Tensors are generalizations of matrices that let you look beyond pairwise relationships to higher-dimensional models (a matrix is a second-order tensor). For instance, one can examine patterns between any three (or more) dimensions in data sets. In a text mining application, this leads to models that incorporate the co-occurrence of three or more words, and in social networks, you can use tensors to encode arbitrary degrees of influence (e.g., ‘friend of friend of friend’ of a user).
Tensors, as generalizations of vectors and matrices, have become increasingly popular in different areas of machine learning and data mining, where they are employed to approach a diverse number of difficult learning and analysis tasks. Prominent examples include learning on multi-relational data and large-scale knowledge bases, recommendation systems, computer vision, mining boolean data, neuroimaging or the analysis of time-varying networks. The success of tensors methods is strongly related to their ability to efficiently model, analyse and predict data with multiple modalities. To address specific challenges and problems, a variety of methods has been developed in different fields of application.
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