A Two-Stage Variable-Scale Clustering Method for Brand Story Marketing of Time-Honored Enterprises

: Brand story, as a communication tool of brand's core values, is proven to be effective in building consumers' trust and loyalty. This paper focuses on the story's protagonist identification and story's audience segmentation problem of consumers' brand storytelling, so as to support managers making brand marketing decisions. After building the scale space signature that characterized the story feature, an object pair scale transformation mechanism (Object Pair-ST) is proposed, which enables to realize the collaborative transformation of the encoded scale feature of both story's protagonists and audiences. According to the Object Pair-ST mechanism, a two-stage variable-scale clustering method (Two-stage-VSC) is put forward. The method could obtain the matched story clues (including the elements of plots, characters, causality and chronology) for every audience cluster as well as the matching degree, which are ordered by the hotness degree of consumers' interest. Experiments collected 11877 real review data on the 2022 first sales platform of time-honored enterprises, Tmall. The comparative experimental results indicate that for various types of brands, the proposed method Two-stage-VSC could always keep the granular deviation of each audience cluster at a low level while accurately identifying its protagonist cluster's story clues with the highest matching degree.


INTRODUCTION
Stories move people more easily, which is no exception in the brand marketing scenarios [1].Considering the narrative modes of story's protagonists, brand stories are able to be classified into brand storytelling [2,3] and consumers' (brand) storytelling [4].The former mode refers to brands (firms) that tell their own stories (like the brand foundation story, CEO and spokesperson's story, history of brand successes or crises, etc.) them selves [5][6][7], while increasing empirical studies figure out that it was the latter mode that had great advantage of improving consumers' brand attitudes, because the story's audiences usually recognize those stories generated by other brand consumers as less biased [8,9].
With the continuous application of emerging digital techniques in the communication field, consumers are more easily to participate in spreading and sharing their brand stories [10].The impact factors on how brand story design should influence consumers' brand attitude are investigated widely.For instance, Ref. [11] shows that compared with underdog brand biographies, the top dog brand biographies could be more likely to enhance consumers' perceived competence.Ref. [12] illustrates that the theme of brand stories has a significant impact on consumers' brand attitude, and the story authenticity plays a mediating role.Ref. [8] further finds out that the relationship between story's protagonists (brand consumers) and story's audiences (target consumers) moderates the influence of story authenticity on brand attitude.
Moreover, time-honored enterprises pay much more attention on brand story marketing, owning to their longterm accumulation of brand history and cross-age customers [13,14].As intangible assets, traditional skills of time-honored enterprises naturally play a significant role on the intangible cultural protection [15].Their enterprise archives also record decades of social change, having great economic, cultural and even legal value, which jointly contribute to the development of the commercial civilization [16].
However, how to utilize the stories generated by consumers to improve the performance of brand marketing still poses many challenges to time-honored enterprises.On the one hand, dynamic audience interest could directly influence the communication effect of brand stories.On the other hand, how well the chosen story matches audience interest also determines consumers' brand attitude.
Therefore, this paper studies the story's protagonist identification and story's audience segmentation problem of consumers' brand storytelling.The main contributions of our research are summarized below: -In order to characterize the feature of brand stories, the scale space signature is established.Compared to the scale space model in Ref. [27], the proposed encoded scale space with signature is capable of mapping the hierarchical structure relationship between scales to the vector space.
-As for the relation between story's protagonists and audiences influences on the effect of brand story marketing, an object pair scale transformation mechanism (Object Pair-ST) is proposed, that enables to realize the collaborative transformation of the encoded scale feature of both protagonists and audiences, instead of the single object-focused transformation mechanismin Ref. [28][29][30].
-A two-stage variable-scale clustering method (Two-stage-VSC) is put forward based on the Object Pair-ST, which could obtain matched story clues for every audience cluster as well as the matching degree.
The paper is organized as follows.Section 2 presents relevant research works, including digital transformation of time-honored enterprises, brand story marketing and variable-scale data analysis methods.Section 3 is the main part methodology of our research.The experiment design and experimental results discussions are described in Section 4. The paper is concluded in detail in Section 5.

