A Conceptual Framework of Data Mining

Transcription

1 1 A Conceptual Framework of Data Mining Yiyu Yao 1, Ning Zhong 2 and Yan Zhao 1 1 Department of Computer Science, University of Regina Regina, Saskatchewan, Canada S4S 0A2 {yyao, yanzhao}@cs.uregina.ca 2 Department of Information Engineering, Maebashi Institute of Technology 460-1, Kamisadori-Cho, Maebashi 371, Japan zhong@maebashi-it.ac.jp Summary. The study of foundations of data mining may be viewed as a scientific inquiry into the nature of data mining and the scope of data mining methods. There is not enough attention paid to the study of the nature of data mining, or its philosophical foundations. It is evident that the conceptual studies of data mining as a scientific research field, instead of a collection of isolated algorithms, are needed for a further development of the field. A three-layered conceptual framework is thus proposed, consisting of the philosophy layer, the technique layer and the application layer. Each layer focuses on different types of fundamental questions regarding data mining, and they jointly form a complete characterization of the field. The layered framework is demonstrated by applying it to three sub-fields of data mining, classification, measurements, and explanation-oriented data mining. 1.1 Introduction With the development and success of data mining, many researchers became interested in the fundamental issues, namely, the foundations of data mining [2, 8, 9, 23]. The study of foundations of data mining should be viewed as a scientific inquiry into the nature of data mining and the scope of data mining methods. This simple view separates two important issues. The study of the nature of data mining concerns the philosophical, theoretical and mathematical foundations of data mining; while the study of data mining methods concerns its technological foundations by focusing on the algorithms and tools. A review of the existing studies show that not enough attention has been paid to the study of the nature of data mining, more specifically, to the philosophical foundations of data mining [23]. Although three dedicated international workshops have been held [7, 8, 9], there still do not exist well-accepted and non-controversial answers to many basic questions, such as, what is data mining? what makes data mining a distinctive study? what are the foundations of data mining? What is the scope of the foundations of data mining?

2 What are the differences, if any, between the existing researches and the research on the foundations of data mining? The study of foundations of data mining attempts to answer these questions. The foundational study is sometimes ignored or underestimated. In the context of data mining, one is more interested in algorithms for finding knowledge, but not what is knowledge, and what is the knowledge structure. One is often more interested in a more implementation-oriented view or framework of data mining, rather than a conceptual framework for the understanding of the nature of data mining. The following quote from Salthe [17] about studies of ecosystem is equally applicable to the studies of data mining: The question typically is not what is an ecosystem, but how do we measure certain relationships between populations, how do some variables correlate with other variables, and how can we use this knowledge to extend our domain. The question is not what is mitochondrion, but what processes tend to be restricted to certain region of a cell. [page 3] A lack of the study of its foundation may affect the future development of the field. There are many reasons accounting for such unbalanced research efforts. The problems of data mining are first raised by very practical needs for finding useful knowledge. One inevitably focuses on the detailed algorithms and tools, without carefully considering the problem itself. A workable program or software system is more easily acceptable by, and at the same time is more concrete and more easily achievable by, many computer scientists than an in-depth understanding of the problem itself. Furthermore, the fundamental questions regarding the nature of the field, the inherent structure of the field and its related fields, are normally not asked at its formation stage. This is especially true when the initial studies produce useful results [17]. The study of foundations of data mining therefore needs to adjust the current unbalanced research efforts. We need to focus more on the understanding of the nature of data mining as a field instead of a collection of algorithms. We need to define precisely the basic notions, concepts, principles, and their interactions in an integrated whole. Many existing studies can contribute to the foundational study of data mining. Here are two examples: (a.) Results from the studies of cognitive science and education are relevant to such a purpose. Posner suggested that, according to the cognitive science approach, to learn a new field is to build appropriate cognitive structures and to learn to perform computations that will transform what is known into what is not yet known [15]. (b.) Reif and Heller showed that knowledge structure of a domain is very relevant to problem solving[16]. In particular, knowledge about a domain, such as mechanics, specifies descriptive concepts and relations described at various levels of abstraction, is organized hierarchically, and is accompanied by explicit guidelines that specify when and how knowledge is to be applied [16]. The knowledge hierarchy is used by Simpson for the study

