Oracle® OLAP Application Developer's Guide 10g Release 1 (10.1) Part Number B10333-02

2 The Multidimensional Data Model

This chapter describes the multidimensional data model and how it is implemented in relational tables and standard form analytic workspaces. It consists of the following topics:

2.1 The Logical Multidimensional Data Model

The multidimensional data model is an integral part of On-Line Analytical Processing, or OLAP. Because OLAP is on-line, it must provide answers quickly; analysts pose iterative queries during interactive sessions, not in batch jobs that run overnight. And because OLAP is also analytic, the queries are complex. The multidimensional data model is designed to solve complex queries in real time.

The multidimensional data model is important because it enforces simplicity. As Ralph Kimball states in his landmark book, The Data Warehouse Toolkit:

"The central attraction of the dimensional model of a business is its simplicity.... that simplicity is the fundamental key that allows users to understand databases, and allows software to navigate databases efficiently."

The multidimensional data model is composed of logical cubes, measures, dimensions, hierarchies, levels, and attributes. The simplicity of the model is inherent because it defines objects that represent real-world business entities. Analysts know which business measures they are interested in examining, which dimensions and attributes make the data meaningful, and how the dimensions of their business are organized into levels and hierarchies.

Figure 2-1 shows the relationships among the logical objects.

2.1.1 Logical Cubes

Logical cubes provide a means of organizing measures that have the same shape, that is, they have the exact same dimensions. Measures in the same cube have the same relationships to other logical objects and can easily be analyzed and displayed together.

2.1.2 Logical Measures

Measures populate the cells of a logical cube with the facts collected about business operations. Measures are organized by dimensions, which typically include a Time dimension.

An analytic database contains snapshots of historical data, derived from data in a legacy system, transactional database, syndicated sources, or other data sources. Three years of historical data is generally considered to be appropriate for analytic applications.

Measures are static and consistent while analysts are using them to inform their decisions. They are updated in a batch window at regular intervals: weekly, daily, or periodically throughout the day. Many applications refresh their data by adding periods to the time dimension of a measure, and may also roll off an equal number of the oldest time periods. Each update provides a fixed historical record of a particular business activity for that interval. Other applications do a full rebuild of their data rather than performing incremental updates.

A critical decision in defining a measure is the lowest level of detail (sometimes called the grain). Users may never view this base level data, but it determines the types of analysis that can be performed. For example, market analysts (unlike order entry personnel) do not need to know that Beth Miller in Ann Arbor, Michigan, placed an order for a size 10 blue polka-dot dress on July 6, 2002, at 2:34 p.m. But they might want to find out which color of dress was most popular in the summer of 2002 in the Midwestern United States.

The base level determines whether analysts can get an answer to this question. For this particular question, Time could be rolled up into months, Customer could be rolled up into regions, and Product could be rolled up into items (such as dresses) with an attribute of color. However, this level of aggregate data could not answer the question: At what time of day are women most likely to place an order? An important decision is the extent to which the data has been pre-aggregated before being loaded into a data warehouse.

2.1.3 Logical Dimensions

Dimensions contain a set of unique values that identify and categorize data. They form the edges of a logical cube, and thus of the measures within the cube. Because measures are typically multidimensional, a single value in a measure must be qualified by a member of each dimension to be meaningful. For example, the Sales measure has four dimensions: Time, Customer, Product, and Channel. A particular Sales value (43,613.50) only has meaning when it is qualified by a specific time period (Feb-01), a customer (Warren Systems), a product (Portable PCs), and a channel (Catalog).

2.1.4 Logical Hierarchies and Levels

A hierarchy is a way to organize data at different levels of aggregation. In viewing data, analysts use dimension hierarchies to recognize trends at one level, drill down to lower levels to identify reasons for these trends, and roll up to higher levels to see what affect these trends have on a larger sector of the business.

Each level represents a position in the hierarchy. Each level above the base (or most detailed) level contains aggregate values for the levels below it. The members at different levels have a one-to-many parent-child relation. For example, `Q1-02` and `Q2-02` are the children of `2002`, thus `2002` is the parent of `Q1-02` and `Q2-02`.

Suppose a data warehouse contains snapshots of data taken three times a day, that is, every 8 hours. Analysts might normally prefer to view the data that has been aggregated into days, weeks, quarters, or years. Thus, the Time dimension needs a hierarchy with at least five levels.

