# WIRE: A Weighted Item Removal Method for Unsupervised Rank Aggregation
## 6 Conclusions and Future Work  
In this paper, we introduced WIRE, a novel item selection approach for weighted rank aggregation applications. WIRE functions as a post-processing step to any weighted rank aggregation method and aims to further improve the quality of the output aggregate list. More specifically, our approach initially groups the input preference lists into a pre-defined number of buckets, according to the weights that have been assigned to their respective rankers by the original weighted aggregator. Based on that bucket, each preference list (that is, its respective ranker) is assigned a confidence score that quantifies its importance in a discretized manner.  
Then, for each element of the aggregate list, WIRE computes a preservation score that derives from the sum of the confidence scores of the rankers who included it in their preference lists. In the sequel, the aggregate list is sorted in decreasing preservation score order. Consequently, WIRE favors the elements that have been selected by multiple expert rankers. The preservation score is designed to be free of manipulation; therefore, it does not depend on external factors like the individual rankings, pairwise wins and losses, or other score values that may have been assigned by the original aggregator. WIRE also employs the aforementioned confidence scores to compute a threshold value that determines the number of elements to be removed from the (sorted) aggregate list.  
Our proposed method was theoretically analyzed and experimentally tested against a collection of 13 state-of-the-art rank aggregation methods in 8 benchmark datasets. The collection included both weighted and non-weighted aggregators, whereas the datasets were carefully selected in order to cover multiple diverse scenarios. The experiments highlighted the high retrieval effectiveness of WIRE in terms of Precision, normalized Discounted Cumulative Gain, and Mean Average Precision. Regarding future work, we intend to enhance WIRE by introducing more sophisticated discretization methods to determine the intervals (and ideally the number) of buckets where the rankers will be grouped. Examples of unsupervised binning methods include buckets of equal widths instead of equally sized buckets, or buckets that derive from the application of a clustering algorithm. We also plan to study alternative mathematical definitions for the confidence, preservation, and protection scores with the aim of improving the effectiveness of WIRE.  
Conceptualization, methodology, software, validation, formal analysis, resources, data curation, writing--original draft preparation, writing--review and editing: L.A. and P.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The datasets used in this study are publicly available on Kaggle: [[https://www.kaggle.com/datasets/lakritidis/rankaggregation](https://www.kaggle.com/datasets/lakritidis/rankaggregation)]([https://www.kaggle.com/datasets/lakritidis/rankaggregation](https://www.kaggle.com/datasets/lakritidis/rankaggregation)). The implementation code of WIRE can be found in the open-source libraries FLAG 1.0.20 & PyFLAG 1.0.20: [[https://flagr.site](https://flagr.site)]([https://flagr.site](https://flagr.site)), [[https://github.com/lakritidis/FLAG](https://github.com/lakritidis/FLAG)]([https://github.com/lakritidis/FLAG](https://github.com/lakritidis/FLAG)), [[https://pypi.org/project/pyflagr/](https://pypi.org/project/pyflagr/)]([https://pypi.org/project/pyflagr/](https://pypi.org/project/pyflagr/)).  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} WIRE & Weighted Item Removal \\ MAP & Mean Average Precision \\ nDCG & normalized Discounted Cumulative Gain \\ \end{tabular}