Opening the parallelogram: Considerations on non-Euclidean analogies

Abstract :

Analogical reasoning is a cognitively fundamental way of reasoning by comparing two pairs of elements. Several computational approaches are proposed to efficiently solve analogies: among them, a large number of practical methods rely on either a parallelogram representation of the analogy or, equivalently, a model of proportional analogy. In this paper, we propose to broaden this view by extending the parallelogram representation to differential manifolds, hence spaces where the notion of vectors does not exist. We show that, in this context, some classical properties of analogies do not hold any longer. We illustrate our considerations with two examples: analogies on a sphere and analogies on probability distribution manifold.

Complete list of metadatas

https://hal.telecom-paristech.fr/hal-02287927
Contributor : Telecomparis Hal <>
Submitted on : Friday, September 13, 2019 - 5:30:08 PM
Last modification on : Thursday, October 17, 2019 - 12:36:59 PM

Identifiers

  • HAL Id : hal-02287927, version 1

Citation

Pierre-Alexandre Murena, Antoine Cornuéjols, Jean-Louis Dessalles. Opening the parallelogram: Considerations on non-Euclidean analogies. International Conference on Case-Based Reasoning (ICCBR 2018), Jul 2018, Stockholm, Sweden. ⟨hal-02287927⟩

Share

Metrics

Record views

3