3 of foundations of mathematics [20]. It follows that the study of foundations of data mining should focus on the basic concepts and knowledge of data mining, as well as their inherent connections, at multi-level of abstractions. Without such kind of understanding of data mining, one may fail to make further progress. In summary, in order to study the foundations of data mining, we need to move beyond the existing studies. More specifically, we need to introduce a conceptual framework, to be complementary to the existing implementation and process-oriented views. The main objective of this chapter is therefore to introduce such a framework. The rest of the chapter is organized as follows. In Section 2, we re-examine the existing studies of data mining. Based on the examination, we can observe several problems and see the needs for the study of foundations of data mining. More specifically, there is a need for a framework, within which to study the basic concepts and principles of data mining, and the conceptual structures and characterization of data mining. For this purpose, in Section 3, a three-layered conceptual framework of data mining is discussed, consisting of the philosophy layer, the technique layer, and the application layer [23]. The relationships among the three layers are discussed. The layered framework is demonstrated in Section 4 by applying it to an example of function-oriented view - classification, an example of theory-oriented view - measurement theory, and an example of procedure-oriented view - explanation-oriented data mining. Section 5 draws the conclusion. 1.2 Overview of the Existing Studies and the Problems Data mining, as a relatively new branch of computer science, has received much attention. It is motivated by our desire of obtaining knowledge from huge databases. Many data mining methods, based on the extensions, combinations, and adaptation of machine learning algorithms, statistical methods, relational database concepts, and the other data analysis techniques, have been proposed and studied for knowledge extraction and abstraction Three views of data mining The existing studies of data mining can be classified broadly under three views. The function-oriented view The function-oriented view focuses on the goal or functionality of a data mining system, namely, the discovery of knowledge from data. In a wellaccepted definition, data mining is defined as the non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns

4 from data [4]. The function-oriented approaches put forth efforts on searching, mining and utilizing different patterns embedded in various databases. A pattern is an expression in a language that describes data, and has a representation simpler than the data. For example, frequent itemsets, association rules and correlations, as well as clusters of data points, are common classes of patterns. Such goal-driven approaches establish a close link between data mining research and real world applications. Depending on the data and their properties, one may consider different data mining systems with different functionalities and for different purposes, such as text ming, Web mining, sequential mining, and temporal data mining. Under the function-oriented view, the objectives of data mining can be divided into prediction and description. Prediction involves the use of some variables to predict the values of some other variables, and description focuses on patterns that describe the data [4]. The theory-oriented view The theory-oriented approaches concentrate on the theoretical studies of data mining, and its relationship to the other disciplines. Many models of data mining have been proposed, critically investigated and examined from the theory-oriented point of view [4, 12, 22, 27]. Conceptually, one can draw a correspondence between scientific research by scientists and data mining by computers [26, 27]. More specifically, they share the same goals and processes. It follows that any theory discovered and used by scientists can be used by data mining systems. Thus, many fields contribute to the theoretical study of data mining. They include statistics, machine learning, databases, pattern recognition, visualization, and many other. There is also a need for the combination of existing theories. For example, some efforts have been made to bring the rough sets theory, fuzzy logic, utility and measurement theory, concept lattice and knowledge structure, and other mathematical and logical models into the data mining models. The procedure/process-oriented view From the procedure/process-oriented view, data mining deals with a nontrivial process consisting of many steps, such as data selection, data preprocessing, data transformation, pattern discovery, pattern evaluation, and result explanations [4, 11, 27, 31]. Furthermore, it should be a dynamically organized process. Under the process-oriented view, data mining studies have been focused on algorithms and methodologies for different processes, speeding up existing algorithms, and evaluation of discovered knowledge Problems and potential solutions The three views jointly provide a good description of data mining research. The function-oriented view states the goals of data mining, the theory-oriented

