In alignment with the distributional hypothesis of language, the work “Quantum Projections on Conceptual Subspaces” (Martínez-Mingo A, Jorge-Botana G, Martinez-Huertas JÁ, et al. Quantum projections on conceptual subspaces. Cogn Syst Res 2023; 82: 101154) proposed a methodology for generating conceptual subspaces from textual information based on previous work (Martinez-Mingo A, Jorge-Botana G and Olmos R. Quantum approach for similarity evaluation in LSA vector space models. 2020). These subspaces enable the utilization of the quantum model of similarity put forth by Pothos and Busemeyer (Pothos E, Busemeyer J. A quantum probability explanation for violations of symmetry in similarity judgments. In Proceedings of the annual meeting of the cognitive science society, 2011, Vol. 33, No. 33), allowing for the empirical examination of the violations of assumptions concerning symmetry and triangular inequality (Tversky A. Features of similarity. Psychol Rev 1977; 84: 327–352; Yearsley JM, Barque-Duran A, Scerrati E, et al. The triangle inequality constraint in similarity judgments. Prog Biophys Mol Biol 2017; 130: 26–32), as well as the diagnosticity effect (Tversky A. Features of similarity. Psychol Rev 1977; 84: 327–352; Yearsley JM, Pothos EM, Barque-Duran A, et al. Context effects in similarity judgments. J Exp Psychol Gen 2022; 151: 711–717), within a data-driven environment. These psychological biases, deeply studied by authors such as Tversky and Kahneman, inform us about the limitations of modeling psychological similarity measures using tools from classical geometry. This commentary aims to offer methodological clarifications, discuss theoretical and practical implications, and speculate on future directions in this field of research. Concretely, it aims to propose the use of different contours (conceptual or contextual) to generate the subspaces, which lead to subspaces of terms or contexts. Once these contours are defined, a differentiation is proposed between Aggregated Terms Subspaces (ATSs), Aggregated Contexts Subspaces (ACSs), and Aggregated Features Subspaces (AFSs) depending on whether we define the subspaces by grouping the terms or contexts within the contour, or from the latent dimensions of the semantic space obtained in the contour window. Finally, new data is provided on the violation of the triangular inequality assumption through the application of the quantum similarity model to ATSs.

中文翻译：

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概念子空间的量子预测：更深入地探讨方法论挑战和机遇

与语言的分布假设相一致，著作“概念子空间的量子投影”（Martínez-Mingo A、Jorge-Botana G、Martinez-Huertas JÁ 等人。概念子空间的量子投影。Cogn Syst Res 2023；82： 101154）基于之前的工作（Martinez-Mingo A、Jorge-Botana G 和 Olmos R. LSA 向量空间模型中相似性评估的量子方法。2020）提出了一种从文本信息生成概念子空间的方法。这些子空间使得能够利用 Pothos 和 Busemeyer 提出的相似性量子模型（Pothos E、Busemeyer J. 对相似性判断中对称性违反的量子概率解释。在认知科学学会年会记录中，2011 年，第 33 卷，第 33 期），允许对对称性和三角不等式的假设的违反进行实证检验（Tversky A. 相似性特征。 Psychol Rev 1977；84：327–352；Yearsley JM，Barque-Duran A， Scerrati E 等人，相似性判断中的三角不等式约束。Prog Biophys Mol Biol 2017；以及诊断效应（Tversky A. 相似性特征。Psychol Rev 1977；84：327-352） ；Yearsley JM、Pothos EM、Barque-Duran A 等人，J Exp Psychol Gen 2022；151：711-717），在数据驱动的环境中。特沃斯基和卡尼曼等作者对这些心理偏差进行了深入研究，告诉我们使用经典几何工具对心理相似性度量进行建模的局限性。本评论旨在提供方法论澄清，讨论理论和实践意义，并推测该研究领域的未来方向。具体来说，它的目的是建议使用不同的轮廓（概念或上下文）来生成子空间，从而产生术语或上下文的子空间。一旦定义了这些轮廓，就可以在聚合术语子空间（ATS）、聚合上下文子空间（ACS）和聚合特征子空间（AFS）之间进行区分，具体取决于我们是否通过对轮廓内的术语或上下文进行分组来定义子空间，或者来自轮廓窗口中获得的语​​义空间的潜在维度。最后，通过将量子相似模型应用于 ATS，提供了关于违反三角不等式假设的新数据。