# A multiple k-means cluster ensemble framework for clustering citation trajectories

arXiv: https://arxiv.org/abs/2309.04949 · HTML: https://mlsanity.com/paper/2309.04949/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 57 references that are in the map.
- First posted on arXiv 10 Sep 2023.

## Builds on (most cited first, 9 of 9)

- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [Quantifying Long-Term Scientific Impact](https://mlsanity.com/paper/1306.3293/) (2013)
- [Scientific Paper Recommendation: A Survey](https://mlsanity.com/paper/2008.13538/) (2020)
- [Defining and identifying Sleeping Beauties in science](https://mlsanity.com/paper/1505.06454/) (2015)
- [Growing complex network of citations of scientific papers -- measurements and modeling](https://mlsanity.com/paper/1607.08370/) (2016)
- [On the categorization of scientific citation profiles in computer sciences](https://mlsanity.com/paper/1503.06268/) (2015)
- ["Smart Girls" versus "Sleeping Beauties" in the Sciences: The Identification of Instant and Delayed Recognition by Using the Citation Angle](https://mlsanity.com/paper/1611.08849/) (2016)
- [Search for Evergreens in Science: A Functional Data Analysis](https://mlsanity.com/paper/1705.00359/) (2017)
- [Anomalous diffusion in the citation time series of scientific publications](https://mlsanity.com/paper/2106.10038/) (2021)

## Built on by (most cited first, 1 of 1)

- [LEA: Label Enumeration Attack in Vertical Federated Learning](https://mlsanity.com/paper/2603.03777/) (2026)

## Abstract (arXiv)

Citation maturity time varies for different articles. However, the impact of all articles is measured in a fixed window. Clustering their citation trajectories helps understand the knowledge diffusion process and reveals that not all articles gain immediate success after publication. Moreover, clustering trajectories is necessary for paper impact recommendation algorithms. It is a challenging problem because citation time series exhibit significant variability due to non linear and non stationary characteristics. Prior works propose a set of arbitrary thresholds and a fixed rule based approach. All methods are primarily parameter dependent. Consequently, it leads to inconsistencies while defining similar trajectories and ambiguities regarding their specific number. Most studies only capture extreme trajectories. Thus, a generalised clustering framework is required. This paper proposes a feature based multiple k means cluster ensemble framework. 1,95,783 and 41,732 well cited articles from the Microsoft Academic Graph data are considered for clustering short term (10 year) and long term (30 year) trajectories, respectively. It has linear run time. Four distinct trajectories are obtained Early Rise Rapid Decline (2.2%), Early Rise Slow Decline (45%), Delayed Rise No Decline (53%), and Delayed Rise Slow Decline (0.8%). Individual trajectory differences for two different spans are studied. Most papers exhibit Early Rise Slow Decline and Delayed Rise No Decline patterns. The growth and decay times, cumulative citation distribution, and peak characteristics of individual trajectories are redefined empirically. A detailed comparative study reveals our proposed methodology can detect all distinct trajectory classes.