## 3 Method
### Problem Definition  
To give readers an insight into structured life narratives, we use [PERSON]'s life stories as an illustrative example. As we can see from Figure 2, the input is life stories from Mr. [PERSON], and the output is the corresponding structured life narrative. The event tree contains 15 nodes, where the _ROOT_ node represents the start of the event tree, \(T1\cdots T4\) nodes represent topic nodes with the form of \"time period: topic one, topic two\", and \(E1\cdots E10\) nodes represent event nodes under different topics with the form of \"time: summary\". Each event node is accompanied by the corresponding life stories. The link between topic nodes indicates a temporal topic evolution relationship. The link between event nodes indicates a temporal or logical event evolution relationship. As illustrated in Figure 2, there are four branches within [PERSON]'s life story hierarchies, where the branch path \(E1\cdots E2\) is about [PERSON]'s education experience, the branch path \(E3\cdots E4\) is about [PERSON]'s soldier experience, the branch path \(E5\cdots E7\) is about [PERSON]'s work experience in North Korea, and the branch path \(E8\cdots E10\) is [PERSON]'s life after his wife died. In addition, we mark each event node with a different color for different frequencies so that users can quickly distinguish them.  
This study aims to structure the life narratives of an older adult into an event tree format that aligns with the logical evolution of events. The event themes constitute the trunk of the event tree, and related events within the same theme are ordered chronologically and logically as branches. Hence, the formal problem description is as follows:  
The input consists of the life story narratives of an older adult, and the output is the corresponding event tree. Let \(d\) donate one life story document, and \(D=\{d_{1},d_{2},\ldots,d_{n}\}\) donate all life stories of one older adult. \(e_{i}\) is the event extracted from one life story \(d_{i}\). Compute event relevancy and, based on this, determine whether events within different story documents express the same event. If such a relation exists, consolidate them into a unified event node denoted as \(E\). Next, determine whether the amalgamated event nodes \(E\) are thematically cohesive, indicating that they are related to the same topic \(T\). If there is such coherence, cluster all relevant event nodes into a single topic. Finally, organize the topic nodes \(T\) and event nodes \(E\) into a hierarchical event tree structure based on chronological and logical sequences, which can be represented by \(\mathit{Tr}=\langle T\{E,Ed\},Td\rangle\), where \(T\) represents the theme nodes, \(Td\) represents the edges connecting the theme nodes, \(E\) represents the event nodes, and \(Ed\) represents the edges connecting the event nodes.  
The hierarchical structure of life narratives, which consists of themes, events, and detailed life stories, supports caregivers in grasping the life trajectory of older adults. It also enables them to delve into specific events, understanding the event details and developmental processes. This structure furnishes caregivers with the necessary data support and decision-making foundation to devise personalized care plans for older adults [33].  
Figure 2: An illustration of the input and output of the algorithm LSH-GEFR, where the input is life stories from the same person and the output is the corresponding life event tree. The event tree contains three types of nodes: the root node, the topic node, and the event node. Events are marked with different colors according to frequency to denote various meanings.