Deriving two-stage learning sequences from knowledge in fuzzy sequential pattern mining

Abstract

A fuzzy sequential pattern consisting of several fuzzy sets represents a frequently occurring behavior related to time and can be discovered from transaction bases. An example is that large purchase amounts of one product were bought by customers after these consumers had bought small purchase amounts of another product. Recently, Hu et al. (2003) proposed a fuzzy data mining method to discover fuzzy sequential patterns. In this method, consumers’ products preferences and consumers’ product buying orders related to purchase behaviors can be found in the fuzzy sequential pattern mining. Since for each decision problem, there is a competence set consisting of ideas, knowledge, information, and skills for solving that problem, we consider knowledge found in fuzzy sequential pattern mining as a needed competence set for solving one decision problem. This paper uses a known competence set expansion method, the minimum spanning table method, to find appropriate two-stage learning sequences that can effectively acquire individual fuzzy knowledge sets found in the fuzzy sequential pattern mining. A numerical example is used to show the usefulness of the proposed method.

Introduction

Sequential pattern mining is the determining of frequently occurring patterns related to time or other sequences [1], where a sequence is an ordered list of itemsets [2]. Actually, sequential patterns can help managers determine which items are bought after other items had been bought [1], or to analyze browsing orders of homepages in a Web site [3]. Recently, Hu et al. [4] have proposed fuzzy sequential pattern mining, and much worthwhile fuzzy knowledge related to consumer purchase behavior, such as “large amounts of product A were frequently purchased for each consumer” or “small amounts of one product and large amounts of another product were purchased sequentially” may be discovered from transaction databases. The former fuzzy representation or term may be roughly interpreted as the consumers’ purchase preference of product A, and the latter fuzzy term may be a fuzzy sequential pattern that roughly represents consumers’ buying order of products. In fact, a fuzzy sequential pattern is derived from consumers’ purchase preference of products and expresses the temporal relation between them. We also find that the fuzzy sequential patterns described by natural languages are well suited for the use by human subjects and will help to increase the flexibility for users in making decisions.

We consider that decision makers can “learn” the above-mentioned fuzzy knowledge as two different types, that is, they can be interested in investigating either consumer behavior or current strategies based on fuzzy sequential patterns. In other words, they can acquire or learn corresponding knowledge from fuzzy sequential patterns. Finally, decision makers should be confident in solving certain decision problems, for example, proposing a more competitive marketing strategy. However, the acquisition of knowledge should be carefully planned rather blindly learned. For example, it seems to be easier to acquire “algorithms” after both “introduction to computer science” and “data structures” have been already acquired, compared to the situation when only “introduction to computer science” has been acquired. That is, how to derive appropriate “learning” sequences from fuzzy knowledge extracted from fuzzy sequential pattern mining for decision makers is an important problem.

Competence sets was initiated by Yu [5], and its mathematical foundation was provided by Yu and Zhang [6]. For each decision problem, there is a competence set consisting of ideas, knowledge, information and skills for its satisfactory solution [5], [6], [7]. From this viewpoint, we can view knowledge found in fuzzy sequential pattern mining as a needed competence set for solving one decision problem. In order to effectively acquire the needed competence set, it is necessary to find appropriate learning sequences for acquiring those useful patterns, the so-called competence set expansion.

Since the set related to “consumers’ product buying orders” (denoted by C2) is derived from the set related to “consumers’ purchase preference of products” (denoted by C1), we assume that it is helpful for decision makers to learn C2 after first learning C1. That is, by treating C1 as an aggregate skill we consider that a two-stage learning sequence is designed to consist of two subsequences: one generated from C1, the other generated from C2. Actually, two-stage learning sequences with minimum costs are derived by a powerful method, the minimum spanning table method (MST), proposed by Feng and Yu [8], since MST is especially powerful for the expansion of set of single skills or terms. From the experimental results, we can see that it is possible to help decision makers effectively acquire a needed competence set found in the fuzzy sequential pattern mining, enabling them to set up strategies for promoting their products or improving their services. It is noted that a compound skill represents a collection of single skills that might be acquired by decision makers [9], [10]; however, it is not considered in this paper for simplicity.

The rest of this paper is organized as follows. Since the fuzzy sequential pattern mining is developed by the simple fuzzy partition method [11], [12], this method is introduced in Section 2. Subsequently, the fuzzy data mining technique for discovering fuzzy sequential patterns is briefly introduced in Section 3, where the generation and representations of C1 and C2 are demonstrated in detail. Section 4 introduces the MST. Detailed experimental results of a numerical example are presented in Section 5. We end this paper with discussions and conclusions in Section 6.