Ontology-Assisted Query Formulation in Multidimensional Association Rule
Mining
1
Chin-Ang Wu
Wen-Yang Lin,
Chuan-Chun Wu
Department of
Information Management,
I-Shou University,
Kaohsiung County, Taiwan
840, R.O.C.
cwu@csu.edu.tw
Department of Computer
Science and Information
Engineering,
National University of
Kaohsiung, Kaohsiung,
Taiwan 811, R.O.C.
Department of
Information Management,
I-Shou University,
Kaohsiung County,
Taiwan 840, R.O.C.
miswucc@isu.edu.tw
wylin@nuk.edu.tw
1Chin-Ang Wu is also a lecturer in Cheng Shiu University, Niaosong Township,Kaohsiung County 833.hsiung County
Abstract
In the information era, the development of various electronic information resources have dramatically grown, mining useful information from large databases has become one of the most important issues in information research for users. Information technologies have provided many applicable solutions, yet there are still many problems that cause users to spend extra time to get real knowledge. In this paper, we show an ontology based system framework for multi-dimensional association rule mining that incorporates ontologies in order to help users develop correct queries, reduce the system resource consumption and improve the efficiency of the mining process.
1. Introduction
In the knowledge economics era, the efficient use of data to promote business competition and opportunities is an important movement. Information technologies have provided many applicable solutions, but many decision analyses are still greatly dependent on professionals’ manual judgments. We expect that a good system should provide efficient, convenient and thorough mining mechanisms, as well as meet the users’ professional demands. In other words, developing a system environment that provides users a way to repeatedly discover important rules or facts based on their professional judgment is absolutely an issue that research workers in the knowledge mining fields can not avoid. Currently, the research on the integration of data mining
and data warehousing are mostly concentrated on data mining from data cube or multi-dimensional database. J. Han’s research group pioneered this research subject. They combined OLAP and data mining to develop DBMiner, a system that provides minings of association rules, classification, prediction and clustering from data cube[3]. To provide OLAP with efficient data storage and data analysis, star schema, proposed by Kimball [5], is a prevalent data model being used in many data warehouse systems. But the hierarchical and other semantic relationships among attributes which may be helpful to the data mining systems are not able to be displayed in the star schema and hence leave data mining with limitations. Thus an ontology, which is used to describe and represent domain knowledge [4], can be applied to collect the semantic knowledge of data warehouse. The main purpose of this paper is to show an ontology based system framework for multidimensional association rule mining that incorporates ontologies in order to help users develop correct queries and reduce the system resource consumption and improve the efficiency of the mining process.
The rest of this paper is organized as follows. In section 2, we introduce multidimensional association rule mining and its query with constriants. The framework of ontology-based multidimensional association rule mining system is explained in section 3. In section 4, query formulation and checking with the help of ontologies are described. And finally this paper concluded in section 5.
2. Multidimensional association rule mining
and its query with constraints
An association rule is an expression of the form X ⇒ Y, where X and Y are sets of items. Such a rule reveals that transactions in the database containing items in X tend to also contain items in Y. X is the body or the antecedent and Y is the head or the consequent. The probability, measured as the fraction of transactions that contain X also contain Y, is called the confidence of the rule. The support of the rule is the percentage of the transactions that contain all items in both X and Y.
A multidimensional association rule explores the association between data values from different dimensional attributes in data warehouses.
Definition 1. Consider a transaction table composed of k
dimensions. Let xim and yjn be the values of dimensions Xi
and Yj, respectively. The form of a multi-dimensional
association rule is:
X1= “x1m”, X2 = “x2m”, …., Xi = “xim” ⇒ Y1 = “y1n”, Y2 =
“y2n”, …., Yj = “yjn”
Following the work in [9], we can divide multi-dimensional association rules into three different types: intra-dimensional association rule, inter-dimensional association rule, and hybrid association rule.
In multidimensional association rule mining, users need to decide what dimensions to use to group data and what interested data items to be projected for mining association rules. For example, if a user is interested in mining association rules among age_group, city and category from each customer’s daily purchased, then “Customer_ID” and “Date” will be the grouping dimensions and “Age_group”, “City” and “Category” will be the interested mining items. Table 1 is this example table for mining multidimensional association rules.
