Concept Hierarchy Generation For Categorical Data

Introduction: Categorical data are discrete data. Categorical attributes have a finite (but possibly large) number of distinct values, with no ordering among the values. Examples include geographic location, job category, and item type. There are several methods for the generation of concept hierarchies for categorical data.

Specification of a partial ordering of attributes explicitly at the schema level by users or experts: Concept hierarchies for categorical attributes or dimensions typically involve a group of attributes. A user or expert can easily define a concept hierarchy by specifying a partial or total ordering of the attributes at the schema level. For example, a relational database or a dimension location of a data warehouse may contain the following group of attributes: street, city, province or state, and country. A hierarchy can be defined by specifying the total ordering among these attributes at the schema level, such as street < city < province or state < country.

Specification of a portion of a hierarchy by explicit data grouping: This is essentially the manual definition of a portion of a concept hierarchy. In a large database, it is unrealistic to define an entire concept hierarchy by explicit value enumeration. On the contrary, we can easily specify explicit groupings for a small portion of intermediate-level data. For example, after specifying that province and country form a hierarchy at the schema level, a user could define some intermediate levels manually, such as “{Alberta, Saskatchewan, Manitobag} ⊂ prairies_Canada” and “{British Columbia, prairies_Canadag }⊂ Western_Canada”.

Specification of a set of attributes, but not of their partial ordering: A user may specify a set of attributes forming a concept hierarchy, but omit to explicitly state their partial ordering. The system can then try to automatically generate the attribute ordering so as to construct a meaningful concept hierarchy. “Without knowledge of data semantics, how can a hierarchical ordering for an arbitrary set of categorical attributes be found?” Consider the following observation that since higher-level concepts generally cover several subordinate lower-level concepts, an attribute defining a high concept level (e.g., country) will usually contain a smaller number of distinct values than an attribute defining a lower concept level (e.g., street). Based on this observation, a concept hierarchy can be automatically generated based on the number of distinct values per attribute in the given attribute set. The attribute with the most distinct values is placed at the lowest level of the hierarchy. The lower the number of distinct values an attribute has, the higher it is in the generated concept hierarchy. This heuristic rule works well in many cases. Some local-level swapping or adjustments may be applied by users or experts, when necessary, after examination of the generated hierarchy.

Example: Concept hierarchy generation using pre-specified semantic connections. Suppose that a data mining expert (serving as an administrator) has pinned together the five attributes number, street, city, province or state, and country, because they are closely linked semantically regarding the notion of location. If a user were to specify only the attribute city for a hierarchy defining location, the system can automatically drag in all of the above five semantically related attributes to forma hierarchy. The user may choose to drop any of these attributes, such as number and street, from the hierarchy, keeping city as the lowest conceptual level in the hierarchy.