Visualizing mental representations: High-dimensional semantic space

  Roy B. Clariana (rclariana@psu.edu)

Clariana, R.B. (2000). Feedback in computer-assisted learning. NETg University of Limerick Lecture Series.
See http://www.ul.ie/techcomm/NETgLectureSeries.htm

Mental representations can be visualized in several ways.  Collins and Quillian (1972) proposed semantic networks that use nodes to represent concepts and lines between nodes to show the relationships between concepts.  For example, some relationship data from McClelland (1981) that describes two fictitious gangs, the Sharks and Jets, can be displayed as a semantic network (see left panel of Figure 1).  For descriptive purposes, added information about Gangs and about Sharks and Jets not in the original data set was added to fill out the semantic network.  The Shark’s gang member named Dave is a divorced drug pusher.  Semantic networks have been used to describe many aspects of information, such as the hierarchical structure of the information.

Figure 1.  A semantic network (left) and a MDS (right) of associations for two fictitious gangs (from McClelland, 1981).

Graphical displays of psychological space have also been called high-dimensional semantic space (HDSS; Foltz, Kintsch, & Landauer, 1998) and cognitive maps (Diekhoff & Wigginton, 1982).  Several recent computational approaches show similarity in mental representations as distances in psychological space rather than as nodes and links (Diekhoff & Wigginton, 1982; McLeod, Plunkett, & Rolls, 1998).  These approaches provide another way of displaying and of thinking about an individual’s mental representation of information.

A scaling procedure, such as multi-dimensional scaling (MDS), can display relationship data visually in fewer dimensions.  For example, to use MDS to display HDSS, first relationship data is described in a weight matrix (see Table 1).  A 1 in the matrix indicates an association between the column and row instance, while a 0 indicates no association.  Each row (or column) in the table is a high-dimensional vector.  Next MDS can be applied to that matrix.  MDS was conducted with Table 1 data using SPSS 9.0 including the standard default values for MDS except for selecting create Euclidean distances and selecting display group plots (see right panel of Figure 1).

Table 1.  Weight matrix of some of McClelland’s (1981) data (with 8 examples of gang members).