Definition 2. Suppose a star schema S containing a fact
table F and m dimension tables {D1, D2, …, Dm}. Let T
be a jointed table from S composed of a1, a2, …, ak
attributes, such that ∀ai, aj∈ Attr(Dk), 1 ≤ i, j ≤ r, 1 ≤ k ≤
m. Here Attr(Dk) denotes the attribute set of dimension
table Dk. A constrained meta-pattern of multidimensional
association rule mining from T is defined as follow, MP: 〈tG, tM, ms, mc, [wc],[hc],[mr]〉,
where ms denotes the minimum support, mc the minimum confidence, tG the group of transaction attributes, tM the
group of interested mining items, for tG, tM⊆ {a1, a2, ….,
ak}. In addition to these four basic elements, the
meta-pattern constraints include wc the where condition for data in the data warehouse, hc the having condition and mr the meta rule. The constraints of the meta-pattern are optional.
Table 1. An example table for multidimensional association rule mining
Grouping_ID Interested Mining_Items
Cust_ID Date Age_group City *Category C01 2007-02-01 21-30 Taipei B,C,D,E C02 2007-02-03 31-40 Tainan A,D,E C03 2007-02-10 31-40 Taichung C,D C01 2007-02-10 21-30 Taipei A,E C05 2007-02-12 41-50 Kaohsiung A,B,C C03 2007-02-15 31-40 Taichung A,E *A: Priter B: Laptop C: Desktop D: Memory E: Hard Disk
A query of multidimensional association rule mining is defined as follows:
Mining multidimensional association rules
[Metarule <meta-rule>]
Grouping_ID <attribute list>
Mining_Item <attribute list>
From <dw_name> [Where <wcondition>]
[Having <hcondition>]
Threshold <ms, mc>
If a user is interested in mining associations of HP printer with age_group, city or other products from each customer’s daily transaction in the market of Japan with minimum support 30% and minimum confidence 50%, the example query is as follow.
Mining multidimensional association rules Metarule Prodcut.Prod_Name=“HP printer”,
B1,..,Bn⇒ H1,..,Hn. Grouping_ID Customer,date, Mining_Item Age_group,City,Prod_Name From Sale_Star Where Country=’Japan’ Threshold ms=30%, mc=50%
3. The framework of ontology-based
multidimensional association rule mining
system
It is well known that the data mining is a knowledge intensive process that requires domain-specific knowledge (ontology) [1][2]. A typical star schema shows only the structural relationships among dimensions and attributes but lack of semantic connections among them.
Therefore, we have proposed a data mining system framework that incorporates ontologies for mining association rules from data warehouse [6]. In this section we will describe and enhance this system framework to make query formulation and checking more specific. Figure 1 illustrates the system framework.
Figure 1. Ontology-based system framework for multidimensional association rule mining
The system framework includes a schema ontology, a schema constraint ontology, some domain ontologies and a user query history ontology. A user can form a mining query interactively in the system with the help of these ontologies. The query can then be processed by the association rule mining engine to generate knowledge patterns.
The schema ontology is used to describe metadata of the data warehouse, including schema structures, dimension hierarchies and the types of measures along dimensions. There exist some constraints of attributes in a data warehouse schema. In [7][8], the authors explored all possible mining spaces of grouping and mining attribute combinations. They then defined allowed range via the predicates functions, such as ignore, together, item-only, group-only, always-group, always-item, decide, follow and repel. These functions convey some constraints which are related to multidimensional association rule mining and these constraints are then recorded in the schema constraint ontology in our system to provide knowledge for users and the system as a reference to select grouping_ID and interested mining attributes. Figure 2 is an example of a schema constraint ontology.
A domain ontology is used to construct domain related knowledge of the mining subject. A domain ontology can contain relationships among classes such as classification and composition. Such knowledge can provide data mining with extra information beyond the data warehouse and hence reduce data mining searching boundaries and bring more innovative mining results.
The query history ontology is applied to collect history mining patterns and their corresponding results
from users’ mining activities. The elements of the meta-pattern defined in definition 2, the result rules and the result statistics will be included in the history ontology. Figure 3 is the graph of the query history ontology. The statistic data including number of frequent item set, average length of items, maximum length of items, minimum length of items, number of rules, average length of rules, maximum length of rules and minimum length of rules.