5 view studies the means with which one can carry out the desired tasks, and the process-oriented view deals with how to achieve the goals based on the theoretical means. However, the general conceptual framework is still not proposed and examined. Intuitively, the terms of technology and science have different meanings. Science studies the nature of the world. On the other hand, technology studies the ways that people develop to control or manipulate the world. Science deals with understanding while technology deals with doing. The scientific study requires the study of foundations of data mining, so that the fundamental questions of the field itself are asked, examined, explained and formalized. The foundations of data mining may not be solely mathematics or logic, or any other individual fundamental disciplines. Considering the different types of databases, the diversity of patterns, the ever changing techniques and algorithms, and the different views, we require a multilevel (or multi-layer) understanding of data mining. By viewing data mining in many layers, one can identify the inherent structure of the fields, and put fundamental questions into their proper perspectives in the conceptual map of data mining. 1.3 A Three-Layered Conceptual Framework A three-layered conceptual framework is recently proposed by Yao [23], which consists of the philosophy layer, the technique layer, and the application layer. The layered framework represents the understanding, discovery, and utilization of knowledge, and is illustrated in Figure The philosophy layer The philosophy layer investigates the basic issues of knowledge. One attempts to answer a fundamental question, namely, what is knowledge? There are many related issues to this question, such as the representation of knowledge, the expression and communication of knowledge in languages, the relationship between knowledge in mind and in the external real world, and the classification and organization of knowledge [21]. Philosophical study of data mining serves as a precursor to technology and application, it generates knowledge and the understanding of our world, with or without establishing the operational boundaries of knowledge. The philosophy layer study is primarily driven by curiosity, and responds to a certain hypothesis The technique layer The technique layer is the study of knowledge discovery in machine. One attempts to answer the question, how to discover knowledge? In the context

6 of computer science, there are many issues related to this question, such as the implementation of human knowledge discovery methods by programming languages, which involves coding, storage and retrieval issues in a computer, and the innovation and evolution of techniques and algorithms in intelligent systems. The main streams of research in machine learning, data mining, and knowledge discovery have concentrated on the technique layer. Logical analysis and mathematical modelling are considered to be the foundations of technique layer study of data mining The application layer The ultimate goal of knowledge discovery is to effectively use discovered knowledge. The question that needs to be answered is how to utilize the discovered knowledge. The application layer therefore should focus on the notions of usefulness and meaningfulness of discovered knowledge for the specific domain, and aim at many attributes, such as efficiency, optimization, reliability, cost-effectiveness, and appropriateness. These notions cannot be discussed in total isolation with applications, as knowledge in general is domain specific. The application layer therefore involves the design and development of a solution to a target problem that serves a real need. Philosophy layer Technique layer Application layer Fig The three-layered conceptual framework of data mining The relationships among the three layers Two points need to be emphasized about the three-layered conceptual framework. First, the three layers are different, relatively independent, and selfcontained.

7 (1.)The philosophical study does not depend on the availability of specific techniques and applications. In other words, it does not matter whether knowledge is discovered or not, utilized or not, and if the knowledge structure and expression are recognized or not. Furthermore, all human knowledge is conceptual and forms an integrated whole [14]. The output of the philosophical study can be expressed as theories, principles, concepts or other knowledge structures. Knowledge structure is built by connecting new bits of information to the old. The study of knowledge at the philosophy layer has important implications for the human society, even if it is not discovered or utilized yet, or it simply provides a general understanding of the real world. (2.)The technical study can carry out part of the philosophic study results but not all, and it is not constrained by applications. The philosophy layer describes a very general conceptual scheme. The current techniques, including hardware and software, may still be insufficient to bring all of it into reality. On the other hand, the existence of a technique/algorithm does not necessarily imply that discovered knowledge is meaningful and useful. The output of the technical study can be expressed by algorithms, mathematical models, and intelligent systems. The technology can be commercialized. The benefits of technological implementation and innovation tend to move the study of technical layer to be more and more profitdriven. (3.)The applications of data mining is the utilization of knowledge in specific domains. They are related to the evaluation of discovered knowledge, the explanation and interpretation of discovered knowledge in a particular domain. The discovered knowledge can be used in many ways. For example, knowledge from transaction databases can be used for designing new products, distributing, and marketing. Comparing to the philosophical and technological studies, the applications have more explicit targets and schedules. Second, the three layers mutually support each other and jointly form an integrated whole. (1.)It is expected that the results from philosophy layer will provide guidelines and set the stage for the technique and application layers. The technology development and innovation can not go far without the conceptual guidance. (2.)The philosophical study cannot be developed without the consideration of reality. Technology development may raise new philosophical questions and promote the philosophical study. Technique layer is the bridge between philosophical view of knowledge and the application of knowledge. (3.)The applications of philosophical and technical outcomes give an impetus for the re-examination of philosophical and technical studies too. The feedbacks from applications provide evidence for the confirmation, reexamination, and modification of philosophical and technical results.

