Prototype Structure and Conceptual Clustering

Prototype Structure and Conceptual ClusteringVeena S. MellarkodArgonne National Labs & Texas Tech Universitymellarko@David L. SallachArgonne National Labs & University of Chicagosallach@AbstractAgent-based modeling has proven to be particularly effective for fine-grain social modeling. However, so far, the modeling of social agents has not involved dynamics based on interpretive interaction. Meaning or interpretation plays a significant role in human interactions. These micro effects might create interesting effects on aggregate dynamics. The goal of the Interpretive Agent (IA) project is to develop a framework in which agent-based modeling can incorporate interpretive mechanisms. We believe that introducing interpretive mechanisms in agents will improve the depth and quality of the simulation models [Sallach, 2003; Sallach & Mellarkod 2004]. The innovation of interpretive behavior in agent models involves at least the following three mechanisms: prototype inference, orientation accounting and situational definition [Sallach 2003]. These mechanisms follow closely the mode by which human interpretation works. Introducing these mechanisms is not straight-forward, as the computational complexity generated by these mechanisms needs to be carefully aligned and integrated. We are working on each of these mechanisms separately and putting them together in the broad framework. The prototype structures are viewed as clusters formed from objects/events/actions of agents’ responses. Thus, the work summarized in this paper captures the computational aspects of prototype structure and inference.Contact:David L. Sallach, Associate DirectorCenter for Complex Adaptive Agent Systems Simulation (CAS2)Decision Information Sciences, Bldg. 900Argonne National LaboratoryArgonne, IL 60439Tel: 1-630-252-5760Fax: 1-630-252-6073Email: sallach@Key Words: social agents, agent-based modeling, interpretive agents, prototype inference, reference point reasoning, and cluster analysisSupport: This work was supported by Argonne National Laboratory through the U.S. Department of Energy contract W-31-109-ENG-109.Prototype Structure and Conceptual ClusteringVeena S. Mellarkod and David L. SallachAgent-based modeling has proven to be particularly effective for fine-grain social modeling. However, so far, the modeling of social agents has not involved dynamics based on interpretive interaction. Meaning or interpretation plays a significant role in human interactions. These micro effects might create interesting effects on aggregate dynamics. The goal of the Interpretive Agent (IA) project is to develop a framework in which agent-based modeling can incorporate interpretive mechanisms. We believe that introducing interpretive mechanisms in agents will improve the depth and quality of the simulation models [Sallach, 2003; Sallach & Mellarkod 2004]. The innovation of interpretive behavior in agent models involves at least the following three mechanisms: prototype inference, orientation accounting and situational definition [Sallach 2003]. These mechanisms follow closely the mode by which human interpretation works.Agents cogitate using prototypes. Prototype conceptual structures are radial with the core center defined by regular exemplars and the periphery containing instances that deviate from the core. For example, the prototype ‘chair’ can be viewed as follows:Figure 1: An example of a prototypeInferences can be drawn on the classification of an object using these prototypes. The second mechanism orientation accounting, illustrated by the fact that, “Normally, people do not hurt (annoy, disgust, enrage or upset) their loved (respected, cared or similar) ones”. While preparing for a communication/act, agents tend to reflect their response and regard whether it might hurt those akin to or otherwise and modify (reorient) their response accordingly. The third mechanism is situational classification. The agents possess the ability to represent salient features of a situation. Using these definitions in conjunction to the circumstances and action/response sequence of other agents, it should be capable of delimiting the set of action alternatives.Introducing these mechanisms is not straight-forward, as the computational complexity generated by these mechanisms needs to be carefully aligned and integrated. We are working on each of these mechanisms separately and putting them together in the broad framework. The prototype structure and inferences mechanism has been discussed in [Mellarkod & Sallach, 2005]. The orientation accounting mechanism was discussed in detail [Sallach &Mellarkod, 2005]. The current paper captures the computational aspects and issues related to prototype structure and inference.Prototype StructurePrototypes [Hampton, 1993; Rosch, 1978] can be thought of as averages or summaries of the categories of representing members or by sets of exemplars representing the category [Lamberts, 1994]. Prototypes form a basis for probabilistic, similarity-driven category assignment. This is in contrast to the formal rule-based categorization.To define the prototype structure, we draw upon Codd’s RM/T, a conceptual extension of the relational model [Codd, 1979]. A prototype is composed by entities, events and/or relationships, where at