between simplicial filtrations over an arbitrary poset with a flow, preserving its universality and geodesicity. (3) We can clarify equivalence between several known metrics on multiparameter hierarchical clusterings. (4) We can illuminate the relationship between the erosion distance by Patel and the graded rank function by Betthauser, Bubenik, and Edwards, which in turn takes us to an interpretation on the representation V-b F-b as a generalization of persistence landscapes and graded rank functions.
CALIBRATION AND VALIDATION OF A MACROSCOPIC TRAFFIC FLOW MODEL BASED ON PLATOON DISPERSION AND QUEUE PROPAGATION
No full textThis paper proposes a preliminary calibration and validation of a macroscopic traffic flow model for signalised junctions. In fact, on the network signal setting design problem, a reliable modelling approach must be adopted to acknowledge the traffic flow effects, considering two phenomena: queue dispersion and spillback. The proposed model is an extension of the space-time discrete Cell Transmission Model (CTM), which can simulate dispersion and horizontal queue. This preliminary calibration and validation use real-world data collected on an arterial of the city of Salerno (south of Italy). Results showed that the estimated parameters are consistent with the literature
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