Object-Centric Process Mining (OCPM)

• Object-centric process mining is a method that models interactions among multiple object types in complex processes, enabling analysis of convergence and divergence phenomena.
• The framework employs process cubes to partition multidimensional event logs, allowing for effective slicing, dicing, and granularity adjustments in enterprise data.
• Integration with advanced discovery algorithms such as object-centric Petri nets and MVP models enhances detection of process variants, performance bottlenecks, and compliance issues.

Object-centric process mining (OCPM) is a specialization of process mining that explicitly models and analyzes the interactions among multiple object types within business processes, overcoming the limitations of traditional, single-case-centric techniques. Unlike classical process mining, which enforces a single case notion for each event—mapping every event to one case—OCPM represents event logs such that events can be simultaneously linked to diverse case notions (for example, orders, items, packages). This paradigm shift addresses phenomena such as convergence and divergence within real-life processes and enables a generalized framework for process analysis and comparison. A central technical advancement in this context is the introduction of object-centric process cubes, which support multidimensional partitioning and comparison of event data, as well as integration with advanced discovery algorithms such as object-centric Petri nets and Multiple Viewpoint (MVP) models (Ghahfarokhi et al., 2021).

1. Conceptual Foundation: Object-Centric Process Mining

Traditional process mining relies on event logs with a one-to-one relationship between events and a "case", implicitly assuming process instances to be mutually exclusive with respect to their associated events. In contrast, OCPM defines event logs such that each event is represented as a tuple $(ei, vmap, omap)$, where $ei$ is the event identifier, $vmap$ maps attributes to values, and $omap$ records the set of objects (instances) of various types involved in that event:

$U_{event} = U_{ei} \times U_{vmap} \times U_{omap}$

This multi-object representation captures complex interrelationships present in real-world business processes, such as convergence (one event related to multiple items), divergence, and synchronized progressions across object types. By allowing explicit modeling of these interactions, OCPM supports deeper, multi-perspective analysis and avoids the information loss inherent in flattening multi-object processes into a single-case abstraction.

2. Object-Centric Process Cubes: Formal Framework

The process cube concept in OCPM extends OLAP-like operations to multi-dimensional event logs incorporating multiple case notions. Formally, a process cube structure is defined as:

$PCS = (D, val, gran)$

where

• $D$ is the set of dimensions (attributes or object types),
• $val$ assigns to each dimension its atomic value set,
• $gran$ assigns a granularity level (sets of set-values) to each dimension.

A process cube view (PCV) is specified as:

$PCV = (D_{sel}, sel)$

where $D_{sel} \subseteq D$ are the dimensions selected for viewing and $sel$ maps each dimension to a collection of values or granularity levels.

The materialization operation computes the set of cube cells and assigns event sets to each, for analysis:

$M_{E, PCV} = \{ (c, events(c)) \mid c \in cells \}$

Cells are defined for every $c \in D_{sel} \rightarrow \bigcup_s$ such that for each $d \in D_{sel}$, $c(d) \in sel(d)$. Events in a cell are selected based on attribute and object-type restrictions as dictated by $c$.

Cube navigation operations, including slice (dimension removal by fixing value sets), dice (filtering of dimensions), and change granularity (adjust alteration of level-of-detail per dimension), are formally defined, generalizing their OLAP counterparts for object-centric event logs.

3. Integration with Process Discovery Algorithms

OCPM seamlessly integrates object-centric process cubes with several process discovery methodologies specifically adapted for multi-case environments:

• Multiple Viewpoint (MVP) models leverage graph representations where nodes are activities and colored edges encode activity flows per object type. This multiplicity enables capturing the concurrent, interconnected evolution of different object classes.
• Object-centric Petri nets provide formal execution semantics for capturing concurrency and synchronization between object types. The Petri net is augmented to enable tokens carrying object type information, thus permitting activity transitions to consume and produce sets of objects with the necessary relationships.

