The Theory of Concept Analysis and Customer Relationship Mining

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1 The Application of Association Rule Mining in CRM Based on Formal Concept Analysis HongSheng Xu * and Lan Wang College of Information Technology, Luoyang Normal University, Luoyang, , China xhs_ls@sina.com Abstract. CRM (Customer Relationship Management) is to select and manage valuable customer relationships and a business strategy, CRM requires a customer-centric corporate culture to support effective marketing, sales and service processes. As a branch of applied mathematics, FCA (formal concept analysis) comes of the understanding of concept in philosophical domain. This paper presents the application of association rule mining in CRM based on formal concept analysis. Experiments show that the proposed algorithm in the CRM more effective than the traditional algorithm. Keywords: Formal concept analysis, CRM, association rule mining. 1 Introduction Customer Relationship Management of the implication is that through the details of clients in-depth analysis, to improve customer satisfaction, thereby enhancing the competitiveness of enterprises as a means of it [1]. CRM (Customer Relationship Management) that is customer relationship management. Literally, is an enterprise with the CRM to manage customer relationships? In different contexts, CRM may be a management academic language, may be a software system, and are usually referred to CRM, is a computer automated analysis of sales, marketing, customer service and application support processes of the software system. Its goal is to reduce the sales cycle and marketing costs, increase revenue, expand their business needs and new markets channels and enhance customer value, satisfaction, profitability and loyalty. CRM is to select and manage valuable customer relationships and a business strategy, CRM requires a customer-centric corporate culture to support effective marketing, sales and service processes. As a branch of applied mathematics, FCA (formal concept analysis) comes of the understanding of concept in philosophical domain. It is to describe the concept in formalization of symbol from extent and intent, and then realize the semantic information which can be understood by computer. It is to extract all connotative concepts and connections between them from formal context according to the binary relationship so as to form a hierarchical structure of concept. Concept lattice in formal concept analysis as the core data structures, in essence, describes the link between * Author Introduce: Xu HongSheng(1979-), Male, lecturer, Master, College of Information Technology, Luoyang Normal University, Research area: Data mining, CRM. D. Jin and S. Lin (Eds.): Advances in CSIE, Vol. 2, AISC 169, pp springerlink.com Springer-Verlag Berlin Heidelberg 2012

2 28 H. Xu and L. Wang objects and features, indicating generalization between the concepts of relationship with patients, the corresponding Hasse diagram is the visual realization of the data of it. In the data mining study, found that the rule has become a central issue. This paper first introduces the concept of a classical lattice-based algorithm for extracting implication rules, the incremental algorithm to build grid, and update the rule set, we needed on the grid structure modified accordingly, so you can get frequent incremental itemsets. This article describes the basic theory of association rule mining knowledge. This paper proposes the association rule mining in CRM using formal concept analysis. The algorithm is based on two concepts removed conjunct implies the rule set as input, the rule set according to their content to be divided, the division will focus on a rule one by one into the other rule set, and thus get the final merged result. 2 The Research of Association Rule Mining Based on Formal Concept Analysis Concept lattice model is the product of introduction and lattice theory combined with practical application, here is some of the basic definitions of introduction and lattice theory. Formal Concept Analysis is a philosophical concept of a mathematical process in which people organize and analyze data in a way, is the data and its structure, nature and visualize dependencies for a description. In formal concept analysis, the concept is to understand the grounds of extension and intension of two parts. Refers to the concept of extension of this concept is the set of all objects, meaning it refers to all characteristics common to these objects (or attributes) set [2]. Concept lattice in formal concept analysis as the core data structures, in essence, describes the link between objects and features, indicating generalization between the concepts of relationship with patients, the corresponding Hasse diagram is the visual realization of the data, vivid and concise reflection of the generalization relationship between these concepts. Therefore, the concept lattice is considered to be a powerful tool for data analysis. Order theory and lattice theory as a practical application combined with a product concept lattice model study has important theoretical significance. A formal context (formal context) is a triple K = (G, M, I), where G is a collection of objects, M is the set of attributes, I G and M is a binary relation between, the I G M. gim that g G and m M there is a relationship between I, read as an object g has attribute m, is shown by equation 1. O G: f( O ) = { m x O ( xim)} M 1 M : g( M 1) = { x d M 1( xid)} If (M, ) is a partial order set, a, b, c and d are the elements of M and b < c. Then set[b, c] : = {x M b x c } called interval (interval), collection (a] : = {x M x a } called principal ideal (principal ideal), set [d) : = {x M x d } called (1)

