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Network embedding has gained more attentions in recent years. It has been shown that the learned low-dimensional node vector representations could advance a myriad of graph mining tasks such as node classification, community detection, and link prediction. A vast majority of the existing efforts are overwhelmingly devoted to single-layered networks or homogeneous networks with a single type of nodes and node interactions. However, in many real-world applications, a variety of networks could be abstracted and presented in a multilayered fashion. Typical multi-layered networks include critical infrastructure systems, collaboration platforms, social recommender systems, to name a few. Despite the widespread use of multi-layered networks, it remains a daunting task to learn vector representations of different types of nodes due to the bewildering combination of both within-layer connections and cross-layer network dependencies. In this paper, we study a novel problem of multi-layered network embedding. In particular, we propose a principled framework – MANE to model both within-layer connections and cross-layer network dependencies simultaneously in a unified optimization framework for embedding representation learning. Experiments on real-world multi-layered networks corroborate the effectiveness of the proposed framework.
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Nucleus I: Adjunction spectra in recommender systems and descent
Recommender systems build user profiles using concept analysis of usage matrices. The concepts are mined as spectra and form Galois connections. Descent is a general method for spectral decomposition in algebraic geometry and topology which also leads to generalized Galois connections. Both recommender systems and descent theory are vast research areas, separated by a technical gap so large that trying to establish a link would seem foolish. Yet a formal link emerged, all on its own, bottom-up, against authors’ intentions and better judgment. Familiar problems of data analysis led to a novel solution in category theory. The present paper arose from a series of earlier efforts to provide a top-down account of these developments.
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- Award ID(s):
- 1662487
- PAR ID:
- 10483795
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Logical Methods in Computer Science
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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