A fast kernel-based multilevel algorithm for graph clustering
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Graph clustering (also called graph partitioning) --- clustering the nodes of a graph --- is an important problem in diverse data mining applications. Traditional approaches involve optimization of graph clustering objectives such as normalized cut or ratio association; spectral methods are widely used for these objectives, but they require eigenvector computation which can be slow. Recently, graph clustering with a general cut objective has been shown to be mathematically equivalent to an appropriate weighted kernel k-means objective function. In this paper, we exploit this equivalence to develop a very fast multilevel algorithm for graph clustering. Multilevel approaches involve coarsening, initial partitioning and refinement phases, all of which may be specialized to different graph clustering objectives. Unlike existing multilevel clustering approaches, such as METIS, our algorithm does not constrain the cluster sizes to be nearly equal. Our approach gives a theoretical guarantee that the refinement step decreases the graph cut objective under consideration. Experiments show that we achieve better final objective function values as compared to a state-of-the-art spectral clustering algorithm: on a series of benchmark test graphs with up to thirty thousand nodes and one million edges, our algorithm achieves lower normalized cut values in 67% of our experiments and higher ratio association values in 100% of our experiments. Furthermore, on large graphs, our algorithm is significantly faster than spectral methods. Finally, our algorithm requires far less memory than spectral methods; we cluster a 1.2 million node movie network into 5000 clusters, which due to memory requirements cannot be done directly with spectral methods.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it