Cube operations (slice, dice, granularity adjustment) facilitate extraction of specific sublogs or subcubes that are subsequently modeled using these advanced discovery algorithms. This enables comparative analysis across process variants, for instance, contrasting a global process model with those derived for distinct slices/dices of the process cube.

4. Applications: Real-World Business Scenarios and Analytical Implications

The object-centric process cube framework is designed with practical deployment in complex enterprise settings, as illustrated by examples from SAP IDES purchasing systems. Real processes—such as purchase-to-pay and order-to-cash—involve multiple interacting objects (orders, items, invoices), with events recording their simultaneous transitions.

Key applications enabled by OCPM and process cubes include:

• Behavioral comparison: Isolation and comparative analysis of process segments (e.g., comparing order-driven sublogs with item-driven sublogs).
• Performance measurement: Multidimensional examination of process performance (e.g., analyzing temporal dynamics at different granularity levels).
• Variant and bottleneck identification: By contrasting models derived from cube cells, analysts can detect localized inefficiencies, variant-rich behavior, and cross-object dependencies not observable in single-case analysis.

This multidimensional structural analysis provides a rigorous basis for targeted process improvements, audit, and compliance monitoring in heterogeneous environments.

5. Mathematical Formulation

Key formal definitions presented in the paper include:

Concept	Formula / Definition
Event Universe	$U_{event} = U_{ei} \times U_{vmap} \times U_{omap}$
Process Cube Structure	$PCS = (D, val, gran)$
Process Cube View	$PCV = (D_{sel}, sel)$
Cube Materialization	$M_{E, PCV} = \{ (c, events(c)) \mid c \in cells\}$
Slice op.	$$slice_{d, V}(PCV) = (D_{sel} \setminus \{d\}, sel')$$, $sel'(d) = \{V\}$
Dice op.	$dice_{fil}(PCV) = (D_{sel}, sel')$, $sel'(d) = fil(d)$ for $d$ in filter, $sel'(d) = sel(d)$ otherwise
Granularity change op.	$chgr_{d,G}(PCV) = (D_{sel}, sel')$, $sel'(d) = G$

Materialization selections for attributes require $\pi_{vmap}(e)(d) \in c(d)$; for object types: $c(d) \subseteq \pi_{omap}(e)(d)$.

These formalizations guarantee correct handling of multidimensional event data and enable compositional operations over both attributes and multi-object relations.

6. Practical Toolchains and Methodological Considerations

The process cube framework has been adopted in experimental tools and libraries (see (Ghahfarokhi et al., 2022) for a PM4PY-MDL based implementation), offering:

• Interactive, GUI-based exploration (e.g., Wizard interfaces permitting event and object attribute-driven cube construction).
• Materialization strategies, supporting user selection of "existence" versus "all" semantics in object property mapping.
• Visualization and direct model comparison (via side-by-side discovery and annotation of frequencies/performance indicators).
• Scalability studies evidencing quasi-linear complexity in the number of events/event attributes; non-linear in the number of object attributes due to event-object relationship multiplicity.

Applications of these tools to real SAP datasets confirm the suitability of the OCPM paradigm and process cube abstraction for industrial process analytics.

7. Impact and Advances Brought by Object-Centric Process Cubes

The OCPM process cube framework is a significant advancement in process mining, bridging the gap between multi-perspective event data and systematic process comparison. By lifting the restriction of single-case analysis and enabling formal, multidimensional partitioning, the approach supports:

• Richer, more faithful model discovery and performance diagnosis than traditional process mining,
• Comparative analysis across arbitrary, analyst-specified process dimensions,
• Integration with advanced process discovery techniques addressing the inherent complexity of enterprise-scale, object-intertwined workflows.

This paradigm is foundational for further innovations in process mining, supporting not only advanced analysis of current operational realities but also process redesign initiatives and continuous improvement frameworks for highly entangled business processes (Ghahfarokhi et al., 2021).