Fechnerian Scaling: Metric from Discriminability

费希纳尺度：可辨别性度量

• 批准号: 0620446
• 负责人: Ehtibar Dzhafarov
• 金额: $ 25万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0620446&HistoricalAwards=false
• 关键词: Fechnerian; Scaling; Metric; Discriminability

This project will investigate the fundamental laws governing perceptual discrimination and will further develop the theory of Generalized Fechnerian Scaling. The term discrimination refers to the ability to decide whether two objects are the same or different (in all respects, in a specified respect, or in the sense of belonging to one and the same category). This is one of the basic cognitive abilities of living organisms and one of the basic requirements of artificial intelligent systems. The principle of Regular Minimality has been proposed as a fundamental property of same-different judgments. It says, in essence, that stimulus Y is least discriminable from stimulus X if and only if X is least discriminable from Y. This intuitively plausible and empirically corroborated principle is the cornerstone of the theory of Generalized Fechnerian Scaling, in which subjective distances among stimuli (i.e., distances "from the point of view" of a perceiver, be it a human observer, group of people, a technical system, or a "paper-and-pencil" computational procedure) are computed from discrimination probabilities. Until recently, however, the logic of this computation was posited to be different for continuous stimulus spaces, such as a space of colors, and for discrete spaces, such as a space of color names. One aim of the project is to remedy this discrepancy by developing a computational logic which would apply to all possible stimulus spaces ("Universal Fechnerian Scaling"). This aim is achieved through a new mathematical concept, Dissimilarity Function, whose axiomatic theory generalizes that of metric spaces. In addition to Regular Minimality, discrimination probabilities typically exhibit another property, called Nonconstant Self-Dissimilarity. If X is least discriminable from Y, and so is A from B, the discriminability of X from Y is not generally the same as that of A from B. The conjunction of Regular Minimality with Nonconstant Self-Dissimilarity has important consequences for understanding same-different comparisons. Thus, this conjunction is incompatible with the hypothesis that the subjective distance between X and Y is monotonically related to the probability with which X is discriminated from Y (the hypothesis underlying, among other things, the widely used techniques of Multidimensional Scaling, when applied to discrimination probabilities). Regular Minimality and Nonconstant Self-Dissimilarity are also shown to be incompatible with the widely used well-behaved Thurstonian-type models, according to which the decision whether X and Y are different or the same is based on random images of X and Y, with each stimulus affecting its image's distribution "sufficiently smoothly." The Thurstonian-type models can, however, approximate Regular Minimality, which makes it critical to determine the limits of precision with which Regular Minimality holds in empirical data. Available data do not answer this question, and this project aims at investigating it by means of specially designed adjustment/matching procedures. A related aim of the project is to investigate, analytically and by means of computer simulations, whether the conventional variants of Thurstonian-type models which can approximate Regular Minimality within limits of experimental error can generate realistic discrimination probability functions.Generalized Fechnerian Scaling and theory of same-different judgments have applications in educational assessment and professional training, in applied statistics, in the construction of artificial cognitive systems and perceptual aids, and in the analysis of large-scale polls of public opinion and consumer surveys. The project is interdisciplinary in its nature, bridging behavioral, social, mathematical, and computer sciences. The project is also international. The investigators are from different countries, and other collaborations will be bolstered by a series of symposia and workshops organized at international conferences. Topics related to this project will be used in courses taught by the investigators at Purdue and Oldenburg Universities. An effort will be made to attract undergraduate students to participate in the project, with a special emphasis on the involvement of women and minorities.

本计画将探讨知觉辨识的基本法则，并进一步发展广义费希纳标度理论。 区别一词是指确定两个物体是相同还是不同的能力（在所有方面，在特定方面，或在属于同一类别的意义上）。 这是生物体的基本认知能力之一，也是人工智能系统的基本要求之一。 正则最小性原则被认为是同异判断的一个基本性质。 它本质上说，当且仅当X与Y最不可区分时，刺激Y与刺激X最不可区分。 这种直观上似乎合理且经经验证实的原理是广义费希纳标度理论的基石，其中刺激之间的主观距离（即，从感知者的“视点”的距离，感知者可以是人类观察者、一组人、技术系统或“纸和笔”计算过程）从辨别概率计算。 然而，直到最近，这种计算的逻辑才被认为对于连续刺激空间（例如颜色空间）和离散空间（例如颜色名称空间）是不同的。 该项目的一个目的是通过开发一种适用于所有可能的刺激空间的计算逻辑（“通用费希纳尺度”）来弥补这种差异。 这一目标是通过一个新的数学概念，相异度函数，其公理理论推广的度量空间。 除了正则最小性之外，判别概率通常还表现出另一个属性，称为非常数自相异性。 如果X与Y的可辨别性最小，A与B的可辨别性也最小，则X与Y的可辨别性通常与A与B的可辨别性不同。 正则极小性与非常数自相异性的结合对于理解同异比较具有重要意义。 因此，这种结合与X和Y之间的主观距离与X与Y区分的概率单调相关的假设不相容（当应用于区分概率时，该假设尤其是广泛使用的多维标度技术的基础）。 规则极小性和非恒定自相异性也被证明与广泛使用的行为良好的瑟斯顿型模型不相容，根据瑟斯顿型模型，X和Y是否不同或相同的决定是基于X和Y的随机图像，每个刺激都影响其图像的分布“足够平滑”。“然而，瑟斯顿型模型可以近似于规则极小值，这使得确定规则极小值在经验数据中的精度极限至关重要。 现有数据不能回答这个问题，本项目旨在通过专门设计的调整/匹配程序对此进行调查。 该项目的一个相关目的是调查，分析和通过计算机模拟，是否传统的变体瑟斯顿型模型，可以近似规则极小值的实验误差范围内可以产生现实的歧视概率functions.Generalized Fechnerian Scaling和理论的相同-不同的判断有应用在教育评估和专业培训，在应用统计，人工认知系统和感知辅助工具的构建，以及大规模民意调查和消费者调查的分析。 该项目是跨学科的性质，桥接行为，社会，数学和计算机科学。 该项目也是国际性的。 调查人员来自不同国家，在国际会议上组织的一系列专题讨论会和讲习班将加强其他合作。 与该项目相关的主题将用于普渡大学和奥尔登堡大学研究人员教授的课程。 将努力吸引本科生参与该项目，特别强调妇女和少数民族的参与。