LITERATURE REVIEW 2.1 Digital Transformation of Time-Honored Enterprises
Digital transformation (DT) has aroused wide attention in both academic and industrial fields globally [17,18].After the thorough investigation in various business industries, the key activities of senior executives or IT& Digital leaders (who are responsible for helping enterprises transform their business models leveraging digital technologies), are mainly classified into four aspects, that is driving business change, adjusting organizational structures, mastering talent demands and prioritizing competency improvement [19,20].It can be seen that the chief digital officers (CDOs) need to handle not only the operational affairs but also the strategic changes during the whole DT process [21].
The time-honored enterprises, that are famous for their long history (established before 1956 [16]), encounter the dilemma of preservation and innovation during the DT process [13].Since most of the time-honored enterprises are not digital companies, how to apply digital technology to improve traditional business and even create new growth points earns the primary importance.
Although there is the predefined information system dedicated to enterprise business capability (EBC) that provides a technical solution to construct digital composable enterprises [22], how to achieve automatic business understanding accurately and effectively [23] using historical business data still limits its performance in time-honored enterprises.

Brand Story Marketing
With the continuous integration of advanced digital techniques in communication field, newly emerged brand story marketing scenarios, like consumers'storytelling and transmedia storytelling, play a more significant role in branding [24].Simultaneously, many time-honored enterprises tend to use digital techniques and data mining methods to assist the creation of their brand stories [13].
Several existing studies suggest that brand managers could indeed enhance consumers' experience through compelling and well-designed brand stories [25].And when story's audience (consumers) recognize the source in the incoming story is similar to themselves, it could imprint more positive brand image and even influence their buying decisions [8,26].
Therefore, those brand story feature and consumers' behaviours characteristics contribute to the establishment of our research model, that is the collaborative transformation of the encoded scale feature of both story's protagonists and audiences, in Section 3.

Variable-Scale Data Analysis Methods
In the perspective of both business managers and data specialists, the variable-scale data analysis theory (VSDA) provides a cross-industrial intelligent decision-making framework covering the whole life cycle of data mining projects [27], including automatic business understanding.Combined with the data understanding stage, the goal of business understanding stage is to clarify the data mining tasks, which are able to optimize the performance of current business activities or discover new business growth points.The scale space [28] is the bridge model that connects the decision-making hierarchies of both business managers and data specialists towards the same object.
What's more, data mining results evaluation is another stage that requires the participation of both business managers and data specialists [29].The granular deviation (GrD) is one of the evaluation indexes to measure the scale transformation effect.Taking the clustering task as an example, the GrD is defined as the knowledge granularity [31,32].G(ʋ/A λ ) divided by the intra-class deviation of each cluster, where ʋ represents the global object set and A λ represents the observation ruler (dimension).
Tab. 1 depicts the summary of the relevant literature compared with our research work, from the aspects of the scale space model, multi-scale data model, scale transformation mechanism and variable-scale data analysis method.Ref. [28] proposes the binary multi-scale data model and the relevant hybrid variable-scale clustering method (Hybrid-VSC), which solves the clustering problems with categorical structured data and text unstructured data.Ref. [29] combines the VSDA with the case-based reasoning theory, and puts forth the variablescale case-based reasoning method (VSCBR).It was the space variable-scale scheduling algorithm for the digital vehicle-to-grid platform (V2G-LST) proposed in Ref. [30] that firstly realizes the collaborative transformation of two observation scales (i.e., the space and time scale).
However, all the algorithms above only focus on the scale transformation of single types of objects, which is not suitable for the brand story marketing scenario with both story's protagonists and audiences.

Table 1 Summary of the relevant literature compared with our research work Variable-scale data analysis theory
The Hybrid-VSC method [28] The VSCBR method [29] The V2G-LST method [30] The proposed method

Radical and conservative scale transformation
Lightning-scale transformation

Object pair scale transformation
Variable-scale data analysis method The hybrid variable-scale clustering The variable-scale casebased reasoning The space variable-scale scheduling The two-stage variable-scale clustering

RESEARCH METHODS
As the variable-scale data analysis theory (VSDA) has the advantages in automatic business understanding for digital transformation from the enterprise side [22,27], as well as the behavioral feature segmentation from the consumer side [28], this section studies the brand story marketing problem based on the VSDA., the value space In general, a data mining task with over one thousand dimensions is regarded as a high-dimensional problem [23], the first three-digit of signature is allocated for the ruler representation.Since the appropriate management scale for humans is about seven [33], considering both business manager and data specialist have their own observation scales on the same dimension, the middle two-digit of signature is assigned for the scale representation.Similar to the ruler representation, the last three-digit of signature is allocated for the (scale) value representation.
For example, Fig. 1 shows a three-hierarchy encoded scale space model of A 1 .It can be seen that according to the scale space signature, the problem-solving space [34] of a decision problem could now be mapped to an eight-digit encoded vector space., , ..., x x x   are interpreted by its signature code.
Hence, object x i could be characterized as the scale feature Since the dynamic interest of story's audiences could directly influence the communication effect of brand stories (see Section 1), the hotness degree measurement is established in Def. 2.
Definition 2 (Hotness Degree): Given the story's audience binary multi-scale data model