8 Three layers of the conceptual framework are tightly integrated, namely, they are mutually connected, supported, promoted, facilitated, conditioned and restricted. The division between the three layers is not a clear cut, and may overlap and interweave with each other. Any of them is indispensable in the study of intelligence and intelligent systems. They must be considered together in a common framework through multi-disciplinary studies, rather than in isolation. 1.4 Enriched Views on the Three-Layered Framework We believe the three-layered conceptual framework establishes a proper foundation of data mining. It can promote the progress of data mining; to advance the science and technology related to data mining. By putting the three existing views that we have discussed in Section 2 into the conceptual framework, we obtain a 3(view)-by-3(layer) Table 1.2 and more insights. We study, from the function-oriented view, not only what data mining programs can and cannot do in the technology and application layer, but also in the abstract, what knowledge is possibly stored in the information system, how programs should store and retrieve specific kinds of information in their specific structure and representation. From the theory-oriented view, the key thing is not only to pile up various theories, algorithms, to beat up the efficiency, or even worse, to reinvent theories and methodologies that have been well-studied in the other domains. It emphasizes the understanding and human-computer interaction. From the procedure-oriented view, it should be guided by the procedure of general scientific research too. View Layer Functionoriented view Theory-oriented view Procedureoriented view Philosophy layer Technique layer Application layer What knowledge can be discovered? What is the nature of the knowledge to be discovered? Which theory is related to data mining? How related is it? What is the benefit? What is the expense? What is the connection between the procedure of general scientific research and the specific procedure of data mining? How to discover this type of knowledge? How to implement this theory for data mining? How to implement each process, or a particular process, of data mining? How to use this type of knowledge for the real life? How to implement this theory for data mining in real life? In real applications, some processes are focused on. Fig Three views and three layers. In this section, we explain three examples with respect to the three-layered framework. The classification is corresponding to the function-oriented view, evaluation and measurement theory is corresponding to the theory-oriented view, and the explanation-oriented data mining extends the procedure-oriented

9 view. We demonstrate how these three views are enriched by the conceptual framework, especially the philosophy layer study Classification on the three-layered framework Classification is considered as one of the most important tasks of data mining. It is therefore associated with the function-oriented view that we discussed in Section 2. Partitions and coverings are two simple and commonly used knowledge classifications of the universe. A partition of a finite universe is a collection of non-empty, and pairwise disjoint subsets whose union is the universe. A covering of a finite universe is a collection of non-empty and possibly overlapped subsets whose union is the universe. Partitions are a special case of coverings. Knowledge is organized in a tower (hierarchy) or a partial ordering. Based on the above discussion, we have partition-based hierarchy and covering-based hierarchy. Hierarchy means that the base or minimal elements of the ordering are the most fundamental concepts and higher-level concepts depend on lower-level concepts [20]. Partial ordering means that the concepts in the hierarchy are reflexive, anti-symmetric and transitive. The first-level concept is formed directly from the perceptual data [14]. The higher-level concepts, representing a relatively advanced state of knowledge, are formed by a process of abstracting from abstractions [14]. On the other hand, the series of lowerlevel concepts, on whom the higher-level concept is formed, are not necessarily unique in content. Within the requisite overall structure, there may be many alternatives in detail [14]. The natural process of knowledge cognition follows the hierarchy from lower-level concepts to higher-level according to the intellectual dependency. The revise process does exist because of impatience, anti-effort, or simple error. Peikoff analyzes that the attempt to function on the higher levels of complex structure without having established the requisite base will build confusion on confusion, instead of knowledge on knowledge. In such minds, the chain relating higher-level content to perceptual reality is broken [14]. A virtual space that can hold knowledge as concepts is called a concept space, namely, it refers to the set or class of the concepts. If we consider the data mining process as searching for concepts in a particular concept space, we need to study different kinds of concept spaces first. Inside the concept space, the concept can be represented and discovered. Generally, a concept space S can hold all the concepts, including the ones that can be defined as a formula, and the ones that cannot. A definable concept space DS is a sub-space of the concept space S. There are many definable concept spaces in different forms. In most situations, one is only interested in the concepts in a certain form. Consider the class of conjunctive concepts, that formula constructed from atomic formula by only logic connective. A concept space CDS is then referred to as the conjunctively definable space, which is a subspace of the definable space DS. Similarly, a concept space is referred to as

