Abstract—This paper focuses on analyzing medical diagnostic data using classification rules in data mining and context reduction in formal concept analysis. It helps in finding redundancies among the various medical examination tests used in diagnosis of a disease. Classification rules have been derived from positive and negative association rules using the Concept lattice structure of the Formal Concept Analysis. Context reduction technique given in Formal Concept Analysis along with classification rules has been used to find redundancies among the various medical examination tests. Also it finds out whether expensive medical tests can be replaced by some cheaper tests. Keywords—Data Mining, Formal Concept Analysis, Medical Data, Negative Classification Rules. I. INTRODUCTION EDICAL history data consists of large number of tests required to diagnose a particular disease. After studying case history of several patients, it has been found that some of the tests are redundant. Also it has been found that some expensive tests can be replaced by cheaper tests. Our paper proposes a method to find out the redundancies among the tests. The idea used has been taken from context reduction of Formal Concept Analysis and classification rule technique of data mining. Data mining refers to extracting information from very large databases [5]. Classification and association are the two mechanisms to represent the extracted information. Association rules are the rules of the type A->B where A and B are sets of attributes (items). Each association rule has a support and confidence measure associated with it. Support of x% means that x number of transactions have A and B together. Confidence of y% means that y number of transactions having A must have B. Classification rules refers to rules where consequent part of the rule is a class. Several algorithms have been proposed to find association rules [1] [2] and classification rules [9] [10]. There are a few algorithms proposed to find classification rules based on association rules [6] [7]. Classification based on Association (CBA) rules gives more accurate results. But rules produced are more in number as compared to traditional Manuscript received June 4, 2005. Anamika Gupta is a Ph.D. Student in the Department of Computer Science, Delhi University, India, doing research in the field of Data Mining and Formal Concept Analysis. Naveen Kumar is working as a reader in the Department of Computer Science, Delhi University, India. Vasudha Bhatnagar is working as a Lecturer in Department of Computer Science, Delhi University, India. methods of classification. In the medical domain we are interested in high accuracy, so we are following CBA method. In the medical examination tests, we are interested in positive as well as negative result of the test. [3] gives a method of finding classification rules based on both positive and negative association rules. We are using the technique mentioned in [3] to find the classification rules and then by using context reduction technique we are finding out the redundant attributes i.e. the medical examination tests. Context reduction refers to reduction of the database in terms of objects (rows) or attributes (columns). Formal Concept Analysis introduces a novel technique for reduction of database that has been explained in this paper. II. BACKGROUND KNOWLEDGE A. Formal Concept Analysis Bernhard Ganter et al. has defined Formal Concept Analysis as a field of applied mathematics based on the mathematization of concept and conceptual hierarchy and thereby it activates mathematical thinking for conceptual data analysis and knowledge processing [4]. Following basic definitions have been taken from [4] which has been used throughout the paper. A formal context K= (G,M,I) consists of two sets G and M and a relation I between G and M. The elements of G are called the objects and the elements of M are called the attributes of the context. For a set A⊆G of objects A’={mεM | gIm for all gεA} (the set of all attributes common to the objects in A). Correspondingly, for a set B of attributes we define B’ = {gεG | gIm for all mεB} (the set of objects common to the attributes in B). A formal concept of the context (G,M,I) is a pair (A,B) with A⊆G,B⊆M, A’=B and B’=A. A is called the extent and B is the intent of the concept (A,B). ζ(G,M,I) denotes the set of all concepts of the context (G,M,I). If (A1,B1) and (A2, B2) are concepts of a context, (A1,B1) is called a subconcept of (A2,B2), provided that A1⊆A2 (which is equivalent to B2⊆B1). In this case, (A2,B2) is a superconcept of (A1,B1) and we write (A1,B1) ≤ (A2,B2). The relation ≤ is called the hierarchical order of the concepts. The set of all concepts of (G,M,I) ordered in this way is called the concept lattice of the context (G,M,I). An ordered set V := (V,≤) is a lattice, if for any two elements x and y in V the supremum x∨y and the infimum Analysis of Medical Data using Data Mining and Formal Concept Analysis Anamika Gupta, Naveen Kumar, and Vasudha Bhatnagar M World Academy of Science, Engineering and Technology International Journal of Medical and Health Sciences Vol:1, No:11, 2007 591 International Scholarly and Scientific Research & Innovation 1(11) 2007 scholar.waset.org/1307-6892/9755 International Science Index, Medical and Health Sciences Vol:1, No:11, 2007 waset.org/Publication/9755