Dejan Slepcev RSS Feed
https://kilthub.cmu.edu/authors/Dejan_Slepcev/3894058
RSS feed for Figshare Profile Dejan Slepcev<![CDATA[A variational approach to the consistency of spectral clustering]]>https://kilthub.cmu.edu/articles/journal_contribution/A_variational_approach_to_the_consistency_of_spectral_clustering/6476741
https://kilthub.cmu.edu/articles/journal_contribution/A_variational_approach_to_the_consistency_of_spectral_clustering/6476741
Fri, 07 Aug 2015 00:00:00 GMT<![CDATA[Average-distance problem for parameterized curves]]>https://kilthub.cmu.edu/articles/journal_contribution/Average-distance_problem_for_parameterized_curves/6476942
https://kilthub.cmu.edu/articles/journal_contribution/Average-distance_problem_for_parameterized_curves/6476942
0 for p ≥ 1 and λ > 0 we consider the functional
E(γ) = Z Rd d(x, Γγ) p dµ(x) + λ Length(γ)
where γ : I → R d , I is an interval in R, Γγ = γ(I), and d(x, Γγ) is the distance of x to Γγ. The problem is closely related to the average-distance problem, where the admissible class are the connected sets of finite Hausdorff measure H1 , and to (regularized) principal curves studied in statistics. We obtain regularity of minimizers in the form of estimates on the total curvature of the minimizers. We prove that for measures µ supported in two dimensions the minimizing curve is injective if p ≥ 2 or if µ has bounded density. This establishes that the minimization over parameterized curves is equivalent to minimizing over embedded curves and thus confirms that the problem has a geometric interpretation.]]>Mon, 01 Dec 2014 00:00:00 GMT<![CDATA[Consistency of Cheeger and Ratio Graph Cuts]]>https://kilthub.cmu.edu/articles/journal_contribution/Consistency_of_Cheeger_and_Ratio_Graph_Cuts/6477125
https://kilthub.cmu.edu/articles/journal_contribution/Consistency_of_Cheeger_and_Ratio_Graph_Cuts/6477125
Mon, 24 Nov 2014 00:00:00 GMT<![CDATA[Continuum limit of total variation on point clouds]]>https://kilthub.cmu.edu/articles/journal_contribution/Continuum_limit_of_total_variation_on_point_clouds/6477140
https://kilthub.cmu.edu/articles/journal_contribution/Continuum_limit_of_total_variation_on_point_clouds/6477140
Tue, 16 Sep 2014 00:00:00 GMT<![CDATA[Existence of Ground States of Nonlocal-Interaction Energies]]>https://kilthub.cmu.edu/articles/journal_contribution/Existence_of_Ground_States_of_Nonlocal-Interaction_Energies/6477377
https://kilthub.cmu.edu/articles/journal_contribution/Existence_of_Ground_States_of_Nonlocal-Interaction_Energies/6477377
Thu, 01 May 2014 00:00:00 GMT<![CDATA[Nonlocal-interaction equations on uniformly prox-regular sets]]>https://kilthub.cmu.edu/articles/journal_contribution/Nonlocal-interaction_equations_on_uniformly_prox-regular_sets/6478553
https://kilthub.cmu.edu/articles/journal_contribution/Nonlocal-interaction_equations_on_uniformly_prox-regular_sets/6478553
Wed, 30 Apr 2014 00:00:00 GMT<![CDATA[Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries]]>https://kilthub.cmu.edu/articles/journal_contribution/Nonlocal_Interaction_Equations_in_Environments_with_Heterogeneities_and_Boundaries/6478550
https://kilthub.cmu.edu/articles/journal_contribution/Nonlocal_Interaction_Equations_in_Environments_with_Heterogeneities_and_Boundaries/6478550
Thu, 31 Oct 2013 00:00:00 GMT<![CDATA[Mean-Curvature Flow of Voronoi Diagrams]]>https://kilthub.cmu.edu/articles/journal_contribution/Mean-Curvature_Flow_of_Voronoi_Diagrams/6478373
https://kilthub.cmu.edu/articles/journal_contribution/Mean-Curvature_Flow_of_Voronoi_Diagrams/6478373
Thu, 01 Aug 2013 00:00:00 GMT<![CDATA[Properties of Minimizers of Average-Distance Problem via Discrete Approximation of Measures]]>https://kilthub.cmu.edu/articles/journal_contribution/Properties_of_Minimizers_of_Average-Distance_Problem_via_Discrete_Approximation_of_Measures/6479171
https://kilthub.cmu.edu/articles/journal_contribution/Properties_of_Minimizers_of_Average-Distance_Problem_via_Discrete_Approximation_of_Measures/6479171
0, the averagedistance problem, in the penalized formulation, is to minimize
(0.1) E λ µ (Σ) := Z Rd d(x, Σ)dµ(x) + λH1 (Σ),
