# Top-N-Rank: A Scalable List-wise Ranking Method for Recommender Systems

## TL;DR

Top-N-Rank introduces a scalable list-wise learning-to-rank model focused on optimizing top-N recommendations by limiting evaluation to top items and leveraging implicit feedback with different trust levels, improving ranking quality and efficiency.

## Contribution

The paper presents a novel list-wise ranking method that optimizes a top-N focused DCG variant, with a ReLU-based approximation for improved efficiency and performance.

## Key findings

- Top-N truncation enhances top N recommendation quality.
- ReLU smoothing improves both ranking performance and runtime.
- Top-N-Rank.ReLU outperforms existing list-wise ranking methods.

## Abstract

We propose Top-N-Rank, a novel family of list-wise Learning-to-Rank models for reliably recommending the N top-ranked items. The proposed models optimize a variant of the widely used discounted cumulative gain (DCG) objective function which differs from DCG in two important aspects: (i) It limits the evaluation of DCG only on the top N items in the ranked lists, thereby eliminating the impact of low-ranked items on the learned ranking function; and (ii) it incorporates weights that allow the model to leverage multiple types of implicit feedback with differing levels of reliability or trustworthiness. Because the resulting objective function is non-smooth and hence challenging to optimize, we consider two smooth approximations of the objective function, using the traditional sigmoid function and the rectified linear unit (ReLU). We propose a family of learning-to-rank algorithms (Top-N-Rank) that work with any smooth objective function. Then, a more efficient variant, Top-N-Rank.ReLU, is introduced, which effectively exploits the properties of ReLU function to reduce the computational complexity of Top-N-Rank from quadratic to linear in the average number of items rated by users. The results of our experiments using two widely used benchmarks, namely, the MovieLens data set and the Amazon Video Games data set demonstrate that: (i) The `top-N truncation' of the objective function substantially improves the ranking quality of the top N recommendations; (ii) using the ReLU for smoothing the objective function yields significant improvement in both ranking quality as well as runtime as compared to using the sigmoid; and (iii) Top-N-Rank.ReLU substantially outperforms the well-performing list-wise ranking methods in terms of ranking quality.