Figure 2. Schema constraint ontology
Figure 3. Query history ontology
4. Ontology assisted user query formulation
Without complete comprehension of the schema and domain related knowledge, end users may develop a query based on their experience or intuition. Therefore, users’ formulation of queries can possibly fall into some improper pits. This may lead to incorrect and redundant mining data space or mining results and waste the efforts accordingly.Through the assistance of ontologies the system will take more responsibilities in controlling the correctness and effectiveness of the query formulation. To get a correct query to feed into the mining process, the system will, after the user finish forming the query, first check the syntax and then perform the semantic checking if syntax check is all right. Figure 4 is the user query checking process.
User query formulation Query history ontology Schema constraint ontology Syntax OK Semantic OK yes yes no no
A correct query for mining process
Figure 4. process of user query checking
While a user is formulating a query, the browse over query history ontology which provides users with abundant query format and result rules and statistics, can be performed to assist an inexperienced user with ideas of how to formulate a query. A user can also draw a query based on a history one or he or she can submit a query in order to compare the results with those have existed in the query history ontology. A query history ontology can therefore provide supplement information for users in order to generate useful queries that match better to the users need.
The system will check syntax of the query first and then progress toward semantic checking, which other systems disregard. While performing the semantic checking, the schema constraint ontology is a very important knowledge source for the system to refer. The schema constraint ontology provides restrictions on attribute combinations of group-by items and interested mining items. For example, the functional dependency relationship between Cust_ID and Sex will cause the mining query of tG = {Cust_ID, Sex} and tM =
{Prod.Name} into a redundant form. In tG, Cust_ID
decides the value of Sex and therefore the groupedg tables of tG = {Cust_ID, Sex} and tG = {Cust_ID} will be
the same. This kind of constraint is defined as decide(Cust_ID, Sex) in the schema constraint ontology. Note that a hierarchical relationship is a special case of functional dependency. The descendant’s value determines its ancestor’s value in the hierarchy.
There are varieties of other constraints that the system will utilize to check against the selected tG and tM. This
can protect users from proposing improper mining queies.
5. Conclusion
In this paper, we have shown multidimensional association rule mining and its query with constraints and explained a system framework that incorporates with schema ontology, schema constraint ontology, domain ontology and query history ontology. The useful information left out by a data warehouse system can be accessible through the assistance of these ontologies. This
system can help the user’s query formulation and do query correctness checking in both syntax and semantics. Through the utilization of ontologies in the system framework, the correctness and efficiency of the mining process can be improved.
Acknowledgements
This work was supported by the National Science Council of R.O.C. under grant NSC 94-2213-E-390-006.
References
[1] J.M. Aronis, F.J. Provost, and B.G. Buchanan, “Exploiting background knowledge in automated discovery,” in Proc. 2nd
Intl. Conf. Knowledge Discovery and Data Mining, 1996.
[2] U. Fayyad, P.S. Gregory, and S. Padhraic, “The KDD process for extracting useful knowledge from volumes of data,”
Communications of the ACM, Vol. 39, No. 11, 1996, pp. 27–34.
[3] J. Han, “Mining knowledge at multiple concept levels,” in
Proc. of ACM International Conference on Information and Knowledge Management, 1995, pp. 19-24.
[4] Jeff Heflin (2004). OWL Web Ontology Language Use Cases and Requirements, http://www.w3.org/TR/webont-req/, Feb. 2004.
[5] R. Kimball, The Data Warehouse Toolkit Practical For Building Dimensional Data Warehouses, John Wiley & Sons,
INC. 1996.
[6] Wen-Yang Lin, Chin-Ang Wu, Ming-Cheng Tseng, Chuan-Chun Wu (2006). “Ontology-Incorporated Mining of Association Rules in Data Warehouse”, The 11th Conference on
Artificial Intelligence and Applications, Kaohsiung, Taiwan, R.O.C.
[7] Chang-Shing Perng, Haixun Wang Ma, Joseph L. Hellerstein, “Farm: A Framework for Exploring Mining Spaces with Multiple Attributes,” 2001 IEEE.
[8] Chang-Shing Perng, Haixun Wang Ma, Joseph L. Hellerstein, “User-directed exploration of Mining Space with Multiple Attributes,” 2002 IEEE.
[9] Hua Zhu, “On-Line Analytical Mining of Association Rules,” Master’s Thesis, Simon Fraser University, U.S.A, Dec 1998.