3 The Application of Association Rule Mining in CRM Based on Formal Concept Analysis 29 principal sub filter (principal filter). Besides, a b a<b and [a, b]={a, b}, is shown by equation 2. t T A t = A t t T Set (A, ) is a partial order set, if for any the unempty set S A, there exists S, (A, ) is called a full merger half lattice. Similarly, if for any the unempty set S A, there exists S, (A, ) is called a full cross half lattice. If (A, ) is a full merger half lattice and also a full cross half lattice, it is a full lattice. The two mapping is called Galois connection between the power set of A and the power set of B. binary group (A1, B1) P (A) x P (B), if meet the A1 = g (B1) and B1 = f (A1), then is called a formal concept of formal context C, A1 called denotation, B1 called connotation, all the formal concept sets of C writes down as F(C), as is shown by equation 3. ({ g G ~ γg x}{, m M x ~ μ }), ψx : = m The progressive construction concept lattice is under the given original formal context K = (X, D, R) corresponding to the original concept lattice L and new object X * situation, solving formal context K * = (X {X *}, D, R) corresponding to the concept lattice L *. Given formal context K = (G, M, I), if formal context K 1 = (G 1, M 1,I 1 ) and K 2 = (G 2, M 2, I 2 ) meet the G 1 G, G 2 G, M 1 M, M 2 M, then says K 1 and K 2 is the same domain formal context, they are all the son formal contexts of K, also says the concept lattice L (K 1 ) of formal context K 1 and the concept lattice L (K 2 ) of formal K 2 are the same domain concept lattice. The similarity is calculated as follows equation 4. B ( ( )) ( GMI) B GM { M} I G ( M { M} ),,, \, \. For the formal contexts K1 = (G,M 1, I 1 ) and K 2 = (G, M 2, I 2 ) of the same object domain, if M 1 M, M 2 M, M 1 M 2 =, then says K 1 and K 2, L (K 1 ) and L (K 2 ) were connotation independent; If M 1 M, M 2 M, M 1 M 2, for any g G and arbitrary m M 1 M 2 meet gi 1 m = gi 2 m, it says K 1 and K 2, L (K 1 ) and L (K 2 ) are respectively connotation consistent [3]. Given formal context K = (G, M, I), if formal context K 1 = (G 1, M 1, I 1 ) and K 2 = (G 2, M 2, I 2 ), if G 1 G, G 2 G, M 1 M, M 2 M, G 1 G 2, M 1 M 2, G 1 G 2, M 1 M 2, then the same domain formal context fold set to (G 1 G 2, M 1 M 2, I 1 I 2 ), as is shown by equation 5. g m γg μ m = ( γg )* γg Let I = {i1, i2, i3,..., im} for the entry space; a collection of items called itemsets, with k-item set of items is called k-itemsets. Transaction database TD of each transaction Tr has a unique identifier TID, and contains a term set T I. Association rule is of the form B A implicate, in which I A, B and B A = Rule is an objective measure of support. Support the rule that the percentage of samples to meet (2) (3) (4) (5)

4 30 H. Xu and L. Wang the rules. Support is the probability P (A B), of which, A B that contains both A and B services, that is, itemsets A and B and. Another association rule is an objective measure of confidence. Confidence is the conditional probability P (B A), which includes the A's work also includes the probability of B. Algorithm 1. association rule mining based on formal concept analysis Input: Concept lattice L. Output: Lattice L and after inserting the updated rule set R1 obtained from the algorithm array Rules [1,..., L ], Rules [N] represents the grid node N set of rules related to output. (1) IF f*({x*}) Intent(inf(L)) THEN; (2) Intent (inf (L)):=Intent (inf (L)) f*({x*}) (3) IF C=0 OR D 1 THEN (4) Rules[N] := GenerateRulesForNode(N); (5) R: = R Rules [N]; (6) FOR each parent node of N, DO D (C, D) (LHS D ) (7) Adding new lattice node H: (Φ, Intent (inf (L)) f * ({x*})), making H becomes inf (L); (8) IF Q THEN; (9) Notes for B [I]: = {C: Intent (C) = I}; (10) return R: = R Reduce (N); A given concept lattice L and inserted into the grid to the new transaction T, T, after inserting a new record for the lattice L'. And then compared to the original lattice L, after you insert the new transaction T, L ', there are three types of nodes. Way to keep the same. The other will change, but only change the extension, which are updated grid nodes. Another is the new grid node, which is to be inserted by the transaction and pay grid nodes generated in the original format does not exist in the content of the composition. The following diagram, as is shown by figure1. Fig. 1. The result of association rule data mining based on formal concept analysis Marked with a simplified approach to the representation of the concept of property, the principle is: the same word in the graph node label attribute appears only once, the top node is unique, its meaning for the empty set, and the extension contains all object file; the bottom node is unique, contains all the terms of its content properties, and the extension of the empty set.

