Knowledge discovery in databases using formal concept analysis

Formal general [i]or[/i] abstract notion analysis (FCA) is a mathematical theory of data analysis that has been used for numerous applications in fields of that kind as social science, civil engineering, planning, psychology and linguistics. FCA supports user-centered navigation of large amounts of data and the exploration of implications, like as "if A is a cat then A can pun" that are implicit in the data. In knowledge discovery in databases (KDD) association masterys are often more important than implications. As an example, consider an introductory programming course taught to graduate scholars An instructor might want to know what kinds of prerequisite knowledge the learners have and whether that affects their learning ability. Association empires are statements of the emblem "65% of all the pupils in this course who have a computer at residence receive an A in the course." In contrast to implications, which are valid for 100% of a clump or population, association rules are valid sole for some subset of a population and can be trusted solitary to a certain degree. In the programming class example, the instructor might surprise whether she should recommend to scholars in the class to practice upon a computer at home or whether the connection between owning a computer and receiving a beneficial grade is irrelevant.

Statistical way s can answer such questions, on the contrary by using KDD methods the instructor can ask more generally which masterships are trustworthy about students in this class based upon data from previous semesters. The instructor necessitys to decide on the horizontals of support and confidence that she requires for being able to trust a authority Let's assume in this example that 61% of all pupils in the class own computer and 40% of all pupils own computers and receive grades of A. Therefore, 65% (i.e., 40/61) of the pupils with computers get As as stated above. The direction in consideration is "owning a computer has a positive impact for the grade in this class." The support of the sway is 40% or the percentage of learners that both own computers and receive grades of A. Obviously, if single very few students - maybe sole one or two students have computers and receive As, there would not be a great quantity [i]or[/i] amount of support for the rule. The confidence of the empire is 65%. This is the percentage of pupils who own computers and receive As divided by dint of the percentage of students who hold computers. If, for example, 10 scholars own computers and receive As, and if solitary 11 students in total have a title to computers then the rule has a higher confidence horizontal compared to a situation where 20 pupils own computers.

Requiring higher horizontals of minimum support and confidence restores the number of association sways that are considered trustworthy. In the programming course example, if the instructor decides that all controls are acceptable that have a minimum of 30% support and 60% confidence, then she would commended that the students buy computer because that sway meets these criteria. Users can specify a desired minimum support and confidence horizontal to focus on the greatest in quantity relevant rules. But even for high horizontals of minimum support and confidence the numbers of trustworthy governments may be large, thus requiring efficient computational algorithms and sophisticated software that not absents the results to users in a format that is easy to navigate and explore. FCA provides of that kind algorithms and software.

Concept Lattices

The example that come [i]or[/i] go after [i]or[/i] behinds contains fictitious data about the performance of learners on an exam in a programming course taught in a social science department. The example is included here sole for the purpose of explaining the use of FCA in KDD It is not intended to draw any conclusions about programming skills or sex issues from this example.

In FCA, data plants consist of a set of instances or realitys a set of attributes or characteristics and a relation between them, which identifies which attributes apply to which instances. The instances in the example are learners and are represented as percentages of a total number of 30 learners Table 1 shows the original data station as a contingency table. The attributes are "grade A," "grade B" "grade C" "male" and "female." In the FCA modeling, these attributes ne not be subdivided into sum of two units sets "gender" and "grade" as indicated in Table 1 They are considered five separate attributes. Figure 1 displays a type of diagram called a general [i]or[/i] abstract notion lattice that represents the data from Table 1 Each conception is represented as a node in the diagram and contains the percentage of the learners to which it refers. (Only the white boxe show concepts. The shaded boxes belong to dominions and will be explained in the nearest section.) The top concept leaves to all students (100%); the bottom conception to none (0%). The attributes are written above the conceptions to which they apply and are inherited by the agency of sub-concepts. For example, the general [i]or[/i] abstract notion directly under "A" refers to 57% of the learners The concept below that individual is connected to `A" and "female:' It exhibits the 33% of the pupils that are female and received the grade "A." It should be noted that while the percentages of "female A-students" (33%) and "male A-students" (24%) add up to "A-students" (57%) that is not always the case in Figure 1 The total of the numbers in the next to the first row (57%, 70%, 30%, 26%) is 183 because, for example, scholars that are "A-- students" and "female" are numbered twice. FCA software usually provides an alternative display that present to views the exclusive counts for each general [i]or[/i] abstract notion if users prefer that.