## 3 Methodology
### Topic Representation and Emerging Trend Analysis
#### 3.3.2 Emerging Trend Analysis  
The early identification of emerging signals and trends in the constantly evolving technology landscape of 6G represents a substantial challenge. By harnessing the concept of weak signals within the extracted topics, this study is dedicated to pinpointing technological topics currently garnering limited attention yet possessing substantial promise for future development. In the realm of 6G patent research, discerning the annual evolution of key technologies is pivotal for foreseeing industry advancements. After leveraging BERTopic to extract evolving topics from 6G patent data, we adopted the Topic Emergence Map (TEM) approach to analyze the emerging trends in the topic evolution. By visualizing each topic's signal state across different years as a heatmap, we can gain more intuitive insights into the development of 6G technology topics and detect emerging trends.  
In order to quantitatively extract future signals and make the result more interpretable, an early study [48] inspired us to employ topic proportions obtained from our time-aware dynamic topic modeling framework and use TEMs to identify future signs of emerging technologies in related 6G fields.  
The TEM is a valuable method for identifying future-oriented signals within research topics. Its underlying principle lies in recognizing that the early detection of emerging signals and trends is crucial in a rapidly evolving technological landscape. The TEM is constructed using two key dimensions. The _x-axis_ represents the average topic proportions derived from the BERTopic model, which reflects a topic's relative significance in the dataset at a given time frame. The _y-axis_, on the other hand, denotes the rate of increase in topic proportions, measuring how quickly a topic's importance changes over time. Based on the mean of the _x-axis_ values and a _y-axis_ value of zero, the TEM is partitioned into four quadrants: strong signals (high average proportion and high growth rate), weak signals (low average proportion but high growth rate), latent signals (low average proportion and low growth rate), and not strong but well-known (NSWK) signals (high average proportion and low growth rate).  
In order to utilize the TEM principle to create a heat map to analyze the evolution of 6G technology topics, a series of steps are involved. First, the 6G patent data, which have been processed with topics extracted by BERTopic, needs further processing. Each topic should be associated with its corresponding patent documents and timestamped according to the patent application year. Then, calculate the topic proportions for each year by dividing the number of patent documents of a specific topic in a year by the total number of patents in that year. Simultaneously, the rate of increase in topic proportions for consecutive years is determined. Afterward, a matrix with rows representing different 6G technology topics and columns representing different years is created. Color each cell in the matrix based on the topic's position in the TEM quadrant in the corresponding year. Finally, data visualization tools are employed to generate the heatmap. Observing the heatmap allows us to analyze the evolution of 6G technology topics, identify trends, and compare different topics in the same year, enabling a comprehensive understanding of the 6G technology landscape over time.  
We segmented the examined period into three-year intervals with one year overlapping to track the temporal evolution and changes in signal patterns. We refer to these intervals as \(\{pi\}\). TEMs were then built for each period, with a signal label assigned to each topic within the TEM across the examined periods.