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We constructed a product network based on the sales data collected and provided by a Fortune 500 speciality retailer. The structure of the network is dominated by small isolated components, dense clique-based communities, and sparse stars and linear chains and pendants. We used the identified structural elements (tiles) to organize products into mini-categories -- compact collections of potentially complementary and substitute items. The mini-categories extend the traditional hierarchy of retail products (group - class - subcategory) and may serve as building blocks towards exploration of consumer projects and long-term customer behavior.
Manipulation and assembly tasks require non-trivial planning of actions depending on the environment and the final goal. Previous work in this domain often assembles particular instances of objects from known sets of primitives. In contrast, we aim t
This paper has been withdrawn from arXiv.org due to a disagreement among the authors related to several peer-review comments received prior to submission on arXiv.org. Even though the current version of this paper is withdrawn, there was no disagreem
Online stores like Amazon and Ebay are growing by the day. Fewer people go to departmental stores as opposed to the convenience of purchasing from stores online. These stores may employ a number of techniques to advertise and recommend the appropriat
Given two small dg categories $C,D$, defined over a field, we introduce their (non-symmetric) twisted tensor product $Coverset{sim}{otimes} D$. We show that $-overset{sim}{otimes} D$ is left adjoint to the functor $Coh(D,-)$, where $Coh(D,E)$ is the
We present a novel tractable generative model that extends Sum-Product Networks (SPNs) and significantly boosts their power. We call it Sum-Product-Quotient Networks (SPQNs), whose core concept is to incorporate conditional distributions into the mod