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.
Random indexing (RI) is a lightweight dimension reduction method, which is used, for example, to approximate vector semantic relationships in online natural language processing systems. Here we generalise RI to multidimensional arrays and therefore enable approximation of higher-order statistical relationships in data. The generalised method is a sparse implementation of random projections, which is the theoretical basis also for ordinary RI and other randomisation approaches to dimensionality reduction and data representation. We present numerical experiments which demonstrate that a multidimensional generalisation of RI is feasible, including comparisons with ordinary RI and principal component analysis. The RI method is well suited for online processing of data streams because relationship weights can be updated incrementally in a fixed-size distributed representation, and inner products can be approximated on the fly at low computational cost. An open source implementation of generalised RI is provided. © 2016, The Author(s).