Bibliographic record
Abstract
Hierarchical clustering has been a popular method in various data analysis applications. It partitions a data set into a hierarchical collection of clusters, and can provide a global view of (cluster) structure behind data across different granularity levels. A hierarchical clustering (HC) of a data set can be naturally represented by a tree, called a HC-tree, where leaves correspond to input data and subtrees rooted at internal nodes correspond to clusters. Many hierarchical clustering algorithms used in practice are developed in a procedure manner. In [9], Dasgupta proposed to study the hierarchical clustering problem from an optimization point of view, and introduced an intuitive cost function for similarity-based hierarchical clustering with nice properties as well as natural approximation algorithms. There since has been several followup work on better approximation algorithms, hardness analysis, and general understanding of the objective functions. We observe that while Dasgupta's cost function is effective at differentiating a good HC-tree from a bad one for a fixed graph, the value of this cost function does not reflect how well an input similarity graph is consistent to a hierarchical structure. In this paper, we present a new cost function, which is developed based on Dasgupta's cost function, to address this issue. The optimal tree under the new cost function remains the same as the one under Dasgupta's cost function. However, the value of our cost function is more meaningful. For example, the optimal cost of a graph $G$ equals $1$ if and only if $G$ has a perfect HC-structure in the sense that there exists a HC-tree that is consistent with all triplets relations in $G$; and the optimal cost will be larger than $1$ otherwise. The new way of formulating the cost function also leads to a polynomial time algorithm to compute the optimal cluster tree when the input graph has a perfect HC-structure, or an approximation algorithm when the input graph almost has a perfect HC-structure. Finally, we provide further understanding of the new cost function by studying its behavior for random graphs sampled from an edge probability matrix.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".