Similarly, a sales manager with a particular target for the upcoming year might want to allocate that target amount among the sales representatives in his territory; the allocation requires a dimension hierarchy in which individual sales representatives are the child values of a particular territory.

Hierarchies and levels have a many-to-many relationship. A hierarchy typically contains several levels, and a single level can be included in more than one hierarchy.

2.1.5 Logical Attributes

An attribute provides additional information about the data. Some attributes are used for display. For example, you might have a product dimension that uses Stock Keeping Units (SKUs) for dimension members. The SKUs are an excellent way of uniquely identifying thousands of products, but are meaningless to most people if they are used to label the data in a report or graph. You would define attributes for the descriptive labels.

You might also have attributes like colors, flavors, or sizes. This type of attribute can be used for data selection and answering questions such as: Which colors were the most popular in women's dresses in the summer of 2002? How does this compare with the previous summer?

Time attributes can provide information about the Time dimension that may be useful in some types of analysis, such as identifying the last day or the number of days in each time period.

2.2 The Relational Implementation of the Model

The relational implementation of the multidimensional data model is typically a star schema, as shown in Figure 2-2, or a snowflake schema. A star schema is a convention for organizing the data into dimension tables, fact tables, and materialized views. Ultimately, all of the data is stored in columns, and metadata is required to identify the columns that function as multidimensional objects.

In Oracle Database, you can define a logical multidimensional model for relational tables using the OLAP Catalog or `AWXML`, as described in Chapter 5. The metadata distinguishes level columns from attribute columns in the dimension tables and specifies the hierarchical relationships among the levels. It identifies the various measures that are stored in columns of the fact tables and aggregation methods for the measures. And it provides display names for all of these logical objects.

2.2.1 Dimension Tables

A star schema stores all of the information about a dimension in a single table. Each level of a hierarchy is represented by a column or column set in the dimension table. A dimension object can be used to define the hierarchical relationship between two columns (or column sets) that represent two levels of a hierarchy; without a dimension object, the hierarchical relationships are defined only in metadata. Attributes are stored in columns of the dimension tables.

A snowflake schema normalizes the dimension members by storing each level in a separate table.

2.2.2 Fact Tables

Measures are stored in fact tables. Fact tables contain a composite primary key, which is composed of several foreign keys (one for each dimension table) and a column for each measure that uses these dimensions.

2.2.3 Materialized Views

Aggregate data is calculated on the basis of the hierarchical relationships defined in the dimension tables. These aggregates are stored in separate tables, called summary tables or materialized views. Oracle provides extensive support for materialized views, including automatic refresh and query rewrite.

Queries can be written either against a fact table or against a materialized view. If a query is written against the fact table that requires aggregate data for its result set, the query is either redirected by query rewrite to an existing materialized view, or the data is aggregated on the fly.

Each materialized view is specific to a particular combination of levels; in Figure 2-2, only two materialized views are shown of a possible 27 (3 dimensions with 3 levels have 3**3 possible level combinations).

2.3 The Analytic Workspace Implementation of the Model

Analytic workspaces have several different types of data containers, such as dimensions, variables, and relations. Each type of container can be used in a variety of ways to store different types of information. For example, a dimension can define an edge of a measure, or store the names of all the languages supported by the analytic workspace, or all of the acceptable values of a relation. Dimension objects are themselves one dimensional lists of values, while variables and relations are designed specifically to support the efficient storage, retrieval, and manipulation of multidimensional data.

 Note: Analytic workspaces are registered in the database data dictionary as tables. However, objects stored in analytic workspaces are not registered in the database data dictionary.

Like relational tables, analytic workspaces have no specific content requirements. You can create an empty analytic workspace, populate it only with OLAP DML programs, or define a single dimension to hold a list of values. This guide, however, describes analytic workspaces that comply with database standard form. Database standard form (or simply, standard form) is a convention for instantiating the logical multidimensional model in a particular way so that it can be managed by the current set of Oracle OLAP utilities. It defines a set of metadata that can be queried by any application. Standard form is discussed extensively in this guide, and is described in Appendix A.

2.3.1 Multidimensional Data Storage in Analytic Workspaces

In the logical multidimensional model, a cube represents all measures with the same shape, that is, the exact same dimensions. In a cube shape, each edge represents a dimension. The dimension members are aligned on the edges and divide the cube shape into cells in which data values are stored.

