Identifying Integral-Separable Dimension Pairs

Presented on Mar 15, 2006

Integral-Separable Dimension Paris

In visualization, a popular technique is to employ two or more graphical attributes of a visual object to represent different attributes of an actual object. The concept of integral-separable visual dimensions tells us whether one display attribute will be perceived independently from another. With integral graphical attributes, different attributes of a visual object are perceived holistically and not independently. For example, a rectangle shape will be perceived as a holistic combination of the rectangle's width and height. On the contrary, with separable graphical attributes, people tend to make separate judgment about each graphical dimension.  This is sometimes called analytic processing. Thus, if the display dimensions are the diameter of a ball and the color of a ball, they will be processed relatively independently.  It is easy to respond independently to ball size and ball color.

Restricted Classification Tasks

In restricted classification tasks, observers are shown sets of three glyphs that are constructed according to the diagram show in Figure 1.  Two of the glyphs (A and B) are made the same on one variable.  A third glyph (C) is constructed so that it is closer to glyph B in feature space, but his glyph differs from the other two in both of the graphical dimensions.  Subjects are asked to group the two glyphs that they think go together best.  If the dimensions are integral, A and C are grouped together because they are closest in the feature space.  If they are separable,  A and B are grouped together because they are identical in one of the dimensions (analytic mode).

Figure 1. The Visual Attributes Space

The width and height of an ellipse creates an integral perception of shape. Thus, in Figure 2, the ellipses B and C appear to be more similar to each other than to the circle A, even though the height of B matches the height of A.  If the two dimensions are separable, subjects act in a more analytic manner and react to the fact that two of the objects are actually identical on one of the dimensions.  Shape and gray value are separable.  Thus, in Figure 3, subjects more probably regard A and B more similar to each other than to C, since A and B have the same width.

Figure 2. B and C are more similar than A and B, which shows that width and height of ellipse are integral dimension pairs.	Figure 3. A and B are more similar than B and C, which shows that width and gray scale are separable dimension pairs.

Experiment Design

In this experiment (http://users.wpi.edu/~xiezx/eva02/), six visual attributes were tested.  They are
1) x-size
2) y-size
3) color
4) gray scale
5) orientation
6) shape (circle, square)
Since some dimension pairs are not available, for example, color and gray scale.  Only eight dimension pairs were tested.  They are:

1) color vs. shape
2) orientation vs. color
3) orientation vs. gray scale
4) x-size vs. color
5) x-size vs. gray scale
6) x-size vs. orientation
7) x-size vs. shape (circle, square)
8) y-size vs. x-size
 

We invited 23 participants to take part in this experiment.  Fourteen of them are graduate students.

Result Analysis

In figure 4, for each dimension pair, we show the percentage of participants regarding  it as a  separable dimension pair.  Obviously, integrality-separability should be described as a continuum, which agrees with the theory about the separable-integral dimension pairs.  In Figure 4, at the top are the most separable dimension pairs based on our experiment.  At the bottom are the most integral dimensions.

Figure 4. Experiment result.  For each dimension pairs, we show the percentage of participants regarding it as separable dimension pair.

Possible Improvement on the Experiment

We can do some improvement on this experiment to obtain some more valuable result.

1) Since restricted classification tasks require subjects to judge which two figure are more similar based on their first sight of the figures, so more strict environment to control display time should be employed.
2) Previous experiment showed that different conclusions exist if two dimensions of two dimensions in Figure 1 are exchanged, so it is necessary design another eight questions to show eight pairs in a different order.
3) We suspect that this perception experiment is related to the culture, gender of subjects, so we can probably find some interesting patterns from the analysis about relationship between culture, gender and experiment result.