There are three general themes to keep in mind when going over this chapter, if you are interested in relating this specific material to the general themes emerging in our course. First, this chapter describes two different kinds of symbol systems (complex tokens, components of the functional architecture) that could be found in long-term memory: metric similarity spaces and nonmetric feature sets. Note that each of these token types will require special kinds of processes so that they can be used to manipulate categories (e.g., make comparisons, generate inductive inferences).
Second, while much of this chapter focuses on algorithmic studies of human categorization (this is what most of the cognitive psychology data is about), it does outline an interesting computational issue: what exactly is similarity? The empirical claim that similarity judgements by humans are not metric is just as important computationally as it is algorithmically, and inspired a very neat computational theory of similarity (Tversky's contrast model).
Third, the general notion of what similarity is has many important implications for cognitive science. For example, when connectionist models degrade gracefully, or when they survive damage, their performance depends crucially upon the similarity of presented material to material that has already been stored. In many senses, similarity -- what it is, and how it affects performance -- is one of the deepest and most prevalent questions facing psychologists.
"We are forever carving nature at its joints, dividing it into categories so that we can make sense of the world." The functional role of categorization is information reduction. "What exactly is a category? For now, let us take a category to be a class of objects that we believe belong together."
A category is a set of objects that seem to belong together. "The critical part of this definition is `seem to belong together', for there are an indefinite number of classes of objects in the world whose members do not seem to belong together." Categories are psychologically coherent: why?
Coding of experience
Categories code our experience. "Coding by category is fundamental to mental life because it greatly reduces the demands on perceptual processes, storage space, and reasoning processes, all of which are known to be limited." Categories are often hierarchical; experience is coded at the middle level of the hierarchy --> this is not true of "artificial" classes.
When a category is applied to an object, we can make inductive inferences about that object. "Very early on, we know that members of the same category are likely to share many invisible properties even if they do not resemble one another." Different levels in the hierarchy of categories support different extents of inductive inference: "basic and subordinate categories support more inferences than do superordinate categories." There are more inductive inferences about natural kinds (categories) than there are about artificial kinds (classes).
Similarity, particularly physical similarity, is a defining characteristic of categories. "In general, we divide the world so as to maximize within category similarity while minimizing between-category similarity." This is primarily true of basic level categories.
Geometric Approach To Measurement of Similarity
In the geometric approach, objects or items are represented as points in some multidimensional space such that the metric distance between tow points corresponds to the dissimilarity between the two items. This psychological space is metric, just like physical Euclidean space: it obeys the principles of minimality, symmetry, and the triangle inequality.
The geometric approach has a history of success in representing perceptual objects, but has not been so good in representing more conceptual categories; for these latter types, metric assumptions are violated. "Minimality is compromised by the fact that the more we know about an item, the more similar it is judged to itself. The axiom of symmetry is undermined by the finding that an unfamiliar category is judged more similar to a familiar or prominent category than the other way around," Smith's approach is to move away from geometric spaces because of these difficulties. (NB: Again, caution is in order here. Smith was one of the leading figures in the major cognitive psychology debate of the 1970s, feature matching models of semantic memory vs semantic network models. Smith was one of the major proponents of the set-theoretic approach, which does not require the metric assumptions of similarity spaces. So, Smith's advice to move away from metric representations need not be viewed as being totally objective!)
Featural Approach To Similarity Measurment
"In the featural approach, an item is represented as a set of discrete features, such as `red', `round', and `hard', and the similarity between two items is assumed to be an increasing function of the features they have in common and a decreasing function of the features that they differ on." For example, consider Tversky's contrast model of similarity, which assumes that features have different levels of salience or importance. By computing functions involving the salience of shared and not-shared features, one can come up with predictions about the similarity judgements that will be made by subjects. However, note that there are at least three kinds of problems with the contrast model. First, it does not say what the features are. Second, it does not offer a theory of the salience function. Third, it is a purely computational theory -- it is silent about an algorithm for feature comparison.
Typicality ratings predict latencies for categorizing -- categorization times decrease with the typicality of the test item.
Typicality is usually described as similarity to a category. Empirical issue: does the contrast model predict typicality? Some experiments indicate that this is indeed the case -- RT is a function of the feature comparison process.
Is categorization of visually presented information any different from the categorization of words? Similar results -- typical items are classified faster. But, different account of this finding is required.
Importance Of Shape
Problem -- most functional properties of categories are not visible in pictures. So, image similarity cannot be used to match image to concept. Instead, object recognition procedures must be involved -- procedures like those described by Biederman.
Typicality As Shape Similarity
This means that instead of using prototypical features, picture categorization must rely on detailed representation of shapes. So, categorization must be based upon some notion of shape similarity. "A novel assumption in this proposal is that the typicality of a visual object depends on its shape similarity to other members of the category." Studies by Kurbat, Smith, and Medin support this view -- area overlap, a measure of pictorial similarity, was highly correlated with subject ratings of picture typicality.
Categorization breakdowns with brain damage are called agnosias, and often occur with damage to the temporal lobe. For instance, prosopagnosia is a deficit in which faces cannot be correctly classified (remember the Farah chapter!).
Smith is interested in cases where subjects are impaired in classifying natural kinds, but not artifacts. E.g., patient JBR cannot describe parrot, daffodil, snail, eel, ostrich, but has no difficulty defining tent, briefcase, compass, torch, dustbin. Such deficits are often verbal, but visual counterparts have been identified too. Sometimes only one is impaired, sometimes both.
Two Hypotheses About Category-Specific Deficits
One hypothesis is structural-similarity hypothesis. Superordinate, natural-kind categories tend to be more similar in shape than superordinate, artifact categories. So, category impairments might be due to inability to process shape information properly.
Other hypothesis is perceptual-functional hypothesis. Deficit here is not at the level of shape descriptions, but is at the level of prototypical features. Idea here is that many prototypical features are perceptual in nature. So, brain damage affects these features, but leaves functional features intact.
Note both of these approaches support a major point of Smith -- that both shape descriptions and prototypical features are used to represent concepts.
The standard verbal- and visual-categorization paradigms do not tap all of the relevant beliefs represented in concepts. In addition to prototypical features and shape descriptions, concepts must include information that is not perceptually available. E.g. about internal organs, lineage, etc. Smith calls this info theoretical features. Claim is that when such theoretical features are available, categorization does not depend upon similarity -- eg., we base categorization on our theory of what the thing is (see also the Atran chapter!)
"A number of empirical phenomena (such as asymmetries in similarity judgements) indicate that the featural approach, particularly Tversky's (1977) contrast model, is best for measuring the similarity among categories and their instances." (NB: Again, take this with a grain of salt -- it is not a neutral conclusion. See the very nice work of Carol Krumhansl, published in Psychological Review in 1978, which shows how nonmetric similarity effects can be generated by metric similarity spaces.)
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