10 a disjunctively definable space if the atomic formulas are connected by logic disjunctive. In [30], we discuss the complete concept space for classification tasks using granular network concepts. The immediate result is that a classification task can be understood as a search of the distribution of classes in a granule network defined by the descriptive attribute set. The analysis shows that the complexity of the search space of a consistent classification task is not polynomially bound. This can be extremely complex especially when the number of possible values of attributes are large, let alone continuous. This forces us to use heuristic algorithms to quickly find solutions in a constrained space. Indeed, the existing heuristic algorithms perform very well. Each of them can be understood as a particular heuristical search within the granule network Rule interestingness evaluation on the three-layered framework Traditionally, when we talk about evaluating the usefulness and interestingness of discovered rules and patterns, we talk about many measures based on, for example, information theory and measurement theory. Thus, the study of interestingness evaluation is a theory-oriented study referring to the categories in Section 2. With respect to the framework, in the philosophical layer, quantitative measures can be used to characterize and classify different types of rules. In the technique layer, measures can be used to reduce search space. In the application layer, measures can be used to quantify the utility, profit, effectiveness, or actionability of discovered rules. From the existing studies, one can observe that rule evaluation plays at least three different types of roles: i. In the data mining phase, quantitative measures can be used to reduce the size of search space. An example is the use of well-known support measure, which reduces the number of itemsets that need to be examined [1]. ii. In the phase of interpreting mined patterns, rule evaluation plays a role in selecting the useful or interesting rules from the set of discovered rules [18, 19]. For example, the confidence measure of association rules is used to select only strongly associated itemsets [1]. iii. In the phase of consolidating and acting on discovered knowledge, rule evaluation can be used to quantify the usefulness and effectiveness of discovered rules. Many measures such as cost, classification error, and classification accuracy play such a role [5]. To carry out the above three roles, many measures have been proposed and studied. We need to understand that measures can be classified into two categories consisting of objective measures and subjective measures [18]. Objective measures depend only on the structure of rules and the underlying data used in the discovery process. Subjective measures also depend on the

11 user who examines the rules [18]. In comparison, there are limited studies on subjective measures. For example, Silberschatz and Tuzhilin proposed a subjective measure of rule interestingness based on the notion of unexpectedness and in terms of a user belief system [18, 19]. Yao et al. [24] suggest that, the rule interestingness measures have three forms: statistical, structural and semantic. Many measures, such as support, confidence, independence, classification error, etc., are defined based on statistical characteristics of rules. A systematic analysis of such measures is given by Yao et al. using a 2 2 contingency table induced by a rule [25, 28]. The structural characteristics of rules have been considered in many measures. For example, information, such as the disjunct size, attribute interestingness, the asymmetry of classification rules, etc., can be used [5]. These measures reflect the simplicity, easiness of understanding, or applicability of rules. Although statistical and structural information provides an effective indicator of the potential effectiveness of a rule, its usefulness is limited. One needs to consider the semantics aspects of rules or explanations of rules [26]. Semantics centered approaches are application and user dependent. In addition to statistical information, one incorporates other domain specific knowledge such as user interest, utility, value, profit, actionability, and so on. Measures defined by statistical and structural information may be viewed as objective measures. They are user, application and domain independent. For example, a pattern is deemed interesting if it has certain statistical properties. These measures may be useful in philosophy layer of the three-layered framework. Different classes of rules can be identified based on statistical characteristics, such as peculiarity rules (low support and high confidence), exception rules (low support and high confidence, but complement to other high support and high confidence rules), and outlier patterns (far away from the statistical mean) [29]. Semantic based measures involve the user interpretation of domain specific notions such as profit and actionability. They may be viewed as subjective measures. Such measures are useful in the application layer of the three-layered framework. The usefulness of rules are measured and interpreted based on domain specific notions Explanation-oriented data mining on the three-layered framework To complement the extensive studies of various tasks of data mining, the explanation task of data mining, more specifically, the concept of explanationoriented data mining, was first proposed in [27]. Some technologies of data mining cannot immediately create knowledge or guarantee knowledge generation, but only retrieve, sort, quantify, organize and report information out of data. Information can turn into knowledge if it can be rationalized, explained and validated. Similarly, explanation-oriented data mining can be explored with respect to the three-layered framework.

