MULTIDIMENSIONAL-SCALING OF SIMILARITY
MULTIDIMENSIONAL-SCALING OF SIMILARITY
复制标题
DOI：
10.1007/bf02289530
复制
发表时间：
1965-01-01
期刊：
影响因子：
3
通讯作者：
TORGERSON, WS
中科院分区：
文献类型：
--
作者：
TORGERSON, WS
我的一位同事曾经用下面的方式总结了统计学在心理学中的应用。“问题是，太多的人知道的统计数据比他们理解的要多。“我一点也不确定，但对于我们这些在多维缩放领域积极工作的人来说，这开始是一个适当的声明。不久前，多维密封中的问题，方法和解决方案似乎相当简单。首先--请原谅我--传统的方法：由理查森[10]的托格森[14，15]在古利克森[4]、绿色、梅西克和阿贝尔森等助产士的帮助下[9]。这个过程或一组过程知道它在做什么，也知道它需要什么。简而言之，它的形式要求过于严格。它不仅要求刺激集的感知或认知结构在本质上是欧几里得的，而且要求对刺激对的相似性的观察与空间中点之间的距离线性相关。但是，当给定的要求没有被严重违反时，人们实际上可以使用相似性来确定一组刺激的潜在感知或认知结构。该模式在许多不同的领域得到了成功的应用，并仍在继续应用。还有Attneave [1]的方法，他从另一个方向攻击了这个问题：假设一个人知道一组刺激的维度和维度，可以确定每个维度上的差异是如何结合在一起的，以给出一个整体的相似性印象。Attneave的结果表明，加性空间比刚才提到的欧几里得空间更合适。不过，稍后再谈。然后是展开方法，由Coombs开始用于一维情况，由Hays推广到多维，后来由Coombs和他实验室的其他工作人员改进[2]。在这种方法中，一个开始与非度量数据和非度量结果结束。在迄今为止提到的所有方法中，相似性被认为是某种空间中距离的补充。GSsta Ekman [3]提供了一个替代方案。在他的模型中，相似性，也许经过适当的变换，被直接解释为标量积或角度
A colleague of mine once summarized the use of statistics in psychology in the following way." The trouble is that too many people know more statistics than they understand." I am not at all sure but what this is beginning to be an appropriate statement for those of us who are actively working in the field of multidimensional scaling.It was not too long ago that the problems, approaches and solutions in multidimensional sealing seemed rather straightforward. There was first of all--if you will pardon me--the traditional approach: by Torgerson [14, 15] out of Richardson [10] with help by such midwives as Gulliksen [4], Green, and Messiek and Abelson [9]. This procedure or set of procedures knew what it was doing and also knew what it required. Briefly, its formal requirements were too severe. It asked not only that the perceptual or cognitive structure of the set of stimuli be Euclidean in nature, but also, that observations on similarity of pairs of stimuli be linearly related to distances between points in the space. But when the given requirements were not seriously violated, one could in fact use similarity to determine the underlying perceptual or cognitive structure of a set of stimuli. The model was used, and is still being used, in quite a number of different areas with success. There was also the approach of Attneave [1], who attacked the problem from the other direction: Assuming that one knows the dimensionality and dimensions of a set of stimuli, can one determine how the differences on each of the dimensions are combined to give an over-all impression of similarity. Attneave's results suggested that an additive space would be more appropriate than the Euclidean space just mentioned. But more about that later. Then there was the unfolding approach, begun by Coombs for the unidimensional case, generalized by Hays to more than one dimension, and later improved upon by Coombs and other workers in his laboratory [2]. In this approach, one begins with nonmetric data and ends with nonmetrie results. In all of the approaches mentioned thus far, similarity was considered to be the complement of distance in a space of one kind or another. GSsta Ekman [3] provided an alternative. In his model, similarity, perhaps after suitable transformations, was interpreted directly as a scalar product or angle