Concept Data Analysis: Theory and Applications

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Formal concepts are very important notions of FCA. And intents and extents are also very important elements of formal concepts. So, if the set of intents is determined, the corresponding concept lattice is identified. Thus, obtaining all intents or extents is very important. Generally, the basic way to obtain all intents or extents is via their definitions. If there are n objects, then we should calculate 2 n times to obtain all intents.

Obviously, the computational costing is very huge. To solve this problem, we give a new method to obtain all intents.

And correspondingly, the formal concepts are determined. This paper is organized as follows. In Section 2 , we briefly review some basic notions related to FCA. In Section 3 , a novel concept acquisition approach is introduced and some related conclusions are given. In Section 4 , the corresponding algorithm is proposed and experimental results are shown to illustrate the validity of our method. Finally, conclusions are drawn in Section 5. The elements of G are called the objects and the elements of M are called the attributes of the context.

We assume that all the formal contexts we study in the sequel are finite and canonical. Let G , M , I be a formal context. The family of all formal concepts of G , M , I forms a complete lattice that is called the concept lattice and is denoted by L G , M , I. Table 1 is a formal context G , M , I. The basic way to obtain all intents or extents is via their definitions.

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If there are n objects, then we should calculate 2 n times to get all intents. Obviously, the amount of computation is very large. So our paper presents a new approach to solve the problem.

In this section, we give this new method and some theorems to explain its rationality and validity. On the contrary, if we want to obtain all extents, the subsets of M can be used to determine subsets of G. This point has been illustrated in the sequel. The proof is immediately obtained from Definitions 1 and 4. Theorem 6 guarantees the convergence of Algorithm 2 involved in the sequel.

Using Theorem 6 repeatedly, we can easily obtain the following results: Now, the process to calculate all intents is summarized as follows. Now all the intents have been found and there is no extra computing. In the following, we use an example in the literature [ 24 ] to examine the main results about the new method to find all intents of formal concepts.

Since we require all the formal contexts in this paper are canonical, we delete the attribute a water from the original formal context.

These results are easily examined from Figure 2. Algorithm 1 is given based on Definition 1 completely.

Description

Algorithm 2 is based on our approach presented by Theorem Comparing with Algorithm 1 , we add a condition to terminate the program. The time complexity of Algorithm 2 is analyzed as follows. So we can get two matters as follows. We present an example demonstrating performance of Algorithm 2.

Suppose there are 12 patients which are denoted by 1,…, 12 and 8 symptoms of patients which are denoted by a ,…, h , where a is headache, b is fever, c stands for painful limbs, d represents swollen glands in neck, e is cold, f is stiff neck, g is rash, and h is vomiting. In this section, we conduct some experiments to compare Algorithm 2 with Algorithm 1. In the experiments, four real life databases we selected are as follows:. It can be seen that Algorithm 2 is much more efficient than Algorithm 1 along with the increase of I.

To find new methods to solve the difficult problems of the concept lattice construction is a hot problem. Constructing concept lattices is a novel research branch for data processing and data analysis. Different methods play essential roles in different problems.

Concept data analysis. Theory and application by Claudio Carpineto

This paper first defines some basic notions. Based on the basic notion of intents, we obtain a new judgment method of finding all intents of formal concepts. Moreover, an example is given to explain the feasibility of this method.

At last, we give the corresponding algorithm of this method and do the experiments to illustrate the effectiveness of this method. For Algorithm 2 , we have the following discussion which can be applied to real application. We can compare G with M of a formal context. Otherwise, according to the duality principle, the subsets of M can be used to determine subsets of G and output the set of extents. We will improve the corresponding algorithm of this method in the future.

The authors declare that there is no conflict of interests regarding the publication of this paper. National Center for Biotechnology Information , U.

Journal List ScientificWorldJournal v. Published online Jul Received Jun 28; Accepted Jul This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract As an important tool for data analysis and knowledge processing, formal concept analysis FCA has been applied to many fields. Introduction Formal concept analysis FCA , proposed by Wille in [ 1 ], is a field of applied mathematics based on the mathematization of concept and conceptual hierarchy. Preliminaries In this section, we recall some basic notions and properties in FCA.

Definition 1 see [ 24 ]. Definition 2 see [ 10 ]. Example 3 see [ 10 ]. Open in a separate window. Table 1 A formal context G , M , I. A Novel Concept Acquisition Approach The basic way to obtain all intents or extents is via their definitions. Each of the two unify instructions functions in two modes depending on whether a term is to be matched from, or being built on, the heap. For matching read mode , these instructions seek to recognize data from the heap as those of the term at corresponding positions, proceeding if successful and failing otherwise. In 0 , failure aborts all further work.

In read mode, these instructions set a global register S to contain at all times the heap address of the next subterm to be matched. L Variable binding creates the possibility that reference chains may be formed. Rather than systematically occupying a heap cell to reference, a constant can be simply assigned as a literal value.

The following instructions are thus added to 0: Other rules are called deep rules. As in Prolog, the scope of variables is limited to the clause or query in which they appear. By Claudio Carpineto "With the appearance of the internet besides the unparalleled quantity of knowledge to be had in digital structure, conceptual information research is extra worthy and useful than ever, simply because this know-how addresses vital barriers of the structures that presently help clients of their quest for info.

1. Introduction

Theory and Algorithms This ebook presents complete insurance of the trendy tools for geometric difficulties within the computing sciences. Proceedings This publication constitutes the refereed lawsuits of the twelfth foreign convention on synthetic Intelligence and Symbolic Computation, AISC , held in Seville, Spain, in December Theory and application by Claudio Carpineto.

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