As the field of recommender systems has developed, authors have used a myriad of notations for describing the mathematical workings of recommendation algorithms. These notations appear in research papers, books, lecture notes, blog posts, and software documentation. The disciplinary diversity of the field has not contributed to consistency in notation; scholars whose home base is in information retrieval have different habits and expectations than those in machine learning or human-computer interaction.
In the course of years of teaching and research on recommender systems, we have seen the value in adopting a consistent notation across our work. This has been particularly highlighted in our development of the Recommender Systems MOOC on Coursera (Konstan et al. 2015), as we need to explain a wide variety of algorithms and our learners are not well-served by changing notation between algorithms.
In this paper, we describe the notation we have adopted in our work, along with its justification and some discussion of considered alternatives. We present this in hope that it will be useful to others writing and teaching about recommender systems. This notation has served us well for some time now, in research, online education, and traditional classroom instruction. We feel it is ready for broad use.
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Ekstrand, Michael D. and Konstan, Joseph A.. (2019). "Recommender Systems Notation". Computer Science Faculty Publications and Presentations, 1-7.