Editing Cognitive categorization (section)

== Examples ==

===Prototype models===

'''Weighted Features Prototype Model'''<ref name=":6" /> An early instantiation of the prototype model was produced by Reed in the early 1970s. Reed (1972) conducted a series of experiments to compare the performance of 18 models on explaining data from a categorization task that required participants to sort faces into one of two categories.<ref name=":6" /> Results suggested that the prevailing model was the weighted features prototype model, which belonged to the family of average distance models. Unlike traditional average distance models, however, this model differentially weighted the most distinguishing features of the two categories. Given this model's performance, Reed (1972) concluded that the strategy participants used during the face categorization task was to construct prototype representations for each of the two categories of faces and categorize test patterns into the category associated with the most similar prototype. Furthermore, results suggested that similarity was determined by each categories most discriminating features.

===Exemplar models===

'''Generalized Context Model<ref name="Nosofsky, R. M. 1986">{{Cite journal |last=Nosofsky |first=Robert M. |date=1986 |title=Attention, similarity, and the identification–categorization relationship. |url=http://doi.apa.org/getdoi.cfm?doi=10.1037/0096-3445.115.1.39 |journal=Journal of Experimental Psychology: General |language=en |volume=115 |issue=1 |pages=39–57 |doi=10.1037/0096-3445.115.1.39 |pmid=2937873 |issn=1939-2222|url-access=subscription }}</ref>''' Medin and Schaffer's (1978) [[context model]] was expanded upon by Nosofsky (1986) in the mid-1980s, resulting in the production of the Generalized Context Model (GCM).<ref name="Nosofsky, R. M. 1986"/> The GCM is an exemplar model that stores exemplars of stimuli as exhaustive combinations of the features associated with each exemplar.<ref name="Kruschke, J. K. 2008"/> By storing these combinations, the model establishes contexts for the features of each exemplar, which are defined by all other features with which that feature co-occurs. The GCM computes the similarity of an exemplar and a stimulus in two steps. First, the GCM computes the [[psychological distance]] between the exemplar and the stimulus. This is accomplished by summing the absolute values of the dimensional difference between the exemplar and the stimulus. For example, suppose an exemplar has a value of 18 on dimension X and the stimulus has a value of 42 on dimension X; the resulting dimensional difference would be 24. Once psychological distance has been evaluated, an [[Exponential decay|exponential decay function]] determines the similarity of the exemplar and the stimulus, where a distance of 0 results in a similarity of 1 (which begins to decrease exponentially as distance increases). Categorical responses are then generated by evaluating the similarity of the stimulus to each category's exemplars, where each exemplar provides a "vote"<ref name="Kruschke, J. K. 2008"/> to their respective categories that varies in strength based on the exemplar's similarity to the stimulus and the strength of the exemplar's association with the category. This effectively assigns each category a selection probability that is determined by the proportion of votes it receives, which can then be fit to data.

===Rule-based models===

'''RULEX (Rule-Plus-Exception) Model<ref>{{Cite journal |last1=Nosofsky |first1=Robert M. |last2=Palmeri |first2=Thomas J. |last3=McKinley |first3=Stephen C. |date=1994 |title=Rule-plus-exception model of classification learning. |url=http://doi.apa.org/getdoi.cfm?doi=10.1037/0033-295X.101.1.53 |journal=Psychological Review |language=en |volume=101 |issue=1 |pages=53–79 |doi=10.1037/0033-295X.101.1.53 |pmid=8121960 |issn=1939-1471|url-access=subscription }}</ref>''' While simple logical rules are ineffective at learning poorly defined category structures, some proponents of the rule-based theory of categorization suggest that an imperfect rule can be used to learn such category structures if exceptions to that rule are also stored and considered. To formalize this proposal, Nosofsky and colleagues (1994) designed the RULEX model. The RULEX model attempts to form a decision tree<ref>{{Cite journal |last1=Simon |first1=Herbert A. |last2=Hunt |first2=E. B. |last3=Marin |first3=J. |last4=Stone |first4=P. |year=1967 |title=Experiments in Induction |url=https://www.jstor.org/stable/1421207 |journal=The American Journal of Psychology |volume=80 |issue=4 |pages=651 |doi=10.2307/1421207|jstor=1421207 |url-access=subscription }}</ref> composed of sequential tests of an object's attribute values. Categorization of the object is then determined by the outcome of these sequential tests. The RULEX model searches for rules in the following ways:<ref name="Navarro, D. J. 2005">{{Cite journal |last=Navarro |first=Danielle J. |date=2005-08-01 |title=Analyzing the RULEX model of category learning |url=https://www.sciencedirect.com/science/article/pii/S0022249605000428 |journal=Journal of Mathematical Psychology |language=en |volume=49 |issue=4 |pages=259–275 |doi=10.1016/j.jmp.2005.04.001 |hdl=2440/17026 |issn=0022-2496|hdl-access=free }}</ref>
* '''Exact''' Search for a rule that uses a single attribute to discriminate between classes without error.
* '''Imperfect''' Search for a rule that uses a single attribute to discriminate between classes with few errors
* '''Conjunctive''' Search for a rule that uses multiple attributes to discriminate between classes with few errors.
* '''Exception''' Search for exceptions to the rule.

