Multidimensionality in Statistical, OLAP, and Scientific Databases

Multidimensionality in Statistical, OLAP, and Scientific Databases 47 Copyright © 2003, Idea Group Inc. Copying or distributing in print or electronic forms without written permission of Idea Group Inc. is prohibited. INTRODUCTION AND BACKGROUND There is a lot of data that can be viewed as multidimensional data. The term multidimensional databases typically refers to a collection of objects, each represented as a point in a multidimensional space. Even data that is represented in a tabular form, such as relations, can be thought of as multidimensional data, if each row (tuple) is thought of as an object, and the columns (attributes) are thought of as the dimensions. For example, consider the following table: employee (personID, age, sex, salary) shown in Figure 1a. If each person is represented as a point in the multidimensional space of (age, sex, salary), then that table can be represented as in Figure 1b. The utility of representing data in the multidimensional space is that it is more natural to view certain features of the data in this way. For example, it is natural to view clusters in the multidimensional space. In Figure 1b, one can easily see that there is a small cluster of highly paid people (perhaps representing managers who are generally older) and a larger cluster of lower paid people. We can also see ìoutliersî as is the case with the younger person with a high salary. Of course, these concepts extends to data in more than three dimensions, but cannot be viewed as easily. The problem of viewing high-dimensional data to identify clusters, outliers, and various patterns has been the subject of several research projects. An extensive review of such methods is provided in Keim & Kriegel (1996) and will not be discussed further here. Some data is naturally multidimensional such as two-dimensional or threedimensional spatial data. For example, climate modelers prefer to view their observed or simulated data in a multidimensional structure representing space (two or three dimensions), time, and variables being measured (temperature, wind velocity, etc.) In this case, certain operations, such a selecting spatial regions or personID age sex salary