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Similarity refers to the psychological nearness or proximity of two mental representations. It is an one of the principles of grouping in Gestalt psychology According to Daniel Schachter "Regions that are similar in color, lightness, shape, or texture are perceived as belonging to the same object"  Research in cognitive psychology has taken a number of approaches to the concept of similarity. Each of them is related to a particular set of assumptions about knowledge representation.
Cognitive psychological approaches
Mental distance approaches
Mental distance approaches (Shepard, 1962) assume that mental representations can be conceptualized as some kind of mental space. Concepts are represented as points within the space. Similarity between concepts is a function of the distance between the concepts in space. Concepts represented by points that are near to each other are more psychologically similar than are points that are conceptually distant. A strength of this approach is there are many mathematical techniques for deriving spaces from data such as multidimensional scaling (Shepard, 1962) and latent semantic analysis (Laudauer & Dumais, 1997).
Featural approaches (Tversky, 1977) were developed to address limitations of the mental distance approaches. For example, spaces are symmetric. The distance between two points is the same regardless of which point you start from. However, psychological similarity is not symmetric. For example, we often prefer to state similarity in one direction. For example, it feels more natural to say that 101 is like 100 than to say that 100 is like 101. Furthermore, many metaphors are also directional. Saying "That surgeon is a butcher" means something quite different from saying "That butcher is a surgeon."
Featural approaches assumed that people represent concepts by lists of features that describe properties of the items. A similarity comparison involves comparing the feature lists that represent the concepts. Features that are shared in the feature lists are commonalities of the pair and features that are contained in one feature set but not the other are differences of the pair. It is possible to account for people's intuitions or ratings of the similarities between concepts by assuming that judgments of similarity increase with the number of commonalities (weighted by the salience of those commonalities) and decreases with the number of differences (weighted by the salience of the differences).
Structural approaches to similarity (Gentner & Markman, 1997) were developed to address limitations of the featural account. In particular, featural approaches assume that the commonalities and differences are independent of each other. However, commonalities and differences are not psychologically independent. In fact, determining the differences between a pair requires finding the commonalities. Consider the comparison between a car and a motorcycle. Both have wheels. That is a commonality. However, cars have four wheels, while motorcycles have two wheels. That is a difference. Because this difference required first finding a commonality between the pair, it is called an alignable difference. Alignable differences contrast with nonalignable differences which are aspects of one concept that have no correspondence in the other. For example, cars have seatbelts and motorcycles do not. Research suggests that alignable differences have a larger impact on people's judgments of similarity than do nonalignable differences. Thus, the relationship between the commonalities of a pair and the differences is important for understanding people's assessments of similarity. Structural approaches to similarity emerged from research on analogy.
Transformational accounts of similarity (Hahn & Chater, 2003) were developed to evaluate similarity independently of the type of mental representation. On this view, any mental representation can be transformed into another mental representation through some series of steps. For any representation system and set of transformations, it is possible to define the shortest set of steps (i.e., the shortest program) that will transform one representation into another. The shorter this minimal program, the more similarity the pair of concepts. Larkey and Markman (2005) found some evidence against this view, showing that the number of steps to transform the colors and shapes of geometric objects does not predict people's similarity judgments for those objects.
Social psychological approaches
In social psychology, similarity refers to how closely attitudes, values, interests and personality match between people. Research has consistently shown that similarity leads to interpersonal attraction.
Many forms of similarity have been shown to increase liking. Similarities in opinions, interpersonal styles, amount of communication skill, demographics, and values have all been shown in experiments to increase liking.
Several explanations have been offered to explain similarity increases interpersonal attraction (like-prefers-like). First, people with similar interests tend to put themselves into similar types of settings. For example, two people interested in literature are likely to run into each other in the library and form a relationship (involving the propinquity effect). Another explanation is that we notice similar people, expect them to like us, and initiate relationships. Also, having relationships with similar people helps to validate the values held in common. Finally, people tend to make negative assumptions about those who disagree with them on fundamental issues, and hence feel repulsion.
- Schacter, Daniel L., Daniel T. Gilbert, and Daniel M. Wegner. Chapter 4.14 Recognizing Objects by Sight. Psychology. ; Second Edition. N.p.: Worth, Incorporated, 2011.
- Gentner, D., & Markman, A.B. (1997). Structure Mapping in analogy and similarity. American Psychologist, 52 (1), 45–56.
- Hahn, U., Chater, N., & Richardson, L.B. (2003). Similarity as transformation. Cognition, 87, 1–32.
- Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction, and representation of knowledge. Psychological Review, 104 (2), 211–240.
- Larkey, L.B., & Markman, A.B. (2005). Processes of similarity judgment. Cognitive Science, 29, 1061–1076.
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- Tversky, A. (1977). Features of similarity. Psychological Review, 84 (4), 327–352.