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The Structure of a Dimensional Database
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One of the most popular data warehouse designs is called a multidimensional database. The term multidimensional conjures up images of Albert Einstein s curved space-time, parallel universes, and mathematical formulas that make solving for integrals sound soothingly simple. The bottom line is that calling a database multidimensional is really a bit of a lie. It s a snazzy term, but when applied to databases it has nothing in common with the multidimensional behavior of particles accelerating near the speed of light or even with the multidimensional aspects of Alice s adventures down the rabbit hole. This section will help you understand what multidimensionality really means in a database context. Suppose that you are the president of a small, new company. Your company needs to grow, but you have limited resources to support the expansion. You have decisions to make, and to make those decisions you must have particular information. In the world of data warehousing, a summarizable numerical value that you use to monitor your business is called a measure. When looking for numerical information, your first question is which measure you want to see. You could look at, say, Sales Dollars, Shipment Units, Total Defects, or Ad Campaign Responses. Suppose that you ask your personal financial analyst to create a report of your company s total Units Sold. Here s what you ll get (imagine that the numbers are in millions, if you prefer):
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Understanding Business Intelligence and Data Warehousing
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Looking at the one value is useful, but frustrating: You want to break it out into something more informative. For example, how has your company done over time You ask for a monthly analysis, and here s the new report:
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Your company has been operating for four months, so across the top of the report you ll find four labels for the months. Rather than the one value you had before, you ll now find four values. The months subdivide the original value. The new number of values equals the number of months. This is analogous to calculating linear distances in the physical world: The length of a line is simply the length. You re still not satisfied with the monthly report. Your company sells more than one product. How did each of those products do over time You ask for a new report by product and by month:
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Your young company sells three products, so down the left side of the report are the three product names. Each product subdivides the monthly values. Meanwhile, the four labels for the months are still across the top of the report. You now have 12 values to consider. The number of values equals the number of products times the number of months. This is analogous to calculating the area of a rectangle in the physical world: Area equals the rectangle s length times its width. The report even looks like a rectangle. The comparison to a rectangle, however, applies only to the arithmetic involved, not to the shape of the report. Your report could be organized differently it could just as easily look like this:
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Part I:
Getting Started with Analysis Services
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Whether you display the values in a list like the one above (where the numerical values form a line) or display them in a grid (where they form a rectangle), you still have the potential for 12 values if you have four monthly values for each of three products. Your report has 12 potential values because the products and the months are independent. Each product gets its own sales value even if that value is zero for each month. Back to the rectangular report. Suppose that your company sells in two different states and you d like to know how each product is selling each month in each state. Add another set of labels indicating the states your company uses, and you get a new report, one that looks like this:
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The report now has two labels for the states, three labels for products (each shown twice), and four labels for months. It has the potential for showing 24 values, even if some of those value cells are blank. The number of potential values equals the number of states times the number of products times the number of months. This is analogous to calculating the volume of a cube in the physical world: Volume equals the length of the cube times its width times its height. Your report doesn t really look like a cube it looks more like a rectangle. Again, you could rearrange it to look like a list. But whichever way you lay out your report, it has three independent lists of labels, and the total number of potential values in the report equals the number of unique items in the first independent list of labels (for example, two states) times the number of unique items in the second independent list of labels (three products) times the number of unique items in the third independent list of labels (four months). Because the phrase independent list of labels is wordy, and because the arithmetic used to calculate the number of potential values in the report is identical to the arithmetic used to calculate length, area, and volume measurements of spatial extension in place of independent list of labels, data warehouse designers borrow the term dimension from mathematics. Remember that this is a borrowed term. A data analysis dimension is very different from a physical dimension. Thus, your report has three dimensions State, Product, and Time and the report s number of values equals the number of items in the first dimension times the number of items in
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