# Discovering Moving Flock Patterns in Movement Data: A Reeb Graph-Based Approach
## 3 Taxonomy of Flock Patterns  
While existing definitions and methods have enhanced the discovery of flock patterns in movement data, classifications of flock patterns remain fragmented. Hence, establishing a comprehensive taxonomy of flock patterns is essential. In this paper, we develop a taxonomy of flock patterns based on the definitions of flock and moving flock introduced in Section 2. To the best of our knowledge, this is the first attempt to systematically categorize flock patterns in this way.  
The taxonomy is primarily developed using the four parameters discussed in Section 2 (i.e., \(r\), \(m\), \(k\), \(d\)). Here, \(r\) identifies group members that are spatially close within a flock, and \(m\) determines the required number of group members. Together, \(r\) and \(m\) form the \"number of members\" factor. \(k\) represents the \"time duration\" factor, while \(d\) distinguishes between a stationary flock and a moving flock, making it the \"displacement\" factor. For the \"number of members\" factor, values can be the minimum, the maximum, or intermediate. Similarly, for the \"time duration\" factor, values can be the shortest, the longest, or intermediate. Thus, each of these two factors has three possible values. For the \"displacement\" factor, values have two cases: smaller than a predefined distance threshold, or not smaller than a predefined distance threshold. Based on the value cases for all three factors, 18 (i.e., 3 \(\times\) 3 \(\times\) 2) types of flock patterns can be derived. The classification of the 18 types of flock patterns within the developed taxonomy is shown in Table 1. Among them, nine types (types 2, 4, 6, 8, 10, 12, 14, 16, and 18) represent moving flock patterns, while the remaining nine denote stationary flock patterns. Given that our primary objective is to discover moving flock patterns, we focus on these nine types of moving flock patterns.  
Figure 1: Illustration of the spatial extent of a flock over two consecutive timestamps.  
Theoretically, each of the nine types of moving flock patterns has distinct significance, and different types may attract different levels of interest. However, in practice, not all types of moving flock patterns are equally interesting. In particular, those patterns where factors assume extreme values, such as the smallest/largest number of members and the shortest/longest time duration, may be of greater interest. Among the nine types in Table 1, only four types (types 2, 6, 14, and 18) fulfill these criteria. Therefore, this paper focuses specifically on these four types of moving flock patterns, which we label as types A, B, C, and D, respectively. An overview of these four types and their corresponding interpretations is provided in Table 2. Each type may indicate a distinct and valuable movement behavior in practical scenarios, with type A generally occurring most frequently, types B and C at intermediate frequencies, and type D least frequently. Due to its unique characteristics, type D may be undetectable in many instances; however, we still include it in our analysis as it can be detected under certain conditions.