‘Data scientists frequently find themselves dealing with high-dimensional feature spaces. As an example, text mining usually involves vocabularies comprised of 10,000+ different words. Many analytic problems involve linear algebra, particularly 2D matrix factorization techniques, for which several open source implementations are available. Anyone working on implementing machine learning algorithms ends up needing a good library for matrix analysis and operations.
But why stop at 2D representations? In a recent Strata + Hadoop World San Jose presentation, UC Irvine professor Anima Anandkumar described how techniques developed for higher-dimensional arrays can be applied to machine learning. 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).
Being able to capture higher-order relationships proves to be quite useful. In her talk, Anandkumar described applications to latent variable models — including text mining (topic models), information science (social network analysis), recommender systems, and deep neural networks. A natural entry point for applications is to look at generalizations of matrix (2D) techniques to higher-dimensional array’