Multi-dimensional databases generally have hierarchies or formula-based relationships of data within each dimension. Consolidation involves computing all of these data relationships for one or more dimensions, for example, adding up all Departments to get Total Division data. While such relationships are normally summations, any type of computational relationship or formula might be defined.
A calculated member is a member of a dimension whose value is determined from other members' values (e.g., by application of a mathematical or logical operation). Calculated members may be part of the OLAP server database or may have been specified by the user during an interactive session. A calculated member is any member that is not an input member.
A single datapoint that occurs at the intersection defined by selecting one member from each dimension in a multi-dimensional array. For example, if the dimensions are measures, time, product and geography, then the dimension members: Sales, January 1994, Candy Bars and United States specify a precise intersection along all dimensions that uniquely identifies a single data cell, which contains the value of candy bar sales in the United States for the month of January 1994.
Members of a dimension that are included in a calculation to produce a consolidated total for a parent member. Children may themselves be consolidated levels, which requires that they have children. A member may be a child for more than one parent, and a child's multiple parents may not necessarily be at the same hierarchical level, thereby allowing complex, multiple hierarchical aggregations within any dimension.
Formulae with all operands within a dimension are common, even in non-OLAP systems: e.g., Profit = Sales - Expense might appear in a simple spreadsheet product. In an OLAP system, such a calculation rule would normally calculate Profit for all combinations of the other dimensions in the cube (e.g., for all Products, for all Regions, for all Time Periods, etc.) using the respective Revenue and Expense data from those same dimensions. Part of the power of an OLAP system is the extensive multi-dimensional application of such a simply stated rule, which could be specified by the OLAP application builder or created by the end user in an interactive session. The true analytical power of an OLAP server, however, is evidenced in its ability to evaluate formulae where there are members from more than one dimension. An example is a multi-dimensional allocation rule used in business unit profitability applications. If, for example, a company has a Business Unit dimension and one of the business units (XYZ) is funding a special advertising campaign for Product A, and the other business units which also sell Product A are willing to share the advertising costs in proportion to their sales of the product, then the formula would be:
ADVERTISING EXPENSE = (PRODUCT A SALES/TOTAL CORPORATION PRODUCT A SALES) * ADVERTISING EXPENSE FOR PRODUCT A FOR BUSINESS UNIT XYZ
Here, Advertising is from the Measures dimension wherever it intersects with other dimensions (e.g., Business Unit, Product), but Product A Sales is more specific; it is Sales from the Measures dimension restricted to the Product A member from the Product dimension. The Advertising Expense to be shared is the Advertising Expense for Product A spent by Business Unit XYZ that the business units which have non-zero sales of Product A agreed to share. These references to several dimensions within the same rule make it a Cross-Dimensional Formula. GENERATION, HIERARCHICAL
Two members of a hierarchy have the same generation if they have the same number of ancestors leading to the top. For example, the top member of a dimension is from Generation 1. There may be two or more members in Generation 1 if there are multiple hierarchies in the dimension.
NOTE: The terms generation and level are both necessary to describe sub-groups of dimension members, since, for example, although two siblings share the same parent and are therefore of the same generation, they won't be from the same level if one of the siblings has a child and the other doesn't.
Synonyms: Peer, Sibling
See: Level, Hierarchical Relationships, Parent, Children
A multi-dimensional database is dense if a relatively high percentage of the possible combinations of its dimension members contain data values. This is the opposite of sparse.
Derived data is produced by applying calculations to input data at the time the request for that data is made, i.e., the data has not been pre-computed and stored on the database. The purpose of using derived data is to save storage space and calculation time, particularly for calculated data that may be infrequently called for or that is susceptible to a high degree of interactive personalization by the user. The tradeoff is slower retrievals.
A dimension is a structural attribute of a cube that is a list of members, all of which are of a similar type in the user's perception of the data. For example, all months, quarters, years, etc., make up a time dimension; likewise all cities, regions, countries, etc., make up a geography dimension. A dimension acts as an index for identifying values within a multi-dimensional array. If one member of the dimension is selected, then the remaining dimensions in which a range of members (or all members) are selected defines a sub-cube. If all but two dimensions have a single member selected, the remaining two dimensions define a spreadsheet (or a "slice" or a "page"). If all dimensions have a single member selected, then a single cell is defined. Dimensions offer a very concise, intuitive way of organizing and selecting data for retrieval, exploration and analysis.
Drilling down or up is a specific analytical technique whereby the user navigates among levels of data ranging from the most summarized (up) to the most detailed (down). The drilling paths may be defined by the hierarchies within dimensions or other relationships that may be dynamic within or between dimensions. For example, when viewing sales data for North America, a drill-down operation in the Region dimension would then display Canada, the eastern United States and the Western United States. A further drill- down on Canada might display Toronto, Vancouver, Montreal, etc.
A formula is a database object, which is a calculation, rule or other expression for manipulating the data within a multi-dimensional database. Formulae define relationships among members. Formulae are used by OLAP database builders to provide great richness of content to the server database. Formulae are used by end users to model enterprise relationships and to personalize the data for greater visualization and insight.
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OLAP Jargons
