## 2 Preliminaries and Literature Review
### Plot Analysis Based on Character Networks
[32] and [PERSON] and [PERSON] [18] have proposed methods for segmenting movies into narrative units in multiple layers (shots \(\in\) scenes \(\in\) substories). They aimed to compose sub-stories as a set of scenes that contains scenes describing related events. Thus, the'sub-story' is conceptually the same as story lines in this study (main plots or subplots). From scenes to story lines, they applied the hidden Markov model, which has occurrences of characters in each scene as observations and story lines containing the scene as hidden states. This approach was applied to discovering scenes likewise. Nevertheless, scenes in a story line do not always have identical occurrence distributions of characters. Subsequently, [PERSON] and [PERSON] [18] summarized movies by applying a top-down selection for entities on the three-layered structure according to the significance of the entities. They measured the significance with three criteria: (i) The number of characters that appeared in an entity, (ii) the number of main characters among the appeared characters, and (iii) the number of dialogues spoken by the main characters. [PERSON] [20] applied the time-sequential characteristics of stories on identifying story lines in TV series. They assumed that social relationships between characters have consistent tendencies in a story line. From this assumption, they proposed two measurements for the persistence and anticipation of social relationships. The two measurements were estimated based on (i) out-degrees of main characters and (ii) proximity between the main characters. They detected transitions between story lines by using changes in the measurements. However, in narrative multimedia, fragments of story lines are located alternatively. Thus, to decompose plot structures, we also need to reassemble story lines by combining the fragments. [PERSON] and [PERSON] [10] decomposed plot structures by using structural changes in character networks. They applied interactions on each scene to measure relevancy between events described in the scenes. By embedding character networks on each scene (e.g., \(N(s_{a,l})\)), they calculated 'narrative relevancy' between \(s_{a,i}\) and \(s_{a,j}\) based on similarity between vector representations of \(N(s_{a,i})\) and \(N(s_{a,j})\). Then, story lines were obtained by clustering scenes according to narrative relevancy. In addition, to discover main plots and major events, they measured the significance of scenes. Similar to the study of [PERSON] and [PERSON] [6], they measured the 'narrative significance' of each scene based on how much the scene changes relationships between characters. The narrative significance of \(N(s_{a,l})\) was measured by comparing \(\sum_{i=1}^{l}N(s_{a,i})\) and \(\sum_{i=1}^{l-1}N(s_{a,i})\) by embedding them. Although [PERSON] and [PERSON] [10] presented only theoretical models, [PERSON] [11] exhibited the efficacy of this approach with real movies. However, as [PERSON] et al. [16] discussed, there studies commonly ignore that relationships between characters significantly change around major events (especially climaxes). Furthermore, the compositions of characters in each story line are not always consistent. For example, in the movie 'The Godfather' (1972), even its protagonist, '[PERSON]', did not appear in many scenes that are in its main plot. To solve this issue, we propose methods for modeling gradual changes in character personalities and applying the changes for decomposing plot structures.