The New “New Math” Behind Coherent Path

Hyperbolic geometry

When Dr. Greg Leibon, a PhD. Scholar in Mathematics at Dartmouth College and one of the co-founders of Coherent Path, talks about math his face lights up like a kid. Arms waving as he talks, his excitement reveals a passion for complex topics few of us can even begin to comprehend. Whether it is explaining the fundamentals of hyperbolic geometry or the advancements he and the team at Coherent Path have made in statistical learning theory to wade through mountains of retail data, talking about math energizes him.

Hyperbolic geometry is one of his favourite topics. It is a different way of looking at data and how information resides within in it. Instead of looking at data as a flat surface with various values, hyperbolic geometry creates a space with millions of possible points of data locations, and perspectives from which to view them. “Imagine it being like the cosmos as viewed from within our solar system,” shared Dr. Leibon. “Our cosmos forms a sort of map,  and with it we can describe navigation within our solar system.  I could tell someone on Venus to point a laser in the direction of andromeda, and if I were to do the same thing from earth, then our lasers would be pointing in basically parallel directions.” he concluded.

Explaining what makes Coherent Path unique can be done using this same analogy. “Now we can imagine that a planet is a customer or a collection of products deep within a retailer’s data,” he stated. “Hyperbolic geometry equips us with such a cosmos like navigation tool, providing a notion of direction and an ability to navigate this space of data.  But, even better, there is flexibility in what we can consider the cosmos allowing us to tailor our cosmos to suit our navigational objectives.  Viewing a customer’s journey using such a map provides a new and informative way to understand that journey and the customer-product relationship”.

Thanks to hyperbolic geometry, Coherent Path’s solution allows retailers to build a better profile of the customers within their space and where they fit compared to a list of products purchased or for sale. Then, the cloud-based platform can identify the patterns and paths of a profile or group in order to predict the overall potential to follow a similar journey. This allows them to not only identify the most ideal customer, but also the sequence of products they would need to present in order to guide the customer’s behaviour.

The team of data scientists at Coherent Path rely on statistical learning theory to help them trek through the mountains of “big data” needed to build maps of product and customer relationships. This process helps Dr. Leibon and his team harness the power of hyperbolic geometry. Without being able to reduce the data to the sets they need to navigate around, the process would be even more challenging.

The combination of these items are what the entire team at Coherent Path lovingly refer to as the “new, new math”, an innovative set of mathematics being applied to an age-old problem: “how do I build a lifetime relationship with a customer based on loyalty”?

Through the use of hyperbolic geometry, Coherent Path is able create a Map of the client’s product and transactional data. The Map is key as it calculates the series of products a buyer should be presented on their way to becoming “an ideal consumer”. It also considers the speed and frequency of engagement needed to keep them moving forward along this journey. As new sales data is entered into the system, the map re-calibrates itself to ensure it takes advantage of trends or seasonal changes.

While the math is complex, the benefits of using hyperbolic geometry are pretty easy to comprehend.  Customers who are provided with relevant products, at the right time, and in the right sequence will be more engaged.  The more engaged they become, the more they value a retailer’s ability to recommend great products.  The end result is a lifelong journey of loyalty – a win-win scenario for both the retailer and the customer.

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