Dynamic Data Analysis Based on Segmentation of Graphical Representations and Structural Features

Abstract

we studied a method for analyzing dynamic data based on segmentation of graphical representations and analysis of structural features. We first converted the original time series into a plotted graph. The method then automatically divided the curve into segments at points where the shape changed noticeably, such as changes in slope, curvature, or small discontinuities. For each segment, we fitted an approximation model (linear, polynomial, exponential, and others) that best described the local behavior of the data. We selected the model by minimizing the approximation error while applying a penalty for excessive model complexity, which prevented overfitting.
We also applied a set of quantitative characteristics to compare neighboring segments. These characteristics describe both statistical properties of the data and the parameters of the fitted models. In this framework, an anomaly is a segment or individual point whose behavior differs substantially from the behavior predicted by models fitted to the other segments. The method, therefore, detects both isolated outliers and sequences of unusual observations, known as collective anomalies, in time-dependent data.
We demonstrated the approach using a synthetic time series and presented a visualization of the resulting segmentation and detected anomalies. A comparison with classical change-point detection methods shows that the proposed method provides interpretable segmentation and remains flexible in its treatment of different structural features, which distinguishes it from purely statistical tests.