In this paper, we aim to learn a low-dimensional Euclidean representation from a set of constraints of the form "item j is closer to item i than item k". Existing approaches for this "ordinal embedding" problem require expensive optimization procedures, which cannot scale to handle increasingly larger datasets. To address this issue, we propose a landmark-based strategy, which we call Landmark Ordinal Embedding (LOE).

Over the past three decades, formal argumentation has established itself as a prominent research area within Artificial Intelligence, owing to its versatility in addressing various reasoning tasks. These include nonmonotonic reasoning, multi-agent systems, rule-based systems, and the analysis of debates or dialogues. Formal argumentation provides a unifying framework for representing diverse reasoning approaches, ranging from highly skeptical to more permissive forms of inference (for a comprehensive introduction to this area, see the handbook [4]). At the heart of formal argumentation lies Dung's abstract argumentation frameworks (AFs) [15], which are modeled as directed graphs, where nodes correspond to arguments, and directed edges represent the attack relations between them. AFs serve as a common foundational core across various reasoning systems in formal argumentation, with many extensions and refinements, e.g.

This paper studies the problem of learning a low-dimensional Euclidean metric from comparative judgments.

Euclidean space given a set of constraints like "item

Given only information in the form of similarity triplets "Object A is more similar

DatalogMTL extends the classical Datalog language with metric temporal logic (MTL), enabling expressive reasoning over temporal data. While existing reasoning approaches, such as materialisation based and automata based methods, offer soundness and completeness, they lack support for handling efficient dynamic updates, a crucial requirement for real-world applications that involve frequent data updates. In this work, we propose DRedMTL, an incremental reasoning algorithm for DatalogMTL with bounded intervals. Our algorithm builds upon the classical DRed algorithm, which incrementally updates the materialisation of a Datalog program. Unlike a Datalog materialisation which is in essence a finite set of facts, a DatalogMTL materialisation has to be represented as a finite set of facts plus periodic intervals indicating how the full materialisation can be constructed through unfolding. To cope with this, our algorithm is equipped with specifically designed operators to efficiently handle such periodic representations of DatalogMTL materialisations. We have implemented this approach and tested it on several publicly available datasets. Experimental results show that DRedMTL often significantly outperforms rematerialisation, sometimes by orders of magnitude.

Neural Information Processing Systems http://nips.cc/

The definition of clustering as the task of grouping similar objects emphasizes the importance of assessing similarity scores for the process of clustering.

Moreover, this is optimal due to Proposition 1. A.3 Future Directions

ABSTRACT An appropriate distance metric is crucial for categorical data clustering, as the distance between categorical data cannot be directly calculated. However, the distances between attribute values usually vary in different clusters induced by their different distributions, which has not been taken into account, thus leading to unreasonable distance measurement. Therefore, we propose a cluster-customized distance metric for categorical data clustering, which can competitively update distances based on different distributions of attributes in each cluster. In addition, we extend the proposed distance metric to the mixed data that contains both numerical and categorical attributes. Experiments demonstrate the efficacy of the proposed method, i.e., achieving an average ranking of around first in fourteen datasets. The source code is available at https://anonymous.4open.science/r/CADM-47D8/