A random walks perspective on maximizing satisfaction and profit

We model consumer behavior such as web browsing, shopping, and entertainment choices as random walks on a weighted association graph. The graph is derived from a relational database that links products, consumers, and attributes such as product categories, consumer demographics, market segments, etc. The Markov chain that describes this walk amalgamates consumer behavior over the whole population; individuals are distinguished by their current state in the chain. We develop a geometrization of the chain that furnishes a key similarity measure for information retrieval—the cosine (correlation) angle between two states. Empirically, this proves to be highly predictive of future choices made by individuals, and is useful for recommending and semi-supervised classification. This statistic is obtained through a sparse matrix inversion, and we develop approximation strategies that make this practical for very large Markov chains. These methods also make it practical to compute recommendations to maximize long-term profit.