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Mathematical Underpinnings of Analytics: Theory and Applications

Peter Grindrod
OXFORD UNIVERSITY PRESS 2014, 280 PAGES
PRICE (HARDBACK) £29.99 ISBN 978-0-19-872509-1

50 visions cover

Have you ever kept a tally of the running cost of the items in your trolley while shopping at the supermarket? Well, the simple arithmetic required for this task is as nothing compared to the complicated mathematical calculations performed on the contents of your trolley by the supermarket itself! Correlating pairs of items from hundreds of thousands of products across multiple customers using similarity matrices and dendrograms is but one example. The detailed analysis of this and other activities in customer-facing sectors such as supermarkets is one aspect of what Professor Peter Grindrod, of the Mathematical Institute at the University of Oxford, calls Analytics.

More generally, Analytics comprises ‘the concepts, methods and practices that can conjure valuable and actionable insights and radical knowledge from large volumes of data.’ In addition to customer-facing sectors such as supermarkets its applications include commercial services, digital media, communications, energy, environment, marketing etc. Anywhere, in fact, where there is an abundance of data. Peter is keen to emphasise that data are just the raw material; analytics are needed to create options for action and to bring a competitive advantage, and mathematics is the tool that underpins all this.

The book has seven chapters beyond the Introduction, covering: Similarity, graphs and networks, random matrices and SVD; Dynamically evolving networks; Structure and responsiveness; Clustering and unsupervised classification; Multiple hypothesis testing over live data; Adaptive forecasting and Customer journeys and Markov chains (there is also an appendix on Uncertainty, Probability and Reasoning). Each chapter has an interesting structure: it begins with some more or less formal mathematics (at undergraduate level, generally) and finishes with a section called A Personal View.

I found these personal view sections fascinating. In addition to allowing a respite from having to concentrate hard to understand such things as the difference between logistic regression and polytomous regression, they provide a varied and valuable guide to the real-world application of the more formal mathematics, drawn from Peter’s extensive experience of such. They also provide a glimpse of some of Peter’s strongly held views (such as ‘Personally, I greatly dislike artificial neural networks…’ or ‘… twenty-five percent of a research portfolio should be aimed beyond the current paradigm …’).

With explosively increasing amounts of data, both public and proprietary, being produced, companies will have to make intelligent use of them in order to grow and compete successfully in the global market place. This means getting to grips with a whole range of relevant mathematical concepts such as are set out in this book. It is an essential read for any mathematician who is thinking of a career that involves analysing ‘big’ data.

Alan Stevens CMath FIMA

Book review published directly onto IMA website (February 2015)