Appropriately defining and efficiently calculating similarities from large data sets are often essential in data mining, both for gaining understanding of data and generating processes, and for building tractable representations. Given a set of objects and their correlations, we here rely on the premise that each object is characterized by its context, i.e. its correlations to the other objects. The similarity between two objects can then be expressed in terms of the similarity between their contexts. In this way, similarity pertains to the general notion that objects are similar if they are exchangeable in the data. We propose a scalable approach for calculating all relevant similarities among objects by relating them in a correlation graph that is transformed to a similarity graph. These graphs can express rich structural properties among objects. Specifically, we show that concepts - abstractions of objects - are constituted by groups of similar objects that can be discovered by clustering the objects in the similarity graph. These principles and methods are applicable in a wide range of fields, and will here be demonstrated in three domains: computational linguistics, music and molecular biology, where the numbers of objects and correlations range from small to very large.