Geometric-k-means: A Bound Free Approach to Fast and Eco-Friendly k-means

This paper introduces Geometric-k-means (or Gk-means for short), a novel approach that significantly enhances the efficiency and energy economy of the widely utilized k-means algorithm, which, despite its inception over five decades ago, remains a cornerstone in machine learning applications. The essence of Gk-means lies in its active utilization of geometric principles, specifically scalar projection, to significantly accelerate the algorithm without sacrificing solution quality. This geometric strategy enables a more discerning focus on data points that are most likely to influence cluster updates, which we call as high expressive data (HE). In contrast, low expressive data (LE), does not impact clustering outcome, is effectively bypassed, leading to considerable reductions in computational overhead. Experiments spanning synthetic, real-world and high-dimensional datasets, demonstrate Gk-means is significantly better than traditional and state of the art (SOTA) k-means variants in runtime and distance computations (DC). Moreover, Gk-means exhibits better resource efficiency, as evidenced by its reduced energy footprint, placing it as more sustainable alternative.

Multivariate de Bruijn Graphs: A Symbolic Graph Framework for Time Series Forecasting

Time series forecasting remains a challenging task for foundation models due to temporal heterogeneity, high dimensionality, and the lack of inherent symbolic structure. In this work, we propose DRAGON (Discrete Representation and Augmented Graph encoding Over deBruijN Graphs), a novel encoder that introduces Multivariate de Bruijn Graphs (MdBGs) to bridge the gap between symbolic representations and neural modeling. DRAGON discretizes continuous input sequences and maps them onto a fixed graph structure, enabling dynamic context recovery via graph-based attention. Integrated as an auxiliary module within a dual-branch architecture, DRAGON augments conventional CNN-based encoders with symbolic, structure-aware representations. All code developed for this study is available at: https://github.com/KurbanIntelligenceLab/MultdBG-Time-Series-Library