INFORMATICA Informatica 1822-88440868-49520868-4952 Vilnius University INFOR554 10.15388/24-INFOR554 Research Article A Temporal Variable-Scale Clustering Method on Feature Identification for Policy Public-Opinion Management WangAib2113131@ustb.edu.cn1∗

A. Wang received her PhD degree in 2021 in management science and engineering and she is currently an associate professor in the School of Humanities and Social Science at University of Science and Technology Beijing, China. She has published papers in respected journals like Future Generation Computer Systems, Applied Soft Computing, Studies in Informatics and Control. Her research interests focus on data mining, intelligent decision making, as well as emergency management.

 GaoXuedonggaoxuedong@manage.ustb.edu.cn2

X. Gao received his bachelor degree from Nankai University, China, in 1983, and the PhD degree from Belarusian State University in 1993. He is currently a professor in the Department of Management Science and Engineering, School of Economics and Management at University of Science and Technology Beijing, China. His research interests include management process optimization, data mining, intelligent decision making.

 TangMincongmincongtang@iuh.edu.vn3

M. Tang graduated from The Chinese University of Hong Kong in 2011 with a PhD in management information systems. His main research areas include information management and systems, artificial intelligence, modelling and simulation in operations and transportation. Dr. Tang currently serves as an editor for several journals, including the International Journal of Computers Communications and Control, International Journal of RF Technologies, Journal of Computing and Information Technology. He has previously worked as a researcher at the International Research Center for Informatics Research at Beijing Jiaotong University and is now a chair professor at Xuzhou University of Technology, visiting professor at the Industrial University of Ho Chi Minh City in Vietnam. His research has been published in numerous international journals, including IEEE Transactions on Fuzzy Systems, IEEE Transactions on Consumer Electronics, Eletronic Markets, Advances in Production Engineering and Management, Information Technology and Management, Information and Management, Journal of Applied Research and Technology, International Journal of Computers, Communications and Control, Studies in Informatics and Control, Applied Soft Computing, Future Generation Computer Systems.

 University of Science and Technology Beijing, Beijing 100083, China School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China Industrial University of Ho Chi Minh City, Vietnam Corresponding author. 202426420243536716861202442024 © 2024 Vilnius University2024 Open access article under the CC BY license.

The development of various digital social network platforms has caused public opinion to play an increasingly important role in the policy making process. However, due to the fact that public opinion hotspots usually change rapidly (such as the phenomenon of public opinion inversion), both the behaviour feature and demand feature of netizens included in the public opinion often vary over time. Therefore, this paper focuses on the feature identification problem of public opinion simultaneously considering the multiple observation time intervals and key time points, in order to support the management of policy-focused online public opinion. According to the variable-scale data analysis theory, the temporal scale space model is established to describe candidate temporal observation scales, which are organized following the time points of relevant policy promulgation (policy time points). After proposing the multi-scale temporal data model, a temporal variable-scale clustering method (T-VSC) is put forward. Compared to the traditional numerical variable-scale clustering method, the proposed T-VSC enables to combine the subjective attention of decision-makers and objective timeliness of public opinion data together during the scale transformation process. The case study collects 48552 raw public opinion data on the double-reduction education policy from Sina Weibo platform during Jan 2023 to Nov 2023. Experimental results indicate that the proposed T-VSC method could divide netizens that participate in the dissemination of policy-focused public opinion into clusters with low behavioural granularity deviation on the satisfied observation time scales, and identify the differentiated demand feature of each netizen cluster at policy time points, which could be applied to build the timely and efficient digital public dialogue mechanism.

 public opinion variable-scale clustering education policy temporal observation scale Introduction

As AI technology has created more attractive application scenarios in the social network domain (Leung, 2023; August et al., 2020), not only the number of netizens but also their activity on multiple digital platforms has increased rapidly (Kuo et al., 2021). That is followed by the emergence of a large amount of online public opinion events, widely disseminated across different platforms (Akhter et al., 2021). On the one hand, online public opinion plays a significant role on the policy making process, since it contains lots of valuable netizens’ demand and attitude information (Xiao and Wong-On-Wing, 2021; Li et al., 2022b; Lili et al., 2020). On the other hand, sometimes the policy itself will also cause heated discussion of online public opinions, that is defined as the policy(-focused) public opinion (Wang et al., 2019).