The method that RULEX uses to perform these searches is as follows:<ref name="Navarro, D. J. 2005"/> First, RULEX attempts an exact search. If successful, then RULEX will continuously apply that rule until misclassification occurs. If the exact search fails to identify a rule, either an imperfect or conjunctive search will begin. A sufficient, though imperfect, rule acquired during one of these search phases will become permanently implemented and the RULEX model will then begin to search for exceptions. If no rule is acquired, then the model will attempt the search it did not perform in the previous phase. If successful, RULEX will permanently implement the rule and then begin an exception search. If none of the previous search methods are successful RULEX will default to only searching for exceptions, despite lacking an associated rule, which equates to acquiring a random rule.

===Hybrid models===

'''SUSTAIN (Supervised and Unsupervised [[Stratified charge engine|Stratified]] Adaptive Incremental Network)<ref name="Love, B. C. 2004">{{Cite journal |last1=Love |first1=Bradley C. |last2=Medin |first2=Douglas L. |last3=Gureckis |first3=Todd M. |date=2004 |title=SUSTAIN: A Network Model of Category Learning. |journal=Psychological Review |language=en |volume=111 |issue=2 |pages=309–332 |doi=10.1037/0033-295X.111.2.309 |pmid=15065912 |issn=1939-1471}}</ref>''' It is often the case that learned category representations vary depending on the learner's goals,<ref>{{Cite journal |last=Barsalou |first=Lawrence W. |date=1985 |title=Ideals, central tendency, and frequency of instantiation as determinants of graded structure in categories.|journal=Journal of Experimental Psychology: Learning, Memory, and Cognition |language=en |volume=11 |issue=4 |pages=629–654 |doi=10.1037/0278-7393.11.1-4.629 |pmid=2932520 |issn=1939-1285}}</ref> as well as how categories are used during learning.<ref name=":5" /> Thus, some categorization researchers suggest that a proper model of categorization needs to be able to account for the variability present in the learner's goals, tasks, and strategies.<ref name="Love, B. C. 2004"/> This proposal was realized by Love and colleagues (2004) through the creation of SUSTAIN, a flexible clustering model capable of accommodating both simple and complex categorization problems through incremental adaptation to the specifics of problems.

In practice, the SUSTAIN model first converts a stimulus' perceptual information into features that are organized along a set of dimensions. The representational space that encompasses these dimensions is then distorted (e.g., stretched or shrunk) to reflect the importance of each feature based on inputs from an attentional mechanism. A set of clusters (specific instances grouped by similarity) associated with distinct categories then compete to respond to the stimulus, with the stimulus being subsequently assigned to the cluster whose representational space is closest to the stimulus'. The unknown stimulus dimension value (e.g., category label) is then predicted by the winning cluster, which, in turn, informs the categorization decision.

The flexibility of the SUSTAIN model is realized through its ability to employ both supervised and unsupervised learning at the cluster level. If SUSTAIN incorrectly predicts a stimulus as belonging to a particular cluster, corrective feedback (i.e., supervised learning) would signal sustain to recruit an additional cluster that represents the misclassified stimulus. Therefore, subsequent exposures to the stimulus (or a similar alternative) would be assigned to the correct cluster. SUSTAIN will also employ unsupervised learning to recruit an additional cluster if the similarity between the stimulus and the closest cluster does not exceed a threshold, as the model recognizes the weak predictive utility that would result from such a cluster assignment. SUSTAIN also exhibits flexibility in how it solves both simple and complex categorization problems. Outright, the internal representation of SUSTAIN contains only a single cluster, thus biasing the model towards simple solutions. As problems become increasingly complex (e.g., requiring solutions consisting of multiple stimulus dimensions), additional clusters are incrementally recruited so SUSTAIN can handle the rise in complexity.