Step-Oriented Variation Trend Analysis

• Step-oriented variation trend is a framework that segments process behavior by analyzing continuous features to detect significant shifts in executed activities.
• It employs a sliding window method combined with Earth Mover’s Distance to automatically identify and validate thresholds where process structures change.
• The approach enables precise case segmentation for enhanced process optimization, anomaly detection, and predictive modeling in operational analytics.

A step-oriented variation trend is the systematic change or segmentation of process behavior, activity flow, or system outcomes driven by a continuous, ordered dimension—such as case duration, evaluated risk score, or other quantifiable case-level features. In the context of process mining and operational analytics, this concept refers to the identification of points along a continuous variable where the execution “steps” of a process exhibit significant structural change. Recent frameworks enable automated, data-driven detection and interpretation of such trends, offering capabilities that transcend traditional time-based concept drift detection.

1. Conceptual Foundation: Step-Oriented Variation and Continuous Feature Segmentation

Traditional techniques in process mining focus predominantly on temporal variation, seeking to detect concept drift or process change points over time. The step-oriented variation trend framework instead extends the analysis to any continuous, case-level feature (such as case duration, risk score, monetary value, etc.), aiming to expose how the sequence and nature of operational steps alter as this feature varies.

Cases from an event log ($L$) are associated with a continuous attribute $\kappa: L \rightarrow \mathbb{R}$ and ordered accordingly. By analyzing groups of cases (“buckets”) sorted along this attribute, the framework systematically identifies thresholds where a substantial change in control-flow structure occurs, thus segmenting the population into meaningful cohorts for targeted analysis and comparison.

2. Methodological Innovations: Sliding Window and Earth Mover’s Distance

The core methodological advance is the use of a sliding window across the sorted buckets, coupled with the Earth Mover’s Distance (EMD) to measure control-flow dissimilarities between adjacent groups. For each position $i$, the local distance metric is defined as: $$ldist_{L, \kappa, w, b}(i) = EMD(W^{l}_{w,i}, W^{r}_{w,i})$$ where $W^{l}_{w,i}$ and $W^{r}_{w,i}$ are windows of $w$ buckets to the left and right of $i$, respectively. The EMD is computed based on the multi-set of executed traces (stochastic languages) in each window, using, for example, the Levenshtein distance as a trace similarity metric. Peaks in the $ldist$ curve reveal candidate change points—values of the continuous feature at which control-flow patterns exhibit discrete shifts.

This approach obviates the need for arbitrary discretization of continuous features, allowing threshold detection to emerge in a data-driven manner and supporting the precise mapping of variation trends to underlying process mechanics.

3. Case Segmentation, Hierarchical Merging, and Pairwise Comparison

Upon identification of significant change points (via $ldist$ exceeding a threshold $\theta$), the cases are divided into contiguous segments—each representing a cohort with homogeneous control-flow behavior for a particular range of the continuous feature. Further hierarchical merging is performed: if the EMD between two segments falls below $\theta$, they are merged, preventing overfragmentation due to noise.

After segmentation, the framework conducts pairwise EMD comparisons between all segments, which are visually summarized in a heatmap. This reveals the global landscape of variation trends—whether the process displays a monotonic transition, abrupt “steps,” or clustered regimes of similar execution behavior.

4. Practical Application: Insurance Case Management Study

The approach was validated on a real event log from UWV (Dutch Employee Insurance Agency), containing over 144,000 cases and 29 activities, spanning case durations from 1 to 575 days. By applying the sliding window EMD method with appropriate parameterization (e.g., $b=100$ buckets, $w=5$ window size, $\theta=0.1$), clear step-oriented variation trends were identified:

• Distinct change points at durations of 17 and 78 days,
• Segmentation into three cohorts: short ([0,17] days, mostly instant rejections), medium ([18,77] days, standard processing), and long ([78,575] days, accepted claims with more complex post-processing),
• Pairwise heatmap analysis confirmed strong behavioral discontinuities at these boundaries,
• Further analysis on claim outcome subpopulations revealed finer-grained trends.

This operationalizes the detection of stages at which process management, customer engagement, or procedural intervention might need to adapt, providing directly actionable intelligence for process optimization.

5. Implications for Efficiency, Abnormality Detection, and Predictive Modeling

Step-oriented variation trend analysis along continuous features allows organizations to:

• Objectively pinpoint thresholds or regimes of inefficiency (e.g., case durations where process steps become redundant or circuitous),
• Detect abnormal behavioral pockets (segments with sharply divergent control flow, possibly requiring root-cause analysis),
• Provide informed segmentation for downstream tasks, such as outcome prediction, conformance checking, or simulation,
• Enable alignment of process design or policy with empirical process “phases” revealed by feature-driven structural change.

Segmented cohorts can serve as distinct classes in predictive models, or as focus areas for deeper qualitative examination.

6. Comparative Positioning and Advantages

Unlike existing research restricted to detecting drift over time, this framework generalizes variation analysis to arbitrary continuous dimensions intrinsic to process performance. It does not require prior manual discretization and forgoes high-dimensional attribute abstraction in favor of direct, semantically meaningful control-flow analysis using EMD. Hierarchical merging and comprehensive pairwise comparison support both fine- and coarse-grained perspectives of process variation, facilitating actionable interpretation.

Aspect	Framework Approach	Typical Outcome/Finding
Dimension of analysis	Arbitrary continuous feature (not just time)	Data-driven detection of critical values
Change detection	Sliding window + EMD	Automatic, interpretable thresholds
Segmentation strategy	Peak finding + hierarchical merging	Robust, meaningful case cohorts
Comparison of behavior	Pairwise EMD heatmap	Identification of distinct process stages
Validation	Real-world event log (UWV)	Actionable recommendations

7. Research and Field Impact

The framework enables comprehensive, technically grounded discovery of step-oriented variation trends, equipping organizations to visualize, interpret, and act on structural changes in process execution correlated with continuous drivers of business outcomes. This facilitates targeted process improvement, supports compliance and auditing, and enhances the interpretability of automated decision support in process mining systems. The methodology's demonstration on a large-scale operational process distinguishes it from prior approaches by both its practical scalability and its specificity in capturing step-driven behavioral transitions over meaningful business features.