Direct Multidimensional Scaling of Separable
Attended and Non-attended Objects and Their Features
Paying attention to object properties facilitates identification and detection.
Psychological similarity of objects and their features explains reaction time (RT) results in
detection, identification, and discrimination of attended targets.
We tend to group objects together into psychologically manageable clusters according to
the similarity of their properties. Developed by Shepard (1962), Multidimensional Scaling
(MDS) is a method for modeling psychological clustering by treating psychological distances as
Euclidean distances. Objects are mapped onto a space of a given dimension that reflects the
properties whose variation explains differences in the perception of the objects. Direct scaling
involves asking subjects to rate objects or sensations based on a consistent, internally defined
scale. Direct MDS applied to basic features can explain both interference and facilitation results
in attention psychophysics.
Treisman (1982) asked subjects to detect a target that differs from surrounding distracters
in some property. For example, people were asked to look for a red ball in the midst of blue
balls. When a target possessed a simple property such as color, orientation, and presence of
intersecting line segments that the distracters lacked, subjects detected the target easily
regardless of the number of distracters. When distracters possessed a property that a target lacks,
subject RTs increases with the number of distracters present. RTs are also dependent on the
number of distracters when a target differed from its distracters in a complex, conjunctive
property. For example, Treisman asked people to look for a red letter N in a field of red and blue
Os and Ns. Increasing the dimensionality of the search problem made the task more difficult as
more distracters are added, because the target property no longer pops out from the display.
RT differences for different types of visual search tasks can be modeled by psychological
distances of constituent features. Using the letters example, we can create a two-dimensional
scale of letters from A to Z and colors from red to yellow to blue to violet and back to red. Note
that a map of these properties lies on outward lines perpendicular to concentric circles. Letters
are not necessarily arranged alphabetically. We may consider a greater number of dimensions
for the letters alone. Similarity ratings for different pairs of colorful letters can be used to map
out an approximate empirical space for these two-dimensional objects. RTs are predicted to be
some monotonic function of the psychological distances between target and distracter objects,
plus some variance that depends on experimental conditions. Note that in conjunction search,
objects vary in two-dimensions, making the RTs larger in general. In one-dimensional search,
RTs for targets and distracters with similar features depend on the number of distracters, because
of the reduction in variance associated with clustering together of the distracters. RTs for
detecting targets with a pop-out feature do not depend on the number of distracters, presumably
because the target-distracter distance is at infinity with respect to the current setup.
Identification of objects varying in two dimensions depends on the separation between
stimuli in similarity space (Monahan & Lockhead, 1977). Experienced subjects were briefly
presented with rectangles of various heights and widths to identify as belonging to one of six
predefined categories. When the six predefined rectangles were spread out in the similarity
space of heights and widths, the RTs for the identification task were faster and the error rates
were lower. When the six rectangles were lying in a line in similarity space, the RTs were
slower and the error rates were higher. Extra dimensionality facilitates identification in this case.
The authors suggest that the RT result is due to the difference in discriminability among objects
presented. Stimuli can be divided into two classes. Integral stimuli yield a Euclidean metric in
similarity scaling (Shepard, 1962), and a decrease in RT when identifying stimuli with
redundantly combined dimensions. Nonintegral stimuli yield a block distance metric, and no
interference when objects vary in an irrelevant dimension in addition to the dimension along
which identification is performed. The authors suggest a definition of integrality as a property of
objects for which attention to one aspect of the stimulus automatically invokes awareness of its
other aspects. Identification of an integral stimulus is automatically invoked; identification of its
attributes is only invoked by attentive effort. Nonintegral, or phenomenological stimulus, on the
other hand, invokes identification of its attributes automatically; its own identity is discerned
only through attention. In Treisman’s experiments, simple target-distracter pairs are
phenomenological, while conjunctive pairs are integral. Indeed, simple targets are detected
easily by discrimination of its attribute among distracters, regardless of dimensionality of the
distracters. Conjunctive targets are found by attentional visual search that becomes more
difficult as distracter dimensionality increases.
Monahan and Lockhead showed that MDS analysis must be adapted to the particular
experimental situation. In their setup, you can’t ask people how different two rectangles are.
