■ A data warehouse is a subject-oriented, integrated, time-variant, and nonvolatile data collection organized in support of management decision making. Several factors distinguish data warehouses from operational databases. Because the two systems provide quite different functionalities and require different kinds of data, it is necessary to maintain data warehouses separately from operational databases.

■ Data warehouses often adopt a three-tier architecture. The bottom tier is a warehouse database server, which is typically a relational database system. The middle tier is an OLAP server, and the top tier is a client that contains query and reporting tools.

■ A data warehouse contains back-end tools and utilities for populating and refreshing the warehouse. These cover data extraction, data cleaning, data transformation, loading, refreshing, and warehouse management.

■ Data warehouse metadata are data defining the warehouse objects. A metadata repository provides details regarding the warehouse structure, data history, the algorithms used for summarization, mappings from the source data to the warehouse form, system performance, and business terms and issues.

■ A multidimensional data model is typically used for the design of corporate data warehouses and departmental data marts. Such a model can adopt a star schema, snowflake schema, or fact constellation schema. The core of the multidimensional model is the data cube, which consists of a large set of facts (or measures) and a number of dimensions. Dimensions are the entities or perspectives with respect to which an organization wants to keep records and are hierarchical in nature.

■ A data cube consists of a lattice of cuboids, each corresponding to a different degree of summarization of the given multidimensional data.

■ Concept hierarchies organize the values of attributes or dimensions into gradual abstraction levels. They are useful in mining at multiple abstraction levels.

■ Online analytical processing can be performed in data warehouses/marts using the multidimensional data model. Typical OLAP operations include roll-up, and drill-( down, across, through), slice-and-dice, and pivot ( rotate), as well as statistical operations such as ranking and computing moving averages and growth rates. OLAP operations can be implemented efficiently using the data cube structure.

■ Data warehouses are used for information processing (querying and reporting), analytical processing (which allows users to navigate through summarized and detailed data by OLAP operations), and data mining (which supports knowledge discovery). OLAP-based data mining is referred to as multidimensional data mining (also known as exploratory multidimensional data mining, online analytical mining, or OLAM). It emphasizes the interactive and exploratory nature of data mining.

■ OLAP servers may adopt a relational OLAP (ROLAP), a multidimensional OLAP (MOLAP), or a hybrid OLAP (HOLAP) implementation. A ROLAP server uses an extended relational DBMS that maps OLAP operations on multidimensional data to standard relational operations. A MOLAP server maps multidimensional data views directly to array structures. A HOLAP server combines ROLAP and MOLAP. For example, it may use ROLAP for historic data while maintaining frequently accessed data in a separate MOLAP store.

■ Full materialization refers to the computation of all of the cuboids in the lattice defining a data cube. It typically requires an excessive amount of storage space, particularly as the number of dimensions and size of associated concept hierarchies grow. This problem is known as the curse of dimensionality. Alternatively, partial materialization is the selective computation of a subset of the cuboids or subcubes in the lattice. For example, an iceberg cube is a data cube that stores only those cube cells that have an aggregate value (e.g., count ) above some minimum support threshold.

■ OLAP query processing can be made more efficient with the use of indexing techniques. In bitmap indexing, each attribute has its own bitmap index table. Bitmap indexing reduces join, aggregation, and comparison operations to bit arithmetic. Join indexing registers the joinable rows of two or more relations from a relational database, reducing the overall cost of OLAP join operations. Bitmapped join indexing, which combines the bitmap and join index methods, can be used to further speed up OLAP query processing.

■ Data generalization is a process that abstracts a large set of task-relevant data in a database from a relatively low conceptual level to higher conceptual levels. Data generalization approaches include data cube-based data aggregation and attribute-oriented induction. Concept description is the most basic form of descriptive data mining. It describes a given set of task-relevant data in a concise and summarative manner, presenting interesting general properties of the data. Concept (or class) description consists of characterization and comparison (or discrimination ). The former summarizes and describes a data collection, called the target class, whereas the latter summarizes and distinguishes one data collection, called the target class, from other data collection(s), collectively called the contrasting class(es).

■ Concept characterization can be implemented using data cube (OLAP-based) approaches and the attribute-oriented induction approach. These are attribute- or dimension-based generalization approaches. The attribute-oriented induction approach consists of the following techniques: data focusing, data generalization by attribute removal or attribute generalization, count and aggregate value accumulation, attribute generalization control, and generalization data visualization.

■ Concept comparison can be performed using the attribute-oriented induction or data cube approaches in a manner similar to concept characterization. Generalized tuples from the target and contrasting classes can be quantitatively compared and contrasted.