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Naidenova, Xenia. "The Concept of Good Classification (Diagnostic) Test." Machine Learning Methods for Commonsense Reasoning Processes: Interactive Models. IGI Global, 2010. 165-210. Web. 23 Feb. 2018. doi:10.4018/978-1-60566-810-9.ch007

APA

Naidenova, X. (2010). The Concept of Good Classification (Diagnostic) Test. In X. Naidenova (Ed.), Machine Learning Methods for Commonsense Reasoning Processes: Interactive Models (pp. 165-210). Hershey, PA: IGI Global. doi:10.4018/978-1-60566-810-9.ch007

Chicago

Naidenova, Xenia. "The Concept of Good Classification (Diagnostic) Test." In Machine Learning Methods for Commonsense Reasoning Processes: Interactive Models, ed. Xenia Naidenova, 165-210 (2010), accessed February 23, 2018. doi:10.4018/978-1-60566-810-9.ch007

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Abstract

In this chapter, the definition of good diagnostic test and the characterization of good tests are introduced and the concepts of good maximally redundant and good irredundant tests are given. The algorithms for inferring all kinds of good diagnostic tests are described in detail.

In chapter 6, we considered the set L(I(T)) of partitions produced by closing atomic partitions of I(T) with the use of operations + and * on partitions. This set is the algebraic lattice with constants over U. Now we consider the table of examples T(U∪К) with partition interpretation I(T∪K) over U’= U∪К and the algebraic lattice L(I(U’)) with constants over U’, where K is a given goal attribute.

Let X ⊆ U is a test for a goal attribute К, and partitions P(X), P(K) are the interpretations of X and K, respectively.

Denote by Q(K) the set of all diagnostic tests for K: Q(K) ={X: X ⊆ U: P(X) ≤ P(K))}.

Sub-lattice LK(I(U’)) of L(I(U’)): LK(I(U’)) = {Р: Р ≤ P(K)} is the principal ideal generated by P(K) in L(I(U’)) (see, please, definition 6.3 of principal ideal in Chapter 6).

For definition of good test, we use partition dependency: P(X) ⊆ P(К) (Х ≤ К ≡ X*K = X ≡ X + K = K).

If P(X) = P(K), then X is the ideal approximation of classification K.

Of all tests X, X ⊆ U, P(X) ⊂ P(K), the good test will be Х such that P(X) is the closest to P(K) element of LK(I(U’)), i. e., for all P(Y), Y ⊆ U condition (P(X) ⊆ P(Y) ⊆ P(K)) implies P(X) = P(Y). Thus, we come to the following definition of a good diagnostic test.

Definition 7.1. A collection X ⊆ U is a good test or a good approximation of К of T if the following conditions are satisfied

а) X ∈ Q(K);

b)

there does not exist a collection of attributes Z, Z ⊆ U, X ≠ Z such that Z ∈ Q(K) and P(X) < P(Z) ≤ P(K).

We introduce the concept of the best diagnostic test as follows.

Definition 7.2. A good test X, X ⊆ U is the best one for a given classification K of T if the number of classes in partition P(X) is the smallest for all tests of Q(K).