Process Cubes, introduced by Wil van der Aalst and his colleagues, play a significant role in multi-dimensional process mining, providing a novel way to analyze event data and gain insights into organizational processes. Here's how they differ from traditional process mining approaches:

1. **Data Structure**:
   - Traditional Process Mining: In classical process mining, the focus is on event data structured as cases (process instances) with activities as their primary dimension.
   - Process Cubes: Introduce a multi-dimensional perspective by considering not only activities but also resources, time, and other relevant dimensions like data attributes. This leads to a cube-shaped data structure, where each cell represents a specific combination of these dimensions.

2. **Focus on Data Dimensions**:
   - Traditional Process Mining: Primarily focuses on the control-flow dimension, i.e., the order in which activities occur.
   - Process Cubes: Emphasize the interdependencies among various dimensions. For example, you can analyze how resources interact with each other while performing tasks (social dimension), or how certain data values influence the process flow (data dimension).

3. **Analysis Capabilities**:
   - Traditional Process Mining: Tools like Petri nets and BPMN can model and analyze control-flow patterns but may struggle to incorporate social and data dimensions effectively.
   - Process Cubes: Enable more comprehensive analysis by supporting various types of cubes, such as:
     - Control-Flow Cube (like classical process mining)
     - Social Cube (focusing on resource interactions)
     - Data Cube (examining the impact of data attributes)
     - Time Cube (studying temporal aspects)

4. **Visualization and Aggregation**:
   - Traditional Process Mining: Visualizations like process trees, Petri nets, or BPMN diagrams focus on activities and control flow.
   - Process Cubes: Utilize 3D visualizations to represent the multi-dimensional data structure, enabling users to explore and aggregate information along different dimensions more intuitively.

5. **Application Scope**:
   - Traditional Process Mining: Primarily applied in business process management (BPM) for optimizing internal workflows.
   - Process Cubes: Applicable across various domains where multi-dimensional analysis is beneficial, such as healthcare processes, supply chain networks, or customer interaction analyses.

In summary, while traditional process mining approaches focus mainly on control-flow dimensions, Process Cubes expand the scope by incorporating multiple dimensions, providing a more holistic view of organizational processes and enabling advanced analytical capabilities.