İsmail Güzel

İsmail Güzel, Atabey Kaygun

In this study, we examine if engineered topological features can distinguish time series sampled from different stochastic processes with different noise characteristics, in both balanced and unbalanced sampling schemes. We compare our classification results against the results of the same classification tasks built on statistical and raw features. We conclude that in classification tasks of time series, different machine learning models built on engineered topological features perform consistently better than those built on standard statistical and raw features.

Korkut Anapa, İsmail Güzel, Ceylan Yozgatlıgil

Purpose: Overall equipment efficiency (OEE) is a key manufacturing KPI, but its volatile nature complicates short-term forecasting. This study presents a novel framework combining time series decomposition and topological data analysis to improve OEE prediction across various equipment, such as hydraulic press systems. Methods: The approach begins by decomposing hourly OEE data into trend, seasonal, and residual components. The residual, capturing short-term variability, is modeled using a seasonal ARIMA with exogenous variables (SARIMAX). These exogenous features include statistical descriptors and topological summaries from related time series. To manage the high-dimensional input space, we propose a hybrid feature selection strategy using recursive feature elimination based on statistically significant SARIMAX predictors, coupled with BIC-guided particle swarm optimization. The framework is evaluated on real-world datasets from multiple production systems. Results: The proposed model consistently outperforms conventional time series models and advanced transformer-based approaches, achieving significantly lower mean absolute error and mean absolute percentage error. Conclusion: Integrating classical forecasting with topological data analysis enhances OEE prediction accuracy, enabling proactive maintenance and informed production decisions in complex manufacturing environments.

İsmail Güzel, Atabey Kaygun

In this article, we define a new non-archimedean metric structure, called cophenetic metric, on persistent homology classes of all degrees. We then show that zeroth persistent homology together with the cophenetic metric and hierarchical clustering algorithms with a number of different metrics do deliver statistically verifiable commensurate topological information based on experimental results we obtained on different datasets. We also observe that the resulting clusters coming from cophenetic distance do shine in terms of different evaluation measures such as silhouette score and the Rand index. Moreover, since the cophenetic metric is defined for all homology degrees, one can now display the inter-relations of persistent homology classes in all degrees via rooted trees.