least one is present. For simplicity, let us consider only prototypes composed of entities, their immediate properties and characteristics. The methodology discussed in this paper can be naturally extended to other definitions. For instance, consider the prototype chair mentioned above. The entities of the prototype contain several attributes including its functionality; presence of legs, armrests, lean backs etc. The presence of legs would include characteristic attributes like number of legs, the height of the legs, the spacing between them etc. Similarly, the lean backs include the characteristic attribute of length, possible slant angle etc.Here is another example which will be used in the entire paper. Consider a hypothetical environment where the agents are divided into different religions and ethnicities. Agents know the religion of others and know their ethnicity by interacting with them for some period of time. Depending on their religion and ethnicity values, they are given a niceness and toughness value. (For the sake of simplicity, niceness and toughness levels are used; in general we can have several dimensionalities like friend, enemy, beauty, truth, cleanliness, integrity, greed etc). The actions of the agents depend on these values. The two actions we would like to consider here are: help and deceive. The agent’s do not directly know the niceness or toughness ratings of the other agents. Agents can see other’s actions, and as a result, they can infer others’ niceness or toughness levels, depending on these actions. The agents can use the actions performed by others in their vicinity and build ‘nice’ and ‘tough’ prototypes. The prototypes include other agents’ contacted/communicated/interacted actions, and are regarded as nice/tough from the agent’s point of view. The view of an agent will be entirely different from that of another as the agents’ views of niceness and toughness are different and change with respect to time and situation. The attributes of nice prototype are: agent1, agent2, action and situation. Some of the instances can be:agent1agent2 action situationa1 a2 help difficulta34 a46 not-deceive comfortablea56 a25 help comfortablea37 a25 not-deceive difficultThe first instance is read as: agent a1 helped agent a2 when it (a1) was in a difficult situation. The last instance is read as: agent a37 did not deceive (when it could have) agent a25 when it (a37) was in a difficult situation. (Situations have not been discussed in detail in this paper, and is beyond the scope of this paper, for simplicity consider the agents are in difficult or comfortable situations in the world and their situations change with time and environment). The instances keep changing with old information replaced with new while some detailed exceptions or outliers and those with profound effect are retained longer. One example of a detailed exception would be an agent helping another while in an extremely difficult situation or an agent who is regarded as very tough, helping another. These outliers form the periphery of the prototype along varying dimensions.The level of detail at which a particular prototype should be represented using RM/T depends on the particular simulation model. This RM/T structure of relationships can be considered as prototype structure which is dismantled. How do we form the prototype using these disassembled parts? Cluster analysis addresses this question in a natural way.Prototype ClustersA cluster is a set of one or more objects that can be considered similar to each other. The similarity can be measured using different clustering algorithms. Given several objects and their attributes (properties), the clustering method involves finding a similarity measure between objects and separating them into clusters of similar objects[Rosemburg, 1984; Spath, 1982]. The clustering methods are of different types. The clustering mechanism used in this paper is hierarchical clustering mechanism. In this method, initially the objects are regarded as separate clusters. At each step, the clustering algorithm merges two similar clusters together. Similarity measure can be defined in several ways [Romesburg, 1984].Given the chair prototype as RM/T; the entities (different types of chairs) can be considered as objects that are to be clustered and their properties as the attributes on which clustering occurs. Clustering would result in the objects (entities) being separated in to different groups (clusters). The clustered objects represent the prototype. How do we differentiate the core and peripheral parts of the prototype clusters? The answer to this can be viewed in two ways. The cluster which is closest to the midpoint1 can be considered as the core and farther the clusters are from the core, the greater they are towards the periphery in varying dimensions. Another method would be to consider most populated cluster as the core and the others as the periphery. The core and periphery distinction mainly depends on the agent’s perception and interpretation process. At this point, there arise many questions that need to be addressed: what is the need for storing the dismantled parts (RM/T) of a prototype; can we just store the clusters of prototype objects; how do we use prototype clusters; does the core and periphery change depending