Psychological Clustering Models

In many fields that use clustering models, most applications have relied on a relatively
small range of the possible representational and similarity assumptions. Great
emphasis is given to partitioning approaches like k-means clustering, and various
tree-fitting approaches using hierarchical representations. Sometimes (although not
always) this emphasis comes at the expense of overlapping representations, which
have hierarchical and partitioning representations as special cases.

One field, perhaps surprisingly, that has a long tradition of using overlapping
clustering models is psychology. In cognitive psychology, a major use of clustering
models has been to develop accounts of human mental representations. This is
usually done by applying a clustering model to data that describes the empirically
observed similarities between objects, and then interpreting the derived clusters
as the cognitive features used by people to represent the object. It has been
understood that “generally, the discrete psychological properties of objects
verlap in arbitrary ways”, and so representations more general than partitions
or hierarchies needed to be used.

Psychological clustering models have also considered a variety of possible similarity
processes. In particular, they have drawn a useful distinction between common
and distinctive features. Common features are those that make two
objects with the feature more similar, but do not affect the similarities of objects
that do not have the feature. For example, think of two people with an unusual
characteristic like blue hair. Having this feature in common makes these two people
much more similar to each other than they otherwise would be, but does not affect
the similarities between other people being considered who have ‘normal’ hair
colors. Distinctive features, on the other hand, are those that make objects both
having and not having the feature more similar to each other. For example, whether
a person is male or female is a distinctive feature. Knowing two people are male
makes them more similar to each other, knowing two people are female makes them
more similar to each other, and knowing one person is male while the other is fe-
male makes them less similar to each other. Using common and distinctive features
allows clustering models to deal with two different kind of regularities: common features
capture the idea of ‘similarity within’, whereas distinctive features captures
the notion of ‘difference between’. In addition, psychological clustering models usually
associate a weight with every cluster, which can be interpreted as measuring
its ‘importance’ or ‘salience’. By combining the weights of common and distinctive
features in various ways, a wide range of similarity assumptions is possible.

A consequence of considering clustering models with great flexibility in both
their representations and similarity measures, however, is that it becomes critical
to control for model complexity. As noted by Shepard and Arabie, an
overlapping clustering model that is also able to manipulate the similarity measures
it uses may be able to fit any similarity data perfectly. The possibility of developing
overly-complicated clustering representations, of course, conflicts with the basic
goals of modeling: the achievement of interpretability, explanatory insight, and
the ability to generalize accurately beyond given information. In psychology, it is
particularly important to control the complexity of cluster representations when
they are used in models of cognitive processes like learning, categorization, and
decision-making. Because the world is inherently dynamic, representations of the
environment that are too detailed will become inaccurate over time, and provide a
poor basis for decision-making and action. Rather, to cope with change, cognitive
models need to have the robustness that comes from simplicitly. It is this need for
simple representations that makes psychological clustering models ideal candidates
for Minimum Description Length (MDL) methods.

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