Process cubes are an advanced concept in the field of process mining, which extends traditional process mining by introducing multi-dimensional analysis. Traditional process mining techniques focus on extracting information from event logs, which store data about the workflow in an information system. These event logs contain information on the sequence of events (activities within a process), the context in which they occurred (resources, roles, timestamps), and sometimes associated outcomes or performance metrics.

In traditional process mining, the primary focus is on discovering, monitoring, and improving processes based on this event log data. The goal is often to create a process model that accurately represents the workflow captured in the event log, detect deviations from the model (conformance checking), and analyze the performance of the process (e.g., bottlenecks, throughput times).

However, traditional process mining approaches tend to work with a single, flat perspective of the process, typically ignoring the multitude of dimensions that can be present in complex business processes. Real-world processes usually have different variants and can be analyzed from multiple perspectives, such as organizational units, geographical locations, products, or customer segments. That's where process cubes come into play.

Process cubes extend the idea of data cubes used in Online Analytical Processing (OLAP) for multi-dimensional data analysis into the realm of process mining. A process cube allows the systematic exploration of process data along different dimensions and at various levels of aggregation. Each 'cell' within a process cube contains event data relevant to a specific combination of dimensions.

The role of process cubes in multi-dimensional process mining includes:

1. **Faceted Analysis**: Analysts can pivot or slice-and-dice the process cube to examine the process from different angles. For example, one might analyze the process for different product types or compare regional performance.

2. **Comparative Analysis**: Process cubes make it easy to compare different process variants side by side. For instance, users can compare the flow of cases in one country versus another, or for different customer segments.

3. **Aggregation/Drill-Down**: Analysts can view processes at different levels of granularity. They might look at the detailed flow of a single case or aggregate data to see high-level trends across thousands of cases.

4. **Temporal Analysis**: One can analyze how processes change over time by considering the time dimension. By analyzing different 'time slices' from the cube, one can spot seasonal patterns, trends, or drifts in the process.

In summary, process cubes differ from traditional process mining approaches mainly by enabling multi-dimensional exploration of process data. They facilitate more versatile and sophisticated analyses, capturing the complexity and variability of real-world processes that are typically not addressed in single-dimensional process mining. This can lead to richer insights and more informed decisions for process improvement and optimization efforts.