Symmetry FoundAnalytic problem solving and communication are easier with a standard languageBy Erik Thomsen Continued from Page 1 Thus, the query In contrast, for the query The dimension and measure symmetry applies to all operations, not just querying (which is supported by many analytic models). TYPE STRUCTURESTypes can have any form of single or multiple hierarchy, which can be leveled, ragged, or mixed. Types, in this sense, provide for very rich dimension structuring. You can combine types through structural operators such as Cartesian product, insert, concatenate, and 1-N and 1-1 correspondence. In this sense, types behave like sets and can support the set-like operators used in relational algebra. Types can also enter into equations with the whole type serving as an independent variable (right-hand side of the equation) or dependent variable (left-hand side of the equation) or with an instance of a type serving, on either side of the equal sign. In other words, formulas may be associated with the instances of a type or between types. Type Schemas. Schemas are type structures in LC form. For example, assume you have the types
"time," "store," "product," and "sales." Using time, store, and product as locators and sales as
contents yields The schema breaks down as follows:
In other words, you take the cross product of the distinct instances of time, store, and product and for every intersection associate some value of sales. This functional definition of a so-called cube or fact table captures the "sales" measurement event. It implies that, when measuring sales, you need to know for which stores, times, and products you are doing the measuring. However, you don't need to know what the sales were. That's why they're being measured! What if instead of measuring the sales values for particular store-time-product combinations, you
wanted to measure the distribution of stores as a function of how much they sold of all products in
2000? How would you express the schema using the same combinatorial operators that were just
introduced? How about the following?
This schema says to take the cross product of every sales bin with the "all" member of the product dimension and the "year 2000" member of the time dimension, and for every defined intersection associate some value for the count of stores. The design, implementation, use, and maintenance of activity-based management systems, enterprise decision support, performance indicators, or any other decision-oriented analytic solution requires clear thinking about and within the notions of type, type structure, schema, and model. In future columns I will leverage these concepts to describe ways of creating different types of analytic solutions, or components of analytic solutions such as formulas, and help the reader think through their associated challenges. Erik Thomsen [erik@dimsys.com] is cofounder of Power Thinking Tools, which developed the first OLAP engine with integrated statistics, visualization, text processing, and object management. He is a researcher and consultant for Dimensional Systems and focuses on integrated multitechnology analytic solutions. He is the author of OLAP Solutions (John Wiley & Sons, 1997) and coauthor of Microsoft OLAP Solutions (John Wiley & Sons, 1999). RESOURCESLC Model paper: www.dsslabcom Related Article at IntelligentEnterprise.com: "Symmetry Lost," March 30, 1999
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