Recommender Systems Notation: Proposed Common Notation for Teaching and Research (1902.01348v1)

Abstract: 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 ap-pear in research papers, books, lecture notes, blog posts, and software documentation. The dis-ciplinary 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 ma-chine learning or human-computer interaction. In the course of years of teaching and research on recommender systems, we have seen the val-ue 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.

• The paper introduces a standard notation to unify representations of various recommendation algorithms.
• It defines clear symbols for users, items, and rating matrices to eliminate ambiguities in notation.
• The flexible framework supports diverse methods, including ranking functions and context-aware models, streamlining research and education.

Introduction to Recommender Systems Notation

Recommender systems have become integral to the way we interact with online content, whether it's for shopping, entertainment, or information retrieval. Despite their widespread use, the academic field has seen a variety of notational systems used to describe the mathematical operations behind these systems, leading to confusion and inefficiencies in teaching and research. In a collaborative effort, Michael D. Ekstrand and Joseph A. Konstan address this issue by proposing a common notation system that promises clarity and flexibility across various types of algorithms.

Achieving Notation Design Goals

With the aim to establish a notation that is broadly applicable and easily understandable, the authors set forth several design goals. The proposed notation is meant to be versatile, accommodating a broad spectrum of recommendation systems algorithms. Clarity is pivotal, ensuring that anyone reading the notation can do so without intensive guesswork. The authors seek a balance between clarity and conciseness, avoiding unnecessary verbosity while also preventing ambiguity. They acknowledge the importance of aligning with common notation from related fields for synergy and ease of understanding, and they emphasize the notation's applicability to handwritten contexts like education and whiteboard collaboration.

Establishing Recommendation Inputs

Central to the paper is the establishment of a consistent and clear way to represent the foundational elements of recommendation systems. This includes distinguishable notations for users and items, as well as user-item preference data, which are organized into a matrix format. The notation accounts for full data sets as well as subsets, and includes concise representations for rating vectors and other related sets. A key goal here is legibility, making distinctions clear while avoiding complexity that would hinder quick interpretation when written by hand.

Analyzing Recommendation Outputs

The notation extends to recommendation outputs, capturing the nuances of various recommendation algorithms—including orderings, scores, and functions dependent on user and item variables. By employing functions, the notation facilitates the description of complex processes, such as top-N ranking and context-aware search engines, all within a consistent framework. The authors' notation can accommodate a variety of common algorithms, from user-based and item-based approaches to matrix factorization, demonstrating its usability across a wide range of research and application scenarios.

Notation Impact and Forward Look

The authors of the paper propose this common notation with the belief that it will be valuable not only for their own work but also for the wider community engaged in research and education on recommender systems. While not intended as a strict standard, its adoption could provide a shared language that reduces barriers in communication and collaboration within the field. By promoting a standardized approach, the proposed notation holds the potential to streamline educational processes and foster more efficient and coherent research dissemination in the rapidly evolving domain of recommender systems.