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Opening the parallelogram: Considerations on non-Euclidean analogies

Pierre-Alexandre Murena, Antoine Cornuéjols, Jean-Louis Dessalles
References
International Conference on Case-Based Reasoning (ICCBR 2018), Stockholm, Suède, July 2018,
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.

Keywords
machine learning, analogy, complexity
Category
Paper in proceedings
Research Area(s)
Computer Science/Machine Learning
Computer Science/Artificial Intelligence
Identifier(s)
Bibliographic key jld-18060701
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Last update
on january 28, 2019 by Jean-Louis Dessalles


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