 
, , , , the hotness degree of the audience cluster A i X is: where audience cluster , and X represents the number of objects What's more, the other challenges for time-honored enterprises implementing brand story marketing in Section 1 show that, how well the chosen story matches audience interest also determines consumers' brand attitude.Therefore, the matching degree is proposed (see Def.
  1, if atl east one value of under is 1 0, if all values of under equal to 0 where protagonist cluster is the cluster center of audience cluster is the scale feature (signature) vector of , is the number of signature in vector A i x .
Algorithm 1 Two-Stage Variable-scale Clustering (Audience − BD S , Protagonist − BD S , SS, α) // Audience − BD S is the binary multi-scale data model of audiences (target consumers), Protagonist − BD S is the encoded multi-scale data model of story's protagonists (brand consumers), SS is the scale space of observation dimension, α is the similarity threshold.
Step 1: Consumers segmentation using the binary variable-scale clustering algorithm on Audience − BD S , and obtaining the satisfied audience clusters   A j X j N   with the GrD and scale feature.
Step 2: Establish the scale feature (signature) vector of all the audience cluster centers and calculate the hotness degree

 
A j HD X of each cluster via Eq.( 1).
Step 3: Identify the cluster A i X with the highest hotness degree of the current audience set, and compare every signature in scale feature vector A Step 4: Calculate the similarity of A i x to all the story's protagonists through dividing the sum of the kth row in Protagonist − BD S by the total number of audience scale feature signatures Step 5: Take all the protagonists whose similarity value is larger than α as the matched story's protagonist cluster P i X for the audience cluster , and calculate the matching degree MD X X via Eq.( 2) and Eq. ( 3).Also, delete all the objects in cluster A i X from the audience set.Step 6: If there are still objects left in the audience set, go to Step 3; otherwise, go to Step 7.
Step 7: Output clustering results, including the GrD and scale feature of all the audience clusters, accompanied by the matched story's protagonist clusters and their hotness degree, scale up transformed feature (which is decoded to the text state by SS) as well as matching degree.Since the relationship between story's protagonists and audiences influences the branding effect, an object pair scale transformation mechanism (Object Pair-ST) is proposed based on the scale space signature (see Fig. 2).
After establishing the scale feature vector of all audience clusters and placing them in the descending order of their hotness degree, the collaborative scale transformation process is activated.If absolute value of the signature difference The time complexity of the Two-stage-VSC is O(tφ), where t is the time complexity of the meta clustering method, φ = min(m, s r ), r is the number of observation rulers and s is the maximum number of scale values in one ruler.

RESULTS AND DISCUSSION 4.1 Experiment Design and Data Collection
According to the consumption innovation report of intangible cultural heritage released by Aliresearch [35], there are 1128 officially recognized Chinatime-honored enterprises in total, which are distributed in various industries, such as the medicine, clothing, liquor, food, daily necessities etc.Over 70% of time-honored enterprises have been included in the national or local intangible cultural heritage list.Moreover, Tmall became the first sales platform for time-honored enterprises in the year 2022, whose turnover jointly exceeded 30 billion yuan.Among them, there were thirty-eight time-honored brands whose platform turnover reached100 million.
Experiments in this section aim to verify the accuracy and efficiency of the proposed two-stage variable-scale clustering method (Two-stage-VSC) in the brand story marketing scenarios of time-honored enterprises.
We collect 11877 real raw review data of the top-selling products from four typical time-honored enterprises (that is Tongrentang, Pientzehuang, Hengyuanxiang and Yanghe) on Tmall platform during Jan 1, 2022 to Oct 31, 2022.These four enterprises are respectively in different industries (i.e., medicine, beauty, clothing and liquor), which provide crucial data foundation to explore the influence of brand types for the proposed method.All four enterprises are in the top 20 brands by the platform turnover (more than 100 million yuan).
During the data preprocessing, we set the minimum review word count to ten, so as to filter spam comments and invalid information, and obtain 4010 qualified data for further experiments.The experimental results were obtained on a personal computer with Intel Core i5 CPU @2.9 GHz and 8 GB RAM.The aroma is more elegant and delicate than others; I felt sweet after a sip awhile and enjoyed a lot. 1.000