12 To add the explanation task into the existing data mining process is based on an important observation, that scientific research and data mining have much in common in terms of their goals, tasks, processes and methodologies. Scientific research is affected by the perceptions and the purposes of science. Martella et al. summarized the main purposes of science, namely, to describe and predict, to improve or manipulate the world around us, and to explain our world [13]. The results of the scientific research process provide a description of an event or a phenomenon. The knowledge obtained from research helps us to make predictions about what will happen in the future. Research findings are a useful tool for making an improvement in the subject matter. Research findings also can be used to determine the best or the most effective ways of bringing about desirable changes. Finally, scientists develop models and theories to explain why a phenomenon occurs. Goals similar to those of scientific research have been discussed by many researchers in data mining. Guergachi stated that the goal of data mining is what science is and has been all about: discovering and identifying relationships among the observations we gather, making sense out of these observations, developing scientific principles, building universal laws from observations and empirical data [6]. Fayyad et al. identified two high-level goals of data mining as prediction and description [4]. Ling et al. studied the issue of manipulation and action based on the discovered knowledge [9]. Yao et al. compared the research process and data mining process [26, 27]. The comparison led to the introduction of the notion of the explanation-oriented data mining, which focuses on constructing models for the explanation of data mining results [27]. In the philosophy level, we need to understand what kind of pattern need to be explained. A target pattern that arouses user s interest, hooks up user s attention and needs to be deep explained resides in the set of discovered patterns. In fact, the targets may differ among the views of individuals. One may question the same target at different times based on different considerations, at different cognitive levels. We also need to understand what knowledge can be applied to explain the target pattern. Explanation-oriented data mining needs background knowledge to infer features that can possibly explain a discovered pattern. We need to note two facts: first, the explanation profiles may not situate in the original dataset. One needs to collect additional information that is characteristically associated with the target pattern, and can be practically transformed to be the explanation context. On the other hand, how one explains determines what one may learn. In general, the better one s background knowledge is, the more accurate the inferred explanations are likely to be. The task of explanation construction and evaluation includes five separate phases that need to be undertaken: explanation subject selection, explanation profiles proposition, explanation construction, explanation evaluation, and explanation refinement. That is, given a target discovered pattern to be explained, in order to result an explanatory account one needs to do the following: First, propose the heuristic for some explanation profiles, transform

13 and associate them with the environment where the target pattern is located. Then, construct some rules by a particular method in the explanation context. After these, the learned results need to be evaluated. According to the evaluation results and the user feedback, the explanation profiles can be sharpened and refined, the same or different methods can be applied to the refined context for another plausible explanation construction until it is satisfied. 1.5 Conclusion A three-layered conceptual framework of data mining is discussed in this chapter, consisting of the philosophy layer, the technique layer and the application layer. The philosophy layer deals with the formation, representation, evaluation, classification and organization, and explanation of knowledge; the technique layer deals with the technique development and innovation; and the application layer emphasizes on the application, utility and explanation of mined knowledge. The layered framework focuses on the data mining questions and issues in different abstract levels, and thus, offers us opportunities and challenges to reconsider the existing three views of data mining. The framework is aimed at the understanding of the data mining as a field of study, rather than a collection of theories, algorithms and tools. References 1. Agrawal, R., Imielinski, T. and Swami, A., Mining association rules between sets of items in large databases, Proceedings of ACM SIGMOD, , Chen, Z., The three dimensions of data mining foundation, Proceedings of IEEE ICDM 02 Workshop on Foundation of Data Mining and Knowledge Discovery, , Craik, K., The Nature of Explanation, Cambridge University Press, London, New York, Fayyad, U.M., Piatetsky-Shapiro, G. and Smyth, P., From data mining to knowledge discovery: an overview, in: Advances in Knowledge Discovery and Data Mining, Fayyad, U.M., Piatetsky-Shapiro, G., Smyth, P. and Uthurusamy, R. (eds.), AAAI/MIT Press, Menlo Park, CA, 1-34, Freitas, A.A., On rule interestingness measures, Knowledge-Based Systems, 12, , Guergachi, A.A., Connecting traditional sciences with the OLAP and data mining paradigms, Proceedings of SPIE: Data Mining and Knowledge Discovery: Theory, Tools, and Technology, 5098, , Lin, T.Y., Hu, X.H., Ohsuga, S. and Liau, C.J. (eds.), Proceedings of IEEE ICDM 03 Workshop on Foundation of New Directions in Data Mining, Lin, T.Y. and Liau, C.J. (eds.), Proceedings of the PAKDD 02 Workshop on Fundation of Data Mining, Communications of Institute of Information and Computing Machinery, 5, , 2002.

