The term "multidimensional data" generally refers to data in which a given fact is quantified by a set of measures, obtained by applying one more or less complex aggregative function (from count or sum to average or percent, and so on) to raw data. Such measures are characterized by a set of variables, called dimensions. In reality, a dimension often consists of a more complex structure than a simple variable, as we will see in the following chapter. Multidimensional data can be modeled by different representations, depending on the application field which uses them. For example, some years ago the term "multidimensional data" referred essentially to statistical data, that is, data whose use was (and is) basically for socio-economic analysis. The visual representation used most was (and is) the table (even if histograms, cakes, graphics, etc. are used too). Recently, the metaphor of the data cube, already proposed at the beginning of the '80s, was taken up again and used for new applications—such as On-Line Analytical Processing (OLAP)—which refer to business analysis.
Many of the problems concerning statistical multidimensional databases and many of the concepts defined in this context, especially if referring to models, operators, and algebras in general, have been up again and enlarged for new management system types and new applications, such as OLAP. Studies on this data type started at the beginning of the '80s. In this introduction we would like to give a brief history of the various topics in this research area, covering the period of the last 20 or more years.
At the beginning of the 1980s, a group of researchers began to look at some of the problems which arose when they considered data obtained by applying simple aggregation functions (count or sum) to row disaggregate data. This was the main reason that prompted some researchers to organize a workshop in California (1st SDBM (1981)) on the main topics of statistical databases (the term used, at that time, for multidimensional aggregate data). This name was coined because such data, organized in a database as flat files or multidimensional "tables," were mainly used to carry out statistical analysis or socio-economic type applications, such as census data on national production and consumption patterns, etc., as discussed in Shoshani (1982), Brown, Navathe, & Su (1983), and Shoshani & Wong (1985). However, they were also used for business applications, such as financial summary reports, sales forecasting, etc., as described in Wong (1984). Generally, these tables are represented by using two dimensions (for this reason they are also called "flat tables"), but, in reality, often a row and/or a column each consists of two or more dimensions.