Direct scaling makes no sense because relationship among the stimulus set, not between stimulus
pairs, is responsible for the RTs. Hence the authors utilized an information-theoretic approach to
evaluate the discriminability of stimulus sets. Sets that vary along a line in two dimensions have
only one degree of freedom while sets that vary maximally in two dimensions have two. Thus
you only need one bit of information to specify the lengths and widths of the one dimensional set;
you need two bits for the two dimensional set. With a brief presentation time that raises the
variances of the perceived target configuration, the increased information associated with twodimensional sets gives us a faster and more accurate identification. This example suggests that
MDS can always be approached from an information theoretic view point (Cutting, 1987).
Perceptual distances specify the information content in discrimination between a pair of objects:
greater Euclidean distance implies greater information content.
Stroop examined a color discrimination task in which subjects were asked to give the
colors in which common words are written. When the color of the word matches the actual or
semantic content of the word, RTs were fast. When the color of the word contradicts the color
term specified by the word, RTs were slow. For example, subjects were fast in specifying the
color green for a patch of green, as well as the word “green” written in green, as well as the word
“grass” written in green. Subjects were slow in specifying the color red for the word “green”
written in red, as well as the word “grass” written in red (with a smaller effect). Stroop showed
that automatic linguistic reactions interfere with the verbal specification of color. In the
language of Monahan and Lockhead, colored words are integral stimuli, because they
automatically invoke a semantic interpretation without regard to their color attribute. Patches of
color are phenomenological stimuli, because their color attribute is immediately perceived.
Indeed, Treisman’s detection task involving a target red ball amongst distracter blue balls is a
detection version of the Stroop control task. Naming the color of incongruent word-color pairs is
a variant of the conjunctive search in which mismatch is maximal.
MDS can be applied to the Stroop Effect as long as we treat a feature equally with an
object and invert the RT-distance relationship amongst objects to account for between-object
interference. In the multi-dimensional space of all words, “grass” and “green” are close with
respect to the distance between “red” and “green.” In the space of all relevant words,
superimpose the dimension of physical color. Presumably, the physical “green” is
psychologically close to the word “green.” The Stroop Effect shows that large distances in this
multi-dimensional similarity space caused by presentation of the red word “green” causes large
RTs and error rates. Note that naming words of a uniform gray color and naming colors of
uniform patches are lower dimensional slices of the MDS map. These tasks are faster because
lower dimensional distances are shorter, indicating smaller interference of information. Note
that unlike detection and identification, interference effects in discrimination reactions make RT
predictions that are proportional to psychological distance between target and distracter stimuli.
Semantic red interferes strongly with message “green,” even though they are at opposite poles of
the scale. One explanation is that the Stroop task involves an excess of attention while the
Treisman and Monahan tasks involves a poverty of attention. Attention hinders performance in
the former case, and facilitates performance in the latter cases. The reason for the effective
asymmetry of attention is the linguistic content of the stimuli in the Stroop task. Thus, the
competition of dissimilar stimuli across two dimensions hinders response in the Stroop task, but
reinforces response in selection and detection. It has been shown that the Stroop Effect still
holds when conjunction of color and word is taken away. For example, specifying the green
color of a patch lying next to the word “red” is slower than specifying the color without the word
(Prinzmetal, 2002). Increasing the distance between the patch and the word decreases the effect.
The spatial dependence of the Stroop Effect can be modeled by increasing the dimensionality of
the MDS to accommodate Euclidean spatial distance.
An information-theoretic approach to MDS allows us to model psychophysical results in
detection, identification, and discrimination. Treating visual search as a special case of
information-maximization via distance-minimization shows the utility of MDS. Unattended
interference in a separate dimension can be explained by coupled MDS and the definition of
integral stimuli. MDS provides a useful generalization for psychophysical models in attention.
References
Cutting, J. E. (1987). Perception and information. Annual Review of Psychology, 38, 61-90.
Monahan, J. S., & Lockhead, G. R. (1977). Identification of integral stimuli. Journal of
Experimental Psychology: General, 106, 94-110.
Prinzmetal, W. (2002). Personal communication. Cognitive Science 126 lecture on attention,
November 14, 2002.
Shepard, R. N. (1962). The analysis of proximities: Multidimensional scaling with an unknown
distance function: I & II. Psychometrika, 27-28, 125-140, 219-246.
Stroop, J. R. (1935). Studies of interference in serial verbal reactions. Journal of Experimental
Psychology, 18, 643-660.
Treisman, A. (1982). Perceptual groupings and attention in visual search for features and for
objects. Journal of Experimental Psychology: Human Perception and Performance, 8,
194-214.
Direct Multidimensional Scaling of Separable
Attended and Non-attended Objects and Their Features
Ray Luo
Cognitive Science 126