14 9. Lin, T.Y. and Ohsuga, S. (eds.), Proceedings of IEEE ICDM 02 Workshop on Foundation of Data Mining and Knowledge Discovery, Lin, T.Y., Yao, Y.Y. and Louie, E., Value added association rules, Proceedings of PAKDD, , Mannila, H., Methods and problems in data mining, Proceedings of International Conference on Database Theory, 41-55, Mannila, H., Theoretical frameworks for data mining, SIGKDD Explorations, 1, 30-32, Martella, R.C., Nelson, R. and Marchand-Martella, N.E., Research Methods: Learning to Become a Critical Research Consumer, Allyn & Bacon, Bosten, Peikoff, L., Objectivism: The Philosophy of Ayn Rand, Dutton, Posner, M.I. (ed.), Foundations of Cognitive Science, Preface: learning cognitive science, The MIT Press, Cambridge, Massachusetts, Reif, F. and Heller, J.I., Knowledge structure and problem solving in physics, Educational Psychologist, 17, , Salthe, S.N., Evolving Hierarchical Systems, their Structure and Representation, Columbia University Press, Silberschatz, A. and Tuzhilin, A., On subjective measures of interestingness in knowledge discovery, Proceedings of KDD, , Silberschatz, A. and Tuzhilin, A., What makes patterns interesting in knowledge discovery systems? IEEE Transactions on Knowledge and Data Engineering, 8, , Simpson, S.G., What is foundations of mathematics? retrieved November 21, Sowa, J.F., Conceptual Structures, Information Processing in Mind and Machine, Addison-Wesley, Reading, Massachusetts, Yao, Y.Y., Modeling data mining with granular computing, Proceedings of the 25th Annual International Computer Software and Applications Conference (COMPSAC 2001), , Yao, Y.Y., A step towards the foundations of data mining, Proceedings of the SPIE: Data Mining and Knowledge Discovery: Theory, Tools, and Technology, 5098, , Yao, Y.Y., Chen, Y.H. and Yang X.D., Measurement-theoretic foundation for rules interestingness, ICDM 2003 Workshop on Foundations of Data Mining, , Yao, Y.Y. and Liau, C.J., A generalized decision logic language for granular computing, FUZZ-IEEE on Computational Intelligence, , Yao, Y.Y. and Zhao, Y., Explanation-oriented data mining, in: Wang, J. (Ed.), Encyclopedia of Data Warehousing and Mining, , Idea Group Inc., Yao, Y.Y., Zhao, Y. and Maguire, R.B., Explanation-oriented association mining using rough set theory, Proceedings of the 9th International Conference of Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, , Yao, Y.Y. and Zhong, N., An analysis of quantitative measures associated with rules, Proceedings of PAKDD 99, , Yao, Y.Y. and Zhong, N. and Ohshima, M., An analysis of peculiarity oriented multi-database mining, IEEE Transactions on Knowledge and Data Engineering, 15, , 2003.

15 30. Zhao, Y. and Yao, Y.Y., Interactive classification using a granule network, Proceedings of ICCI 05, , Zhong, N., Liu, C. and Ohsuga, S., Dynamically organizing KDD processes, International Journal of Pattern Recognition and Artificial Intelligence, 15,