Fechnerian scaling: Metric from discriminability

费希纳标度：可辨别性的度量

• 批准号: 0318010
• 负责人: Ehtibar Dzhafarov
• 金额: --
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2007-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0318010&HistoricalAwards=false
• 关键词: Fechnerian; scaling; Metric; discriminability

This project elaborates and expands the theory and applications of Multidimensional Fechnerian Scaling (MDFS). Intuitively, MDFS is about how to compute distances among objects "from the point of view" of a perceiver (human observer, technical system, group of people, neurophysiological system), based on the probabilities with which this perceiver discriminates (tells apart) very similar objects. Discrimination probabilities impose on the set of perceived objects a local geometric structure (generalized Finsler geometry), and this local structure can be extracted and expanded into a global metric. Essentially, this is an idea with which, albeit in a very limited context, G.T. Fechner launched scientific psychology some 150 years ago. MDFS is motivated by the expectation that, the discrimination among stimuli being arguably the most basic ability of a perceiving system, and the probability of discrimination being a universal measure of discriminability, distances computed from discrimination probabilities may have a fundamental status among social and behavioral measurements. Originally developed for sets of continuously parametrized stimuli (such as colors, sounds, or mixtures of food ingredients) and critically based on computation of derivatives, in the present project MDFS is expanded to discrete sets of objects, such as alphabets, words, or consumer products. When a discrete set of objects is subjected to the proposed modification of MDFS, it is transformed into a network with inter-object distances. A subsequent immersion of this network in a Euclidean space (by means of conventional metric multidimensional scaling) allows one to identify the relevant features that determine the dissimilarities among the objects. The theoretical work in this part of the project will be complemented and guided by the collection of large data sets on discrimination probabilities for such objects as letters of familiar and unfamiliar alphabets and schematic faces. The adaptation of MDFS to discrete object spaces is a non-trivial enterprise that is only enabled by the recent discovery and documentation of two basic properties of discrimination probabilities (regular minimality and nonconstant self-similarity). Their further experimental analysis constitutes the second part of the project. These two properties have far reaching consequences both within and without MDFS. Thus it has been shown that no "random utility" type model in which random representations depend on objects sufficiently smoothly can account for these properties (the models referred to are those in which objects are mapped into random entities in some unobservable "internal" space, and the decision as to whether the objects are the same or different is determined by the realizations of these random entities). The third part of the project is aimed at an in-depth analysis of the relationship between MDFS, the "random utility" type models, and the recently proposed alternative to such models in which random entities are replaced by "uncertainty blobs" of perceived objects.A successful completion of the project will improve our understanding of the fundamental notions of discrimination and dissimilarity, and it will advance the foundations of measurement in social and behavioral sciences. The project also has a clear applied focus. Thus, the development of algorithms and software for MDFS in discrete object spaces will provide a new useful tool for analyzing large-scale polls of public opinion, for consumer surveys, and for educational testing.

该项目阐述和扩展了多维Fechnerian Scaling（MDFS）的理论和应用。直观地说，MDFS是关于如何从感知者（人类观察者，技术系统，人群，神经生理系统）的“观点”计算对象之间的距离，基于感知者区分（区分）非常相似对象的概率。辨别概率对感知对象的集合施加局部几何结构（广义Finsler几何），并且该局部结构可以被提取并扩展为全局度量。从本质上讲，这是一个想法，尽管在一个非常有限的背景下，G. T。费希纳在大约150年前创立了科学心理学。MDFS的动机是期望，刺激之间的歧视可以说是感知系统的最基本的能力，和歧视的概率是一个通用的措施，歧视概率计算的距离可能有一个社会和行为的测量中的基本地位。最初开发的连续参数化的刺激（如颜色，声音，或食物成分的混合物），并严格基于计算的衍生物，在本项目MDFS扩展到离散的对象集，如字母，单词，或消费品。当一个离散的对象集受到建议的修改MDFS，它被转换成一个网络与对象间的距离。随后将该网络浸入欧几里德空间（通过传统的度量多维缩放），可以识别确定对象之间不相似性的相关特征。该项目这一部分的理论工作将通过收集关于熟悉和不熟悉字母的字母和示意性面孔等物体的辨别概率的大型数据集得到补充和指导。MDFS的适应离散对象空间是一个不平凡的企业，只有最近发现和文件的两个基本属性的歧视概率（定期极小值和非常数自相似性）。他们的进一步实验分析构成了该项目的第二部分。这两个属性在MDFS内部和外部都有深远的影响。因此，它已经表明，没有“随机效用”类型的模型，其中随机表示依赖于对象足够顺利地可以考虑这些属性（所指的模型是那些对象被映射到随机实体在一些不可观察的“内部”空间，并决定是否对象是相同的或不同的是由这些随机实体的实现）。本研究的第三部分旨在深入分析MDFS、“随机效用”型模型和最近提出的替代模型之间的关系，在该模型中，随机实体被感知对象的“不确定性斑点”所取代。它将推进社会和行为科学的测量基础。该项目也有一个明确的应用重点。因此，在离散对象空间中的MDFS算法和软件的开发将为分析大规模民意调查、消费者调查和教育测试提供一个新的有用工具。