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We study the problem of representation learning for multiple types of entities in a co-ordered network where order relations exist among entities of the same type, and association relations exist across entities of different types. The key challenge in learning co-ordered network embedding is to preserve order relations among entities of the same type while leveraging on the general consistency in order relations between different entity types. In this paper, we propose an embedding model, CO2Vec, that addresses this challenge using mutually reinforced order dependencies. Specifically, CO2Vec explores indirect order dependencies as supplementary evidence to enhance order representation learning across different types of entities. We conduct extensive experiments on both synthetic and real world datasets to demonstrate the robustness and effectiveness of CO2Vec against several strong baselines in link prediction task. We also design a comprehensive evaluation framework to study the performance of CO2Vec under different settings. In particular, our results show the robustness of CO2Vec with the removal of order relations from the original networks.
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This content will become publicly available on February 1, 2026
Product Design Incorporating Competition Relations: A Network-Based Design Framework Considering Local Dependencies
Abstract System design has been facing the challenges of incorporating complex dependencies between individual entities into design formulations. For example, while the decision-based design framework successfully integrated customer preference modeling into optimal design, the problem was formulated from a single entity’s perspective, and the competition between multiple enterprises was not considered in the formulation. Network science has offered several solutions for studying interdependencies in various system contexts. However, efforts have primarily focused on analysis (i.e., the forward problem). The inverse problem still remains: How can we achieve the desired system-level performance by promoting the formation of targeted relations among local entities? In this study, we answer this question by developing a network-based design framework. This framework uses network representations to characterize and capture dependencies and relations between individual entities in complex systems and integrate these representations into design formulations to find optimal decisions for the desired performance of a system. To demonstrate its utility, we applied this framework to the design for market systems with a case study on vacuum cleaners. The objective is to increase the sales of a vacuum cleaner or its market share by optimizing its design attributes, such as suction power and weight, with the consideration of market competition relations, such as inter-brand triadic competition involving three products from different brands. We solve this problem by integrating an exponential random graph model (ERGM) with a genetic algorithm. The results indicate that the new designs, which consider market competition, can effectively increase the purchase frequency of specific vacuum cleaner models and the proposed network-based design method outperforms traditional design optimization.
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- Award ID(s):
- 2203080
- PAR ID:
- 10637502
- Publisher / Repository:
- American Society of Mechanical Engineers
- Date Published:
- Journal Name:
- Journal of Mechanical Design
- Volume:
- 147
- Issue:
- 2
- ISSN:
- 1050-0472
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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