In an analytic workspace, the cube shape also represents the physical storage of multidimensional measures, in contrast with two-dimensional relational tables. An advantage of the cube shape is that it can be rotated: there is no one right way to manipulate or view the data. This is an important part of multidimensional data storage, calculation, and display, because different analysts need to view the data in different ways. For example, if you are the Sales Manager for the Pacific Rim, then you need to look at the data differently from a product manager or a financial analyst.

Assume that a company collects data on sales. The company maintains records that quantify how many of each product was sold in a particular sales region during a specific time period. You can visualize the sales measure as the cube shown in Figure 2-3.

Figure 2-3 compares the sales of various products in different cities for January 2001 (shown) and February 2001 (not shown). This view of the data might be used to identify products that are performing poorly in certain markets. Figure 2-4 shows sales of various products during a four-month period in Rome (shown) and Tokyo (not shown). This view of the data is the basis for trend analysis.

A cube shape is three dimensional. Of course, measures can have many more than three dimensions, but three dimensions are the maximum number that can be represented pictorially. Additional dimensions are pictured with additional cube shapes.

2.3.2 Database Standard Form Analytic Workspaces

Figure 2-5 shows how dimension, variable, formula, and relation objects in a standard form analytic workspace are used to implement the multidimensional model. Measures with identical dimensions compose a logical cube. All dimensions have attributes, and all hierarchical dimensions have level relations and self-relations; for clarity, these objects are shown only once in the diagram. Variables and formulas can have any number of dimensions; three are shown here.

2.3.3 Analytic Workspace Dimensions

A dimension in an analytic workspace is a highly optimized, one-dimensional index of values that serves as a key table. Variables, relations, formulas (which are stored equations) are among the objects that can have dimensions.

Dimensions have several intrinsic characteristics that are important for data analysis:

• Referential integrity. Each dimension member is unique and cannot be `NA` (that is, null). If a measure has three dimensions, then each data value of that measure must be qualified by a member of each dimension. Likewise, each combination of dimension members has a value, even if it is `NA`.

• Consistency. Dimensions are maintained as separate containers and are shared by measures. Measures with the same dimensionality can be manipulated together easily. For example, if the sales and expense measures are dimensioned by time and line, then you can create equations such as profit = sales - expense.

• Preserved order of members. Each dimension has a default status, which is a list of all of its members in the order they are stored. The default status list is always the same unless it is purposefully altered by adding, deleting, or moving members. Within a session, a user can change the selection and order of the status list; this is called the current status list. The current status list remains the same until the user purposefully alters it by adding, removing, or changing the order of its members.

Because the order of dimension members is consistent and known, the selection of members can be relative. For example, this function call compares the sales values of all currently selected time periods in the current status list against sales from the prior period.

```lagdif(sales, 1, time)

```
• Highly denormalized. A dimension typically contains members at all levels of all hierarchies. This type of dimension is sometimes called an embedded total dimension.

In addition to simple dimensions, there are several special types of dimensions used in a standard form analytic workspace, such as composites and concat dimensions. These dimensions are discussed later in this guide.

2.3.3.1 Use of Dimensions in Standard Form Analytic Workspaces

In an analytic workspace, data dimensions are structured hierarchically so that data at different levels can be manipulated for aggregation, allocation, and navigation. However, all dimension members at all levels for all hierarchies are stored in a single data dimension container. For example, months, quarters, and years are all stored in a single dimension for Time. The hierarchical relationships among dimension members are defined by a parent relation, described in "Analytic Workspace Relations".

Not all data is hierarchical in nature, however, and you can create data dimensions that do not have levels. A line item dimension is one such dimension, and the relationships among its members require a model rather than a multilevel hierarchy. The extensive data modeling subsystem available in analytic workspaces enables you to create both simple and complex models, which can be solved alone or in conjunction with aggregation methods.

As a one-dimensional index, a dimension container has many uses in an analytic workspace in addition to dimensioning measures. A standard form analytic workspace uses dimensions to store various types of metadata, such as lists of hierarchies, levels, and the dimensions composing a logical cube.

