Tensor as a multi-dimensional generalization of matrix has received increasing attention in industry due to its success in personalized recommendation systems. Traditional recommendation systems are mainly based on the user-item matrix, whose entry denotes each user's preference for a particular item. To incorporate additional information into the analysis, such as the temporal behavior of users, we encounter a user-item-time tensor. Existing tensor decomposition methods are mostly established in the non-sparse regime where the decomposition components include all features. In online advertising, the ad-click tensor is usually sparse due to the rarity of ad clicks.
In this talk, I will discuss a new sparse tensor decomposition method that incorporates the sparsity of each latent component to the CP tensor decomposition. In theory, in spite of the non-convexity of the optimization problem, it is proven that an alternating updating algorithm attains an estimator whose rate of convergence significantly improves those shown in non-sparse decomposition methods. The potential business impact of our method is demonstrated via an application of click-through rate prediction for personalized advertising.
In the second part of the talk, I will discuss an extension of the proposed sparse tensor decomposition to handle multiple sources of tensor data. In online advertising, the users’ click behavior on different ads from multiple devices forms a user-ad-device tensor, and the ad characteristics data forms an ad-feature matrix. We propose a unified learning framework to extract latent features embedded in both tensor data and matrix data. We conduct cluster analysis of advertisements based on the extracted latent features and provide meaningful insights in linking different ad industries.