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CLASSIFICATION OF OBJECTS, GIVEN THEIR CLASSIFICATION BY A NUMBER OF CLASSIFIERS

机译:根据许多分类器对对象进行分类

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摘要

Objects may belong to one of s different mutually disjoint classes or categories. The task of assigning an object to one of these classes is called classification in this dissertation. If a number n of classifiers is used then i('th) classifiers will give his decision x(,i) = 0 or 1, or 2 or ... s where x(,i) = 0 means i('th) classifiers failed to give his decision. When all the n classifiers have given their decisions we observe X = (x(,1), ..., x(,n)). The vector X can be mapped into N = (n(,0), n(,1), ..., n(,s)) where n(,i) is the number of x's equal to i . N can be used to take a decision regarding the class x to which the object is to be finally assigned. The n classifiers together with the rule to take decisions constitute a system. Every individual classifiers will have a pattern matrix q('(r)) = (q('(r))(,ij)) where q('(r))(,ij) = P(x(,r) = j (theta) = i). The system will have a pattern matrix Q(n) = (Q(,ij)(n))) where Q(,ij)(n) = P(x = i (theta) = i). Here (theta) is the true class to which this object belongs. The possible rules applied to N discussed in this paper are: (1) the majority rule, (2) the mode rule, (3) sequential rules.;The estimation of Q(n) can be done by using a master set which can be obtained with the help of experts who, we assume, make no mistakes in identifying the objects. Q(n) is good if it has high probabilities of correct classification and low probabilities of misclassification or leaving objects unclassified. How different hypotheses can be tested on Q(n) is discussed in this paper.;The mode rule gives higher values of Q(,ii)(n) compared to the majority rule. Similarly Q(,ij)(n) (i (NOT=) j, j (NOT=) 0) for mode rule is higher than that of majority rule. But Q(,i0)(n) for mode rule is lower than that of the majority rule. Among the 2 sequential rules discussed the first has the same Q(,ij)(n) as the simple majority rule. The second sequential rule discussed takes decisions only for odd values of n, 2 being an exception among even numbers.;In the absence of master set also q('(r)) can be estimated provided there is an expert available whose pattern matrix q is known. The estimators of q('(r)) obtained are asymptotically unbiased. A test on whether q('(r))(,ij) are the same for all r = 1, 2, ..., n is also discussed.
机译:对象可能属于不同互不相交的类或类别之一。将对象分配给这些类之一的任务在本文中称为分类。如果使用了n个分类器,则第i个分类器将给出其决策x(,i)= 0或1或2或... s,其中x(,i)= 0表示第i('th)分类者没有给出他的决定。当所有n个分类器都给出了决策后,我们观察到X =(x(,1),...,x(,n))。向量X可以映射为N =(n(,0),n(,1),...,n(,s)),其中n(,i)是x等于i的数量。 N可以用来决定最终要分配对象的类别x。 n个分类器与制定决策的规则一起构成一个系统。每个单独的分类器都将具有模式矩阵q('(r))=(q('(r))(,ij)),其中q('(r))(,ij)= P(x(,r)= j(θ)= i)。该系统将具有模式矩阵Q(n)=(Q(,ij)(n))),其中Q(,ij)(n)= P(x = i(θ)= i)。这里(theta)是该对象所属的真实类。本文讨论的适用于N的可能规则是:(1)多数规则,(2)模态规则,(3)顺序规则;; Q(n)的估计可以通过使用主集来完成,可以在专家的帮助下获得,我们假设在识别对象时不会犯任何错误。如果Q(n)具有正确分类的高概率和错误分类的低概率或使对象未分类的概率低,则它很好。本文讨论了如何在Q(n)上检验不同的假设。与众数规则相比,众数规则给出更高的Q(,ii)(n)值。类似地,模式规则的Q(,ij)(n)(i(NOT =)j,j(NOT =)0)高于多数规则。但是,模式规则的Q(,i0)(n)低于多数规则。在讨论的2个顺序规则中,第一个具有与简单多数规则相同的Q(,ij)(n)。讨论的第二个顺序规则仅对n的奇数值做出决定,2是偶数中的例外。;在没有主集的情况下,只要有专家可用其模式矩阵q,也可以估计q('(r))是众所周知的。所获得的q('(r))的估计量是渐近无偏的。还讨论了关于所有r = 1,2,...,n的q('(r))(,ij)是否相同的测试。

著录项

  • 作者

    QADRI, SYED SAMIULLAH.;

  • 作者单位

    The Ohio State University.;

  • 授予单位 The Ohio State University.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 1984
  • 页码 85 p.
  • 总页数 85
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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