Consistency of Cheeger and Ratio Graph Cuts
Authors: Nicolás García Trillos, Dejan Slepčev, James von Brecht, Thomas Laurent, Xavier Bresson
JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Furthermore we provide numerical experiments that illustrate the results and explore the optimality of scaling in dimension two. ... In Section 8 we present numerical experiments which illustrate our results; we also investigate the issues related to Remark 2. |
| Researcher Affiliation | Academia | Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213, USA; Department of Mathematics and Statistics California State University, Long Beach Long Beach, CA 90840, USA; Department of Mathematics Loyola Marymount University 1 LMU Dr Los Angeles, CA 90045, USA; Institute of Electrical Engineering Swiss Federal Institute of Technology (EPFL) 1015 Lausanne, Switzerland |
| Pseudocode | No | The paper describes algorithms and methods but does not present them in structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper uses an existing algorithm: "We use the steepest descent algorithm of Bresson et al. (2012) to solve the graph-based Cheeger cut problem on these graphs." There is no explicit statement about releasing the authors' own implementation code for the work described in this paper. |
| Open Datasets | No | We always take ρ(x) := 1/vol(D) as the constant density. The data points Xn := {x1, . . . , xn} therefore represent i.i.d. samples from the uniform distribution. ... Each figure depicts a computed optimal partition Yn (in black) of one random realization of the random geometric graph Gn = (Xn, Wn) for each k {0, 1, . . . , 7}, where n = 1000 2k, ε = n 0.3 and the domain considered is D1. |
| Dataset Splits | No | The paper describes generating i.i.d. samples from a uniform distribution for its numerical experiments, but it does not specify any training/test/validation dataset splits, as it is not a traditional machine learning training scenario. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (CPU, GPU models, memory, etc.) used for running the numerical experiments. |
| Software Dependencies | No | We conduct all of our experiments using the Cheeger cut algorithm of Bresson et al. (2012); we omit the ratio cut for the sake of brevity and to avoid redundancy. ... We use the steepest descent algorithm of Bresson et al. (2012) to solve the graph-based Cheeger cut problem on these graphs. |
| Experiment Setup | Yes | We initialize it with the ground-truth partition Y i n := Ai Xn in an attempt to avoid sub-optimal solutions and to bias the algorithm towards the correct continuum cut. We terminate the algorithm once three consecutive iterates show 0% change in the corresponding partition of the graph. |