The Dimension Reduction Challenge

Email + Hyperbolic Geometry = More Engaged Shoppers | Coherent Path

By Dr. Greg Leibon, CTO

The behaviour of an individual can be viewed as a time series of messages received and transactions made. In nearly any problem involving a time series like this there is a tricky problem of dimension reduction.

Imagine we are attempting to understand changing food consumptions tastes over time, perhaps with the goal of encouraging someone to consume a more healthy diet. Well, with 100s of options for each dinner, after a week there are 100,000,000,000,000 possible sequences of meals. It’s easy to see that very quickly you are unlikely to have a large enough sample population to discern much about the sequences in a direct statistical sense!

There are many tricks to compress this information, most of which involve labeling and grouping both the product and the population and picking out expert-defined relevant summary statistics. The statistics and machine learning community has also developed tools and methodologies for dealing with such sequences. Most of the usual tools (Bayesian networks, kernel regression, regression trees, multilayer perceptrons, K-nearest neighbour regression, radial basis functions, support vector regression, Markov Models … ) have been souped-up to handle time series data, but in my experience the traditional models could only handle a limited class of problems, ones involving essentially a single next step, and were not at all good at long term problems like the healthier eating problem.

A New Approach to Dimension Reduction

In this case, we need our dimension reduction to retain enough information about each unique journey in order to move an individual in a specified direction at a learned rate. After several years of research and field testing in related problem areas, I learned that maps built using hyperbolic geometry (described in more detail in the research paper available on Plos One) could provide a new canvas upon which we could build a new model – one designed specifically to handle challenges like those presented in the healthier eater problem. More generally, this patent pending approach is ideally suited to address problems that involve a longer-term objective function, like forming loyal customers… or even getting my wife to appreciate a good horror movie!

For the mathematically inclined out there – what’s your perspective on the dimension reduction challenge?

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