among pathwise connected, closed sets, Σ. Here d(x, Σ) is the distance from a point to a set and H1 is the 1-Hausdorff measure. In a sense the problem is to find a onedimensional measure that best approximates µ. It is known that the minimizer Σ is topologically a tree whose branches are rectifiable curves. The branches may not be C 1 , even for measures µ with smooth density. Here we show a result on weak second-order regularity of branches. Namely we show that arc-length-parameterized branches have BV derivatives and provide a priori estimates on the BV norm. The technique we use is to approximate the measure µ, in the weak-∗ topology of measures, by discrete measures. Such approximation is also relevant for numerical computations. We prove the stability of the minimizers in appropriate spaces and also compare the topologies of the minimizers corresponding to the approximations with the minimizer corresponding to µ.]]>Tue, 08 Jan 2013 00:00:00 GMT<![CDATA[A linear optimal transportation framework for quantifying and visualizing variations in sets of images.]]>https://kilthub.cmu.edu/articles/journal_contribution/A_linear_optimal_transportation_framework_for_quantifying_and_visualizing_variations_in_sets_of_images_/6096221
https://kilthub.cmu.edu/articles/journal_contribution/A_linear_optimal_transportation_framework_for_quantifying_and_visualizing_variations_in_sets_of_images_/6096221
Tue, 01 Jan 2013 00:00:00 GMT<![CDATA[Counterexample to regularity in average-distance problem]]>https://kilthub.cmu.edu/articles/journal_contribution/Counterexample_to_regularity_in_average-distance_problem/6477167
https://kilthub.cmu.edu/articles/journal_contribution/Counterexample_to_regularity_in_average-distance_problem/6477167
0λ>0, d(x,Σ)d(x,Σ) is the distance from x to the set Σ , and H1H1 is the one-dimensional Hausdorff measure. Here we provide, for anyd⩾2d⩾2, an example of a measure μ with smooth density, and convex, compact support, such that the global minimizer of the functional is a rectifiable curve which is not C1C1. We also provide a similar example for the constrained form of the average-distance problem.]]>Mon, 01 Oct 2012 00:00:00 GMT<![CDATA[Crossover of the coarsening rates in demixing of binary viscous liquids]]>https://kilthub.cmu.edu/articles/journal_contribution/Crossover_of_the_coarsening_rates_in_demixing_of_binary_viscous_liquids/6477191
https://kilthub.cmu.edu/articles/journal_contribution/Crossover_of_the_coarsening_rates_in_demixing_of_binary_viscous_liquids/6477191
Thu, 12 Apr 2012 00:00:00 GMT<![CDATA[An optimal transportation approach for nuclear structure-based pathology.]]>https://kilthub.cmu.edu/articles/journal_contribution/An_optimal_transportation_approach_for_nuclear_structure-based_pathology_/6096284
https://kilthub.cmu.edu/articles/journal_contribution/An_optimal_transportation_approach_for_nuclear_structure-based_pathology_/6096284
Tue, 01 Mar 2011 00:00:00 GMT<![CDATA[Confinement in nonlocal interaction equations]]>https://kilthub.cmu.edu/articles/journal_contribution/Confinement_in_nonlocal_interaction_equations/6477119
https://kilthub.cmu.edu/articles/journal_contribution/Confinement_in_nonlocal_interaction_equations/6477119
Thu, 27 Jan 2011 00:00:00 GMT<![CDATA[Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion]]>https://kilthub.cmu.edu/articles/journal_contribution/Existence_and_uniqueness_of_solutions_to_an_aggregation_equation_with_degenerate_diffusion/6477368
https://kilthub.cmu.edu/articles/journal_contribution/Existence_and_uniqueness_of_solutions_to_an_aggregation_equation_with_degenerate_diffusion/6477368
Tue, 01 Sep 2009 00:00:00 GMT<![CDATA[Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations]]>https://kilthub.cmu.edu/articles/journal_contribution/Global-in-time_weak_measure_solutions_and_finite-time_aggregation_for_nonlocal_interaction_equations/6477560
https://kilthub.cmu.edu/articles/journal_contribution/Global-in-time_weak_measure_solutions_and_finite-time_aggregation_for_nonlocal_interaction_equations/6477560
Sat, 27 Jun 2009 00:00:00 GMT<![CDATA[Nonlinear mobility continuity equations and generalized displacement convexity]]>https://kilthub.cmu.edu/articles/journal_contribution/Nonlinear_mobility_continuity_equations_and_generalized_displacement_convexity/6478541
https://kilthub.cmu.edu/articles/journal_contribution/Nonlinear_mobility_continuity_equations_and_generalized_displacement_convexity/6478541
Thu, 01 Jan 2009 00:00:00 GMT