Weighted Theta Functions and Embeddings with Applications to Max-Cut, Clustering and Summarization
Authors: Fredrik D. Johansson, Ankani Chattoraj, Chiranjib Bhattacharyya, Devdatt Dubhashi
NeurIPS 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Experiments |
| Researcher Affiliation | Academia | Fredrik D. Johansson Computer Science & Engineering Chalmers University of Technology G oteborg, SE-412 96, Sweden frejohk@chalmers.se Ankani Chattoraj Brain & Cognitive Sciences University of Rochester Rochester, NY 14627-0268, USA achattor@ur.rochester.edu Chiranjib Bhattacharyya Computer Science and Automation Indian Institute of Science Bangalore 560012, Karnataka, India chiru@csa.iisc.ernet.in Devdatt Dubhashi Computer Science & Engineering Chalmers University of Technology G oteborg, SE-412 96, Sweden dubhashi@chalmers.se |
| Pseudocode | Yes | Algorithm 1 ϑ-means clustering 1: Input: Graph G, with weight matrix S and node weights σ. 2: Compute kernel K K(G, σ, S) 3: α i arg maxαi f(α; K), as in (4) 4: Sort alphas according to ji such that αj1 αj2 ... αjn 5: Let k = ˆϑ where ˆϑ ω(K) = f(α ; K) 6: either a) 7: Initialize labels Zi = arg maxj {j1,...,jk} Kij 8: Output: result of kernel k-means with kernel K, k = ˆϑ and Z as initial labels 10: Compute U : K = U T U, with columns Ui, and let C {Uji : i k} 11: Output: result of k-means with k = ˆϑ and C as initial cluster centroids |
| Open Source Code | No | The paper does not provide a specific link to source code nor states that the code is included in supplementary materials. It only mentions 'Supplementary material, 2015' in [16], but this is a reference, not an access statement for their code. |
| Open Datasets | Yes | Elsner & Schudy [7] constructed five affinity matrices for a subset of the classical 20-newsgroups dataset. |
| Dataset Splits | No | The paper mentions 'Average (and std. deviation) over 5 splits' for the newsgroup dataset but does not specify exact train/validation/test percentages or sample counts for reproducibility of the data partitioning. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers (e.g., library or solver names with version numbers like Python 3.8, CPLEX 12.4) needed to replicate the experiment. |
| Experiment Setup | Yes | To reduce complexity, while preserving accuracy [9], we use a rank d = 2n truncated SVD, see section 3.1. We apply the Goemans Williamson random hyperplane rounding [9] to partition the embedding into two sets of points, representing the cut. The rounding was repeated 5000 times, and the maximum cut is reported. |