on a situation?In answering these questions, let us consider a hypothetical military occupation with a regularized structure. An occupying force has stationed colonels at geographically spaced areas. The occupied public’s mood depends, in part, on the sanctions they receive from the occupier. At regular intervals of time, the colonels report the public’s demonstrated mood to their general. Changes in the sanctioning strategy ultimately depend on these reports. Consider the colonel has a history of sanctions and the resulting public’s mood swings of the previous times. When there is a new sanction in place, the colonel can use the history and recall (retrieve) those sanctions/moods that are similar to the new sanction and determine/infer the mood changes of the public. If the prototype clusters are stored without the dismantled pieces, this information will be lost and the colonel will not be able to infer correctly. To retrieve similar events from history, join operators of RM/T would be used. Apart from retrieving select information, RM/T can also be used to store information in a concise way. This arises from the fact that several prototypes can possess the same/similar data/information. This data is stored only once in RM/T leading to intersecting prototypes. In the nice/tough example, the religion and ethnicity are stored separately and this will be used along with attributes of nice to determine the niceness of the agent. Storing data in RM/T also contributes to easier blending of two or more prototypes, which will be discussed later. This answers the question whether we need the prototypes expressed as RM/T. The clusters of prototype objects are also required and will keep changing regularly. The need to store them depends on the agent’s point of reference and is related to reference point reasoning [Rosch, 1983].An agent’s interpretation works with the prototype clusters, using clusters to determine whether an object/event/act belongs to a particular prototype. The agent can also use a set of prototypes and a new object/event/act to determine the membership of the object. Given a prototype of chair, and an object, the agent can determine whether the new object is a chair or something else. Given prototypes of joke and insult, the agent can assess whether an act of another is a joke or otherwise. Using the ‘nice’ prototype, the agent can find whether an action is considered nice. This mapping of events to prototypes is an important step towards interpretive behavior. Each agent has a distinctive view of the world, and dissimilar information regarding events/actions of other agents. In conjunction to the above variations, each agent also differs in their perception. This leads to dissimilar definitions of prototypes and hence differences in their classification mechanism.Situations affect the boundary between core and periphery in prototypes. Though the nature of a situation opens a different view of the prototype; for the most part, the main portions of the core and periphery are unchanged with respect to transient responses. Further reflections can lead to drastic changes in prototypical definitions. To illustrate this, agents normally use their defined prototypical clusters to classify object and events; they can radically change their views and definitions during their reflective process. The prototype clusters are reconsidered and cluster re-analysis is performed when necessary, thereby resulting in new clusters or groups. This represents the agents’ changed view of the world.1 This paper considers the UPGMA clustering method to merge objects to clusters. The Euclidean distance between any two object is considered as the similarity basis. The midpoint would mean the centroid of all the clusters put together. There are other clustering methods that can also be used.While using hierarchical clustering, there is another issue to be addressed. Each step of the clustering algorithm merges two most similar clusters to one, at the end of execution, there will be only one cluster remaining. While cluster analysis uses this method for a different purpose, we are not interested in forming one whole cluster. We would rather like the algorithm to stop clustering at some point where there are several clusters which are different from each other in varying dimensions. The question that arises naturally is: when do we stop the clustering algorithm? The span of absolute judgment and immediate memory in humans impose severe limitations on the amount of information that we are able to receive, process, and remember [Miller, 1956]. Bounded rationality plays an important role in our day-to-day lives. The way we address this problem is to get clusters within the range of Miller’s magic number seven plus or minus two [Miller, 1956].In the niceness example above, the agents can infer nice actions of others using the prototype. Now, we would like to find a niceness factor of the agents or in other words find a prototype of niceness of the agents. Using the instances of the nice prototype in RM/T, the agent should form a data matrix that would be used for clustering. The data matrix has (not limited to) the following fields:# help_same_religion, #help_diff_religion,# help_same_eth, #help_diff_eth,# help_difficult_situ, #help_comfortable_situ# ndeceive_same_religion, # ndeceive _diff_religion,# ndeceive _same_eth, # ndeceive _diff_eth,# ndeceive_difficult_situ, # ndeceive _comfortable_situThe first field, ‘#help_same_religion’ is read as: The number of times an agent helped another agent of the same religion. The last attribute, ‘#ndeceive_difficult_situ’ is read as: The number of times an agent did not deceive another agent (given a chance) in a comfortable situation. Using this matrix, finding the resemblance matrix and performing clustering should be straight-forward. Note that, some fields in this data matrix can be unknown and normally, we can also find some fields not applicable for certain cases. For these cases, it is easier to use the clustering methods defined keeping in view these details [Gower, 1971; Romesburg, 1984].Prototype BlendsAnother topic to be considered is the blending of two or more prototypes. Blending of prototypes is a common phenomenon in human actors. For example, when a human actor is in a restaurant along with a friend, and sees a stranger entering with a gun which his friend did not notice, he normally warns the friend before exiting through the back door. The prototypes restaurant, friend and danger blend together with high importance to danger and the new blended prototype is the new situation which has arisen.At a computational level, the blending of prototypes is two fold: the agent forms integrated data sets for clustering using the join operators of RM/T; these merged data sets are used to form new prototype clusters. The integrated data sets comprises of joining attributes related to two or more separate prototypes. When clustering is performed, the entities are clustered depending on the properties of all the prototypes considered and hence the clusters formed are a blend of the previous prototypes concerned.Consider the nice example again. Since agents can see others’ actions, they can develop an idea of similar agents. Similarity can be established by projecting other’s actions to their own situations. The result will be a prototype of ‘similarity’ of an agent with other agents. The cluster, in which the particular agent is a member, refers to the most similar agents. The farther the clusters, the more dissimilar the agents are. Let us suppose that an agent wants to ask or request another agent in vicinity for a favor. The agent wants to increase the odds that it receives help from the other. It needs to find which of the other agents in its vicinity might be more likely to help. One way of doing this would be to use the similarity and nice prototypes. The attributes of similarity and nice definitions can be joined together (blended) and the whole is clustered to achieve the result. If the others in vicinity are members of the core clusters then they can be requested for help with higher probability of receiving it.Weighted ClustersFinally, we would like to talk about weighted clusters. In clustering methods, the contribution of attributes in clustering plays a significant role [Romesburg, 1984]. Frequently the clustering mechanism gives equal weight to all the attributes present: representing equal contributions. These contributions can be changed by weighting the attributes differently. Weighting attributes affects the view relative to which similar objects are clustered. For instance, while forming a similarity prototype, agents can give more weight to religion or ethnicity or behavior or sets of their combinations, depending on their circumstances. While calculating a niceness factor, the agents can give additional weight to actions (like help) performed in difficult situations--which are viewed as nicer--than in comfortable situations.Weighted clusters can also play a role in blending two or more prototypes. The prototype weighted more forms the main basis for clustering and the others shape or modify it. For instance, in the nice/tough example, the agent can blend the two prototypes giving more importance to nice prototype than to similarity if the agent’s ethnicity is more inclusive; else it can give heavier weight to the similarity prototype, pointing to belief that similar agents (religion/ ethnicity/ behavior) have more reason to help. In either case, agent assumptions and intent structures the form of knowledge employed.ConclusionPrototype concepts and reference point reasoning are mechanisms that control complexity for compute-bound reasoners. What makes them effective for human actors with bounded rationality, also helps them work for computational agents. Accordingly, they are promising components for constructing finer-grain agent models that are oriented by meaning. This paper considers illustrative uses of these mechanisms, as well as examples of their computational implementation.References[Codd, 1979] E. F. Codd, 1979, “Extending the Database Relational Model to Capture More Meaning”, ACM Transactions on Database Systems, 4(4): 397-434.[Gower, 1971] J. C. Gower, 1971, “A General Coefficient of Similarity and Some of its Properties”, Biometrics, 27: 857-74[Hampton, 1993] J. A. Hampton, 1993, “Prototype models of concept representation”, Categories and concepts: theoretical views and inductive data analysis, I. an Mechelen, J. A. Hampton, R. S. Michalski, & P. theuns (eds), 64-83. 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