A class of network models recoverable by spectral clustering
Authors: Yali Wan, Marina Meila
NeurIPS 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | As obtaining general results in comparing the various recovery conditions in the literature would be a tedious task, here we undertake to do a numerical comparison. While the conclusions drawn from this are not universal, they illustrate well the stringency of various conditions, as well as the gap between theory and actual recovery. For this, we construct HPFM models, and verify numerically if they satisfy the various conditions. We have also clustered random graphs sampled from this model, with good results (shown in the extended version). ... After running Algorithm 1, the mis-clustering rate is r = 0.0008, which satisfies the theoretical bound. |
| Researcher Affiliation | Academia | Yali Wan Department of Statistics University of Washington Seattle, WA 98195-4322, USA yaliwan@washington.edu Marina Meil a Department of Statistics University of Washington Seattle, WA 98195-4322, USA mmp@stat.washington.edu |
| Pseudocode | Yes | Algorithm 1: Spectral Clustering |
| Open Source Code | No | The paper does not provide any statement or link indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | The paper states: 'We generate S from the HPFM model with K = 5, n = 5000. Each wi is uniformly generated from (0.5, 1). n1:K = (500, 1000, 1500, 1000, 1000), grow > 0, λ1:K = (1, 0.8, 0.6, 0.4, 0.2).' This describes synthetic data generation, not the use of a publicly available dataset with concrete access information. |
| Dataset Splits | No | The paper describes generating synthetic data of size n=5000 for numerical comparison but does not specify any training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., GPU/CPU models, memory) used for running the numerical comparisons or experiments. |
| Software Dependencies | No | The paper mentions using 'Algorithm 1' and 'K-means algorithm' but does not specify any software names with version numbers for reproducibility (e.g., 'Python 3.8, PyTorch 1.9'). |
| Experiment Setup | Yes | We generate S from the HPFM model with K = 5, n = 5000. Each wi is uniformly generated from (0.5, 1). n1:K = (500, 1000, 1500, 1000, 1000), grow > 0, λ1:K = (1, 0.8, 0.6, 0.4, 0.2). The matrix R is given below; note its last row in which r55 < P4 l=1 r5l. .80 .07 .02 .02 .09 .04 .52 .24 .12 .08 .01 .20 .65 .15 .00 .01 .08 .12 .70 .08 .13 .21 .02 .32 .33 |