Q-Analysis

Topological Foundations

The original aim of Q-analysis was to develop mathematical methods appropriate for categorical analysis of human affairs, what one researcher referred to as a “qualitative mathematics.” Ideally, this mathematics would not be limited to functions and must be able to represent complex structures of relations. To meet these needs, a topological approach to analyzing connectivity in point sets was adopted, one heavily employing graphical representation of data.

For example, a point can be assigned to represent a relation between a news story and a topic category. A group of such points can be used to represent the various topics contained in a single story, and if lines are used to connect the points, a story can be represented as a polygon. An entire day's newspaper coverage of a topic such as the drug war can be represented as a group of such polygons. Because stories often overlap in covering a certain topic, such as crime, different stories can share points as well as lines. Such a combination of stories results in a structure of relations among coverage topics, represented graphically by interconnected polygons.

An example illustrates this process more concretely, such as a news story about a death resulting from a bombing. The story explains that the death resulted from a fight between two parties involved in the drug business and describes their business relations. It might be coded as Death, Bombing, and Profits. The same day's news coverage might include another story about a death that occurred during a police raid. It reports a neighborhood resident's lack of fear in the face of potential danger associated with drug trafficking in her [Page 730]neighborhood. This might be coded as Death, Profits, and Fearless.

The coverage overlap in these two stories is represented by two shared points, Death and Profits, as well as by the shared line between these points. A large number of stories can be graphed in this way to represent how topics are connected in drug war news coverage.

Such overlapping polygons can be produced starting with a rectangular data matrix, in Q-analysis called an incidence matrix. Assume the rows of this matrix to be stories and the columns to be coverage topics. Assume further that each story may be coded for the presence of multiple topics and that each cell entry can be represented as a point.

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