Exactness of Semidefinite Relaxations for Nonlinear Optimization Problems with Underlying Graph Structure

2014 ◽  
Vol 24 (4) ◽  
pp. 1746-1778 ◽  
Author(s):  
Somayeh Sojoudi ◽  
Javad Lavaei
1999 ◽  
Vol 9 (3) ◽  
pp. 755-778 ◽  
Author(s):  
Paul T. Boggs ◽  
Anthony J. Kearsley ◽  
Jon W. Tolle

Information ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 525
Author(s):  
Franz Hell ◽  
Yasser Taha ◽  
Gereon Hinz ◽  
Sabine Heibei ◽  
Harald Müller ◽  
...  

Recent advancements in deep neural networks for graph-structured data have led to state-of-the-art performance in recommender system benchmarks. Adapting these methods to pharmacy product cross-selling recommendation tasks with a million products and hundreds of millions of sales remains a challenge, due to the intricate medical and legal properties of pharmaceutical data. To tackle this challenge, we developed a graph convolutional network (GCN) algorithm called PharmaSage, which uses graph convolutions to generate embeddings for pharmacy products, which are then used in a downstream recommendation task. In the underlying graph, we incorporate both cross-sales information from the sales transaction within the graph structure, as well as product information as node features. Via modifications to the sampling involved in the network optimization process, we address a common phenomenon in recommender systems, the so-called popularity bias: popular products are frequently recommended, while less popular items are often neglected and recommended seldomly or not at all. We deployed PharmaSage using real-world sales data and trained it on 700,000 articles represented as nodes in a graph with edges between nodes representing approximately 100 million sales transactions. By exploiting the pharmaceutical product properties, such as their indications, ingredients, and adverse effects, and combining these with large sales histories, we achieved better results than with a purely statistics based approach. To our knowledge, this is the first application of deep graph embeddings for pharmacy product cross-selling recommendation at this scale to date.


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