2.3.4 Analytic Workspace Variables

A variable is a data value table, that is, an array with a particular data type and indexed by a specific list of dimensions. The dimensions themselves are not stored with the variable.

Each combination of dimension members defines a data cell, regardless of whether a value exists for that cell or not. Thus, the absence of data can be purposefully included or excluded from the analysis. For example, if a particular product was not available before a certain date, then the analysis may exclude null values (called `NA`s) in the prior periods. However, if the product was available but did not sell in some markets, then the analysis may include the `NA`s.

No special physical relationship exists among variables that share the same dimensions. However, a logical relationship exists because, even though they store different data that may be a different data type, they are identical containers. Variables that have identical dimensions compose a logical cube.

If you change a dimension, such as adding new time periods to the Time dimension, then all variables dimensioned by Time are automatically changed to include these new time periods, even if the other variables have no data for them. Variables that share dimensions (and thus are contained by the same logical cube) can also be manipulated together in a variety of ways, such as aggregation, allocation, modeling, and numeric calculations. This type of calculation is easy and fast in an analytic workspace, while the equivalent single-row calculation in a relational schema can be quite difficult.

2.3.4.1 Use of Variables to Store Measures

In an analytic workspace, facts are stored in variables, typically with a numeric data type. Each type of data is stored in its own variable, so that while sales data and expenses data might have the same dimensions and the same data type, they are stored in two distinct variables. The containers are identical, but the contents are unique.

An analytic workspace provides a valuable alternative to materialized views for creating, storing, and maintaining summary data. A very sophisticated aggregation system supports modeling in addition to an extensive number of aggregation methods. Moreover, finely grained aggregation rules enable you to decide precisely which data within a single measure is pre-aggregated, and which data within the same measure will be calculated at run-time.

Pre-aggregated data is stored in a compact format in the same container as the base-level data, and the performance impact of aggregating data on the fly is negligible when the aggregation rules have been defined according to known good methods. If aggregate data needed for the result set is stored in the variable, then it is simply retrieved. If the aggregate data does not exist, then it is calculated on the fly.

2.3.4.2 Use of Variables to Store Attributes

Like measures, attributes are stored in variables. However, there are significant differences between attributes and measures. While attributes are often multidimensional, only one dimension is a data dimension. A hierarchy dimension, which lists the data dimension hierarchies, and a language dimension, which provides support for multiple languages, are typical of the other dimensions.

Attributes provide supplementary information about each dimension member, regardless of its level in a dimension hierarchy. For example, a Time dimension might have three attribute variables, one for descriptive names, another for the period end dates, and a third for period time spans. These attributes provide Time member `OCT-02` with a descriptive name of `October 2002`, an end date of `31-OCT-02`, and a time span of `31`. All of the other days, months, quarters, and years in the Time dimension have similar information stored in these three attribute variables.

2.3.5 Analytic Workspace Formulas

A formula is a stored equation. A call to any function in the OLAP DML or to any custom program can be stored in a formula. In this way, a formula in an analytic workspace is like a relational view.

In a standard form analytic workspace, one of the uses of a formula object is to provide the interface between aggregation rules and a variable that holds the data. The name of a measure is always the name of a formula, not the underlying variable. While the variable only contains stored data (the base-level data and precalculated aggregates), the formula returns a fully solved measure containing data that is both stored and calculated on the fly. This method enables all queries against a particular measure to be written against the same column of the same relational view for the analytic workspace, regardless of whether the data is calculated or simply retrieved. That column presents data acquired from the formula.

Formulas can also be used to calculated other results like ratios, differences, moving totals, and averages on the fly.

2.3.6 Analytic Workspace Relations

Relations are identical to variables except in their data type. A variable has a general data type, such as `DECIMAL` or `TEXT`, while a relation has a dimension as its data type. For example, a relation with a data type of `PRODUCT` only accepts values that are members of the `PRODUCT` dimension; an attempt to store any other value causes an error. The dimension members provide a finite list of acceptable values for a relation. A relation container is like a foreign key column, except that it can be multidimensional.

In a standard form analytic workspace, two relations support the hierarchical content of the data dimensions: a parent relation and a level relation.

A parent relation is a self-relation that identifies the parent of each member of a dimension hierarchy. This relation defines the hierarchical structure of the dimension.

A level relation identifies the level of each member of a dimension hierarchy. It is used to select and sort dimension members based on level.