Consistency of Spectral Partitioning of Uniform Hypergraphs under Planted Partition Model
Authors: Debarghya Ghoshdastidar, Ambedkar Dukkipati
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the claims of Corollaries 2 and 3, where we stated that for higher order tensors, the number of misclustered nodes decays to zero at a faster rate. We run Algorithm 1 on both the models of subspace clustering and point-set matching, varying the number of nodes n, the results for each n being averaged over 10 trials.We now turn to practical applications, and test the performance of Algorithm 1 in motion segmentation. We perform the experiments on the Hopkins 155 dataset [24] |
| Researcher Affiliation | Academia | Debarghya Ghoshdastidar Ambedkar Dukkipati Department of Computer Science & Automation Indian Institute of Science Bangalore 560012, India {debarghya.g,ad}@csa.iisc.ernet.in |
| Pseudocode | Yes | Algorithm 1 Spectral partitioning of m-uniform hypergraph 1. From the mth-order affinity tensor An, construct b An using (2). 2. Let Wn = b An b AT n, and Dn Rn n be diagonal with (Dn)ii = Pn j=1(Wn)ij. 3. Set Ln = D 1/2 n Wn D 1/2 n . 4. Compute leading k orthonormal eigenvectors of Ln, denoted by matrix Xn Rn k. 5. Cluster the rows of Xn into k clusters using k-means clustering. 6. Assign node-i of hypergraph to jth partition if ith row of Xn is grouped in jth cluster. |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code or provide a link to a code repository for the described methodology. |
| Open Datasets | Yes | We perform the experiments on the Hopkins 155 dataset [24] and We now consider a matching problem using points sampled from images in Mpeg-7 database [25]. |
| Dataset Splits | No | The paper does not provide specific dataset split information (e.g., percentages, sample counts for train/validation/test sets) for reproducibility. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific software dependency details, such as library or solver names with version numbers, needed to replicate the experiment. |
| Experiment Setup | Yes | For the clustering model (Section 2.1), we choose p = 0.6, q = 0.4, and consider two cases of k = 2 and 3 cluster problems. [...] for the matching problem (Section 2.2), where we use p = 0.9, q = 0.1 and the number of correct matches as n. [...] We used 4th-order tensors in the approach, where the large dimensionality of b An is tackled by using only 500 uniformly sampled columns of b An for computing Wn. |