5 The Application of Association Rule Mining in CRM Based on Formal Concept Analysis 31 3 Application of Formal Concept Analysis in the Association Rule Mining of CRM CRM is an enterprise business strategy, which according to customer segmentation and effective organization of corporate resources, develop a customer-centric business practices and the implementation of customer-centric business processes, and as a means to improve profitability capacity, revenue and customer satisfaction. Customer is an important asset, customer care center of the CRM, customer care and aim to establish long-term customers with the selection and effective business relationship with each customer "touch points" are closer to the customer, to understand customers, maximize profits and profit share [4]. Concept lattice, in addition to the classification and definition from the data concepts, it can be used to find objects, properties, dependencies between. This has two meanings: (1) part or all of the scanning grid structure can be used to generate the rule set in the future; (2) browse lattice structure, to test a certain given rules established. New grid node: set transaction with item set T to be inserted into the lattice L Tr, if a grid node N1 = (C1, D1) satisfy: (1) T, Intersection = D1 while for L in any of the node N2 have Intersection; (2) Intent (N2) for L in any meet N3> N1 node N3, Intersection; T Intent (N3) the N1 is generated as a sub-grid nodes, the N1 can produce a new grid node (C=C1+1, Z=D1 T). Algorithm 2. Application of association rule mining in CRM based on formal concept analysis Input: Conjunct implies the rule set R:P Q as well as an array Rules[1 L ], Rules[N] represents the grid node N set of rules related to L. Output: R=R 1 R 2. Rule sets R1 and R2 set the rules of the division R2 (Di), R1 and R2 are the same domain and two independent sets of rules. (1) R1 will be divided according to their content, build into the relationship between father and son; (2) IF inf(l) = (φ, φ) THEN (3) FOR k := 0 TO size DO (4) Intent(inf(L)) Intent(inf(L)) f*({x*}); (5) Notes for B [I] : = {C: Intent (C) = I}; (6) IF D k =D i THEN exit algorithm ENDIF (7) Int: = Intent(C) f ({x*})); (8) GenerateRulesForPartition(G k, Count 1k, D k ); (9) R:= R Reduce(N); (10) IF Intent(C) = f({x*})) THEN exit algorithm; The paper is using WindowsXP operating system, and using Visual C to achieve the above rule sets and computing algorithms. For randomly generated data sets, 80% probability of their relationship, the number of attributes is 50, we do scalability testing, each increase in the number of objects 582, recorded by the child form the background to generate the corresponding concept lattice implication and operation of the rule set time spent Apriori at the same time a direct comparison of the original form of the background corresponding to the generated concept lattice implication rules set the time, comparing the results shown in Figure 2.

6 32 H. Xu and L. Wang Fig. 2. The compare of association rule mining in CRM based on FCA with Apriori 4 Summary As a branch of applied mathematics, FCA (formal concept analysis) comes of the understanding of concept in philosophical domain. It is to describe the concept in formalization of symbol from extent and intent, and then realize the semantic information which can be understood by computer. This paper presents the application of association rule mining in CRM based on formal concept analysis. Experiments show that the proposed algorithm in the CRM more effective than the traditional algorithm. Acknowledgement. This paper is supported by not only Henan Science and Technology Agency science and technology research in 2010 (Key Project) under Grant no , but also Education Department of Henan Province Natural Science Research Program (2010A520030). References 1. Lin, S.-C., Tung, C.-H., Jan, N.-Y., Chiang, D.-A.: Evaluating Churn Model in CRM: A Case Study in Telecom. JCIT 6(11), (2011) 2. Burusco, A., Fuentes-González: Concept lattices defined from implication operators. Fuzzy Sets and Systems 114, (2000) 3. Wille, R.: Concept Graphs and Formal Concept Analysis. In: Delugach, H.S., Keeler, M.A., Searle, L., Lukose, D., Sowa, J.F. (eds.) ICCS LNCS (LNAI), vol. 1257, pp Springer, Heidelberg (1997) 4. Liu, B., Hsu, W., Ma, Y.: Mining association rules with multiple minimum supports. In: Proc. KDD 1999, San Diego, CA, USA, pp (1999)