Experiment Results and Discussion
Tab. 3 to Tab. 6 shows the experimental results of our proposed method Two-stage-VSC on four types of timehonored enterprises.The medicine brand Tongrentang results in Tab. 3 depict that there are five satisfied object pair <Story's protagonists, Audiences>divided by the twostage variable-scale clustering method.Most of the audience consumers are interested in the "effect, two courses of treatment, sixty pills at a time, no alcohol, repurchase", earning the highest hotness degree 1.000.
According to audience interest, the Two-stage-VSC efficiently identifies matched story clues (whose matching degree exceeds 80%) following the Object Pair-ST mechanism, such as scaling up the concept hierarchy to the usage and dosage level.
Tab. 4 shows the experimental results of Pientzehuang's beauty brand.It can be seen that the object pair  It can be seen that the GrD of all audience clusters is less than a relatively low level 2.2, indicating that the proposed method Two-stage-VSC is able to accurately divide similar objects and accomplish the audience segmentation.At the same time, over 85% of audience clusters' matching degree exceed 0.600, which demonstrates that the Two-stage-VSC could efficiently identity the most matching story clues for each audience cluster.

CONCLUSIONS
We address the story's protagonist identification and audience segmentation problem for brand story marketing based on the variable-scale data analysis.The research starts from the study of scale space signature considering the appropriate management scale for humans with the aim to map the hierarchical problem-solving space of a decision problem to a computable vector space.
The solution framework proposed in our research is to establish the collaborative transformation of the encoded scale feature of object pairs < story's protagonists, audiences>.An object pair scale transformation mechanism (Object Pair-ST) is proposed based on the scale space signature.As a novelty, the Object Pair-ST improves the original single object-focused scale transformation modes (i.e., the generalized scale transformation) to a hybrid bidirectional approach.Finally, a two-stage variable-scale clustering method (Two-stage-VSC) is put forth on consumers' storytelling, considering the hotness degree of consumers' interest.The accuracy and efficiency of the proposed Two-stage-VSC method is verified by 11877 real review data from the first sales platform Tmall.Comparative experimental results indicate that for various types of brands, the proposed method Two-stage-VSC could always keep the granular deviation of each audience cluster at a low level while identifying its protagonist cluster's story clues with the highest matching degree.
Our future work will establish the verification mechanism of the encoded scale space model to judge whether the newly established or updated scale space reaches theoretical saturation.

Definition 1 (
Scale space signature): Given a scale space model r A of observation ruler (dimension), A r the signature of one scale value r sp V in r A is a digital position code following the order of ruler-scale-value, i.e.,

Figure 1
Figure 1 Example of the encoded scale space model Tab. 1 further depicts the encoded binary multi-scale data model 3).Definition 3 (Matching Degree): Given the story's protagonist encoded binary multi-scale data model

1 :
If the absolute value of the difference between one  and a signature of A i x  is equal to 0, keep the values of all story's protagonists under A r in Protagonist − BD S the same.Step 3.2: If the absolute value of the difference set the values of all the story's protagonists under A r in Protagonist − BD S to 0of all story's protagonists under A r in Protagonist − BD S the same.

Figure 2
Figure 2The mechanism of the object pair scale transformation (Object Pair-ST)


keep the values of all story's protagonists under observation ruler A r the same; if the absolute value exceeds 10 5 , set the values of all the story's protagonists under A r to 0; Otherwise, scale up r sp V following the scale space model until the absolute value of signature difference reaches 0.According to the basic idea of the object pair scale transformation, a two-stage variable-scale clustering method (Two-stage-VSC) is put forward, shown in Algorithm 1.The first stage of the Two-stage-VSC is the audience segmentation, and the second stage is the protagonist identification through the Object Pair-ST.

800 Figure 3
Figure 3 Comparative experimental results on differentiate time-horoned enterprises

Fig. 3
describes the comparative experimental results on all the object pairs of four time-honored enterprises.The black broken line represents the granular deviation (GrD); the height of rectangles represents the matching degree (MD); the color of rectangles represents the hotness degree (HD), where red is g., .

Table 2
Example of the encoded binary multi-scale data model

Table 3
Experiment results of the Two-stage-VSC method on themedicine brand Tongrentang

Table 4
Experiment results of the Two-stage-VSC method on the beauty brand Pientzehuang

Table 5
Experiment results of the Two-stage-VSC method on the clothing brand Hengyuanxiang

Table 6
Experiment results of the Two-stage-VSC method on the liquor brand Yanghe