Cem Iyigun | Searcharxiv

arXiv2026

A Foundational Perspective for Partitional Clustering on Networks

This study presents a theoretical analysis of partitional clustering on networks, analyzing both hard and soft assignment schemes with different objective functions. Cluster centers are not restricted to vertices but can also be located along the edges. We examine four key models: P-Median (PMP) and Sum of Squares Clustering (SSC) under hard assignment, and Probabilistic Distance Clustering (PDC) and Fuzzy C-Means (FCM) under soft assignment. Through mathematical analysis, we uncover structural properties that differentiate these models, such as the significance of assignment bottleneck points and the role of vertex-restricted solutions in determining optimal cluster centers. Our findings reveal that, while SSC and FCM can yield optimal centers along edges, PMP and PDC inherently favor vertex placement, leading to insights into clustering behavior on networks. These insights offer new directions for designing efficient algorithms and have implications ranging from facility location and network design to clustering on the embedding graphs that power similarity search in modern retrieval systems.

math.OC↗

arXiv2016

Temporal Clustering of Time Series via Threshold Autoregressive Models: Application to Commodity Prices

This study aimed to find temporal clusters for several commodity prices using the threshold non-linear autoregressive model. It is expected that the process of determining the commodity groups that are time-dependent will advance the current knowledge about the dynamics of co-moving and coherent prices, and can serve as a basis for multivariate time series analyses. The clustering of commodity prices was examined using the proposed clustering approach based on time series models to incorporate the time varying properties of price series into the clustering scheme. Accordingly, the primary aim in this study was grouping time series according to the similarity between their Data Generating Mechanisms (DGMs) rather than comparing pattern similarities in the time series traces. The approximation to the DGM of each series was accomplished using threshold autoregressive models, which are recognized for their ability to represent nonlinear features in time series, such as abrupt changes, time-irreversibility and regime-shifting behavior. Through the use of the proposed approach, one can determine and monitor the set of co-moving time series variables across the time dimension. Furthermore, generating a time varying commodity price index and sub-indexes can become possible. Consequently, we conducted a simulation study to assess the effectiveness of the proposed clustering approach and the results are presented for both the simulated and real data sets.

stat.ML↗