Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Towards an Axiomatic Approach to Hierarchical Clustering of Measures
Authors: Philipp Thomann, Ingo Steinwart, Nico Schmid
JMLR 2015 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications. The basic idea is to let the user stipulate the clusters for some elementary measures. This is done without the need of any notion of metric, similarity or dissimilarity. Our main results then show that for each suitable choice of user-defined clustering on elementary measures we obtain a unique notion of clustering on a large set of distributions satisfying a set of additivity and continuity axioms. We illustrate the developed theory by numerous examples including some with and some without a density. |
| Researcher Affiliation | Academia | Philipp Thomann EMAIL Ingo Steinwart EMAIL Nico Schmid EMAIL Institute for Stochastics and Applications University of Stuttgart, Germany |
| Pseudocode | No | The paper describes its approach through definitions, axioms, lemmas, propositions, and theorems, without including any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about the release of source code, nor does it provide links to any code repositories or mention code in supplementary materials. |
| Open Datasets | No | The paper illustrates its theoretical concepts with 'numerous examples' and 'illustrations' such as 'twin peaks density' or 'measures supported on curves in the plane', rather than conducting experiments on explicitly named or referenced public datasets. |
| Dataset Splits | No | The paper focuses on a theoretical framework and does not describe any empirical experiments involving datasets, thus no dataset split information is provided. |
| Hardware Specification | No | The paper is purely theoretical and does not report on any experimental setup or results, therefore no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe the implementation or execution of any algorithms, so it does not list software dependencies with version numbers. |
| Experiment Setup | No | The paper describes an axiomatic approach and theoretical framework, rather than reporting on empirical experiments, thus no experimental setup details, hyperparameters, or training configurations are provided. |