Multidimensional quantification
Multidimensional quantification
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多维量化
DOI：
10.1007/bf02949809
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发表时间：
1953
影响因子：
1
通讯作者：
Chikio Hayashi
中科院分区：
文献类型：
--
作者：
Chikio Hayashi
本文是文献[1]、[2]的继续，在文[1]、[2]中，我们讨论了多维分析中定性数据的一些量化方法，特别是从统计学的角度，利用定性模式的量化来确保对现象的预测的最大成功率。多维分析中的重要问题是设计复杂现象(动态环境中单元相互关联的行为模式)的量化方法，然后再设计它们的分类方法。量化是指对模式进行分类并赋予数值，以便能够将它们作为几个指标来处理，而分类意味着对现象的预测。多维量化的目的是对相互关联的模式进行综合的数值表示，以最大限度地提高分类效率(预测成功率)。量化并不意味着寻找数值，而是从操作的角度给予适当意义上的模式。在本文中，当外部变量(由外部标准表示)以定性分类的形式给出时，将考虑定性模式的量化方法。在这种情况下，最重要的是我们必须设计出实现有效性属性的方法。让我们以n个元素组成的宇宙为例，每个元素都有由调查方法分类的行为模式，并且根据明确的外部标准(这是外部变量)仅被分类为一类。在这里，外部标准必须以绝对尺度为基础，而不能根据宇宙的哪些元素被分类(判断)而改变。也就是说，J(O)=J(OJ)=独立于i，j的常数；i=~=j，~，j=L，2，-.-，n其中J(O~)象征性地表示第i个元素O被分类(判定)时的准则框架。我们的目标是利用过去的数据，通过量化的方法，预测该元素在未来将属于哪一类，目前具有明确的行为模式。
The present paper is a continuation of the papers [1],[2], previously pub-]/shed, in which we treated some methods of quantification of qualitative data in multidimensional analysis and especially the use of quantification of qualitative patterns to secure the maximum success rate of prediction of phenomena fr,, m the statistical point of view. The important problem in multidimensional analysis is to devise the methods of quantification of complex phenomena (intercorrelated behaviour patterns of units in dynamic environments) and then the methods of classification of them. Quantification means that the patterns are categorized and given numerical values in order that they may be able to be treated as several indices,, and classification means a prediction of phenomena. The aim of multi~ dimensional quantification is to make numerical representation of intercorrelated patterns syuthetically to maximize the efficiency of classification (success rate of prediction). Quantification does not mean to find numerical values but to give them to the patterns from the operational point of view in the proper sense. In the present paper, the methods of quantification of qualitative patterns will be considered in case where an outside variable (reMized by the outside criterion) is given in the form af qualitative classification. In this case it is most important that we must devise the methods to fulfil the property of validity. Let us take a universe of n elements, each of which has, as a la~ e], behaviour patterns categorized by a survey method and is classified into only one clas~ by the definite outside criterion of (this is an outside variable). Here the outside criterion must be based on the absolute scale and must not change according t, what elements of universe are classified (judged). That is to say, J (O,)= J (Oj)= constant independent of i, j; i=~= j,~, j= l, 2,-.-, n where J (O~) represents symbolically the frame of criterion for the/-th element O, when it is classified (judged). It is our aim to predict to which class the element will belong in future which has a definite beheviour pattern at present, by the method of quantification using the past data.