Moreover, the phenomena of public opinion inversion has aroused wide attention in both academic and industrial fields (Yuan et al., 2017; Tan and Hua, 2019). The public opinion inversion refers to netizens’ attitude, emotions or points of view quickly reversed in the opposite direction over time (Zhang et al., 2023; Yang, 2023), which is proved to be the result of the synergistic evolution between multiple subjects in the dissemination of public opinion (Zhao et al., 2023; Ai et al., 2023; Zhu, 2023). It can be seen that the time attribute is an important dimension in observing the state of public opinion, while different observation time intervals (temporal scales) might lead to obtain different netizens’ features. In particular, for the policy-focused public opinion, some key observation time points, like the promulgation time of relevant policies, have a more significant impact on public opinion. Therefore, in order to manage online public opinion, it is crucial to timely and accurately identify netizens’ features following dynamic observation time.

The variable-scale data analysis theory (VSDA) (Wang and Gao, 2022) is used to study the influence of different types of observation scales on decision-making results, by simulating the scale transformation process of decision makers. The framework of VSDA could be classified into main three stages. Firstly, select a single scale data set for scale transformation from the multi-scale data model. Then (taking the clustering data analysis task as an example) perform the cluster analysis on the current single scale data model, and evaluate the satisfaction of the clustering results. Finally, iteratively adjust the observation scale of single scale data model according to the evaluation results, until all the divided clusters meet the satisfaction standard of management scenarios (Wang and Gao, 2021a).

Since different data types (such as spatial data (Radosevic et al., 2023), numerical data (Wang and Wang, 2021), categorical data (Lee and Jung, 2021), binary data (Shati et al., 2023), etc.) are suitable for different data structures, the structure representation model of different observation scales in the VSDA (i.e. the scale space model) also has different connection modes between multiple scale hierarchies (Wang and Gao, 2022). Although Wang and Gao (2021b) propose a variable-scale dynamic clustering method that is capable of describing the timeliness characteristics of time-related observation scales (like the material inventory data of aerospace project), its numerical scale space model could only reflect the single perspective that the latest period data provides more significance during the decision-making process. It is unable to meet the jointly observation requirements of multiple time intervals and key time points on the management of policy-focused public opinion.

Therefore, this paper studies the feature identification problem of public opinion considering the multiple observation time intervals and policy time points simultaneously, based on the variable-scale data analysis theory. The main contributions of our research are summarized as follows:

In order to characterize the multi-level analysis requirements of time dimensions for the policy-focused public opinion management, the temporal scale space model is established to describe all the candidate temporal observation scales, which are organized following the time points of relevant policy promulgation (policy time points).

According to the proposed temporal scale space model above, the multi-scale temporal data model is established to represent netizens’ different behaviours in the dissemination of public opinion under every temporal observation scale, instead of just keeping one maximum value of the original time series in the research work (Wang and Gao, 2021b).

A temporal variable-scale clustering method (T-VSC) is put forward. Compared to the traditional variable-scale dynamic clustering method for numerical data, the proposed T-VSC enables to combine the subjective attention of decision-makers and objective timeliness of public opinion data together during the scale transformation process for netizens’ demand feature identification.

The paper is organized as follows. Section 2 introduces the previous research works, including public opinion management and variable-scale clustering methods. Section 3 presents the main part methodology of our research in detail. A case study on the real public opinion dataset of the double-reduction education policy is described in Section 4. The paper is concluded in the last Section.

 Literature Review Public Opinion Management

Online public opinion has gained wide attention not only in the policy-making process of governmental departments (Li, 2021; Awad et al., 2020), but also in optimizing strategic decisions of enterprises in various industries (Fortin and Cimon-Morin, 2023; Rogowski, 2023; Krause and Gahn, 2023). Due to the diversity of participants in public opinion discussion and the complexity of information dissemination channels, an efficient identification of netizens’ features becomes one of the key factors to manage public opinion (Ma et al., 2023). Previous research works mainly focus on two aspects: the identification of netizens’ demand and behaviour features.

As for the demand feature identification, Yang (2024) puts forward a theme clustering algorithm to obtain the theme portraits of public opinion on sudden public events. He (2023) proposes a short text mining algorithm to analyse netizens’ attitude and emotion through online public opinion. Meanwhile, for the behaviour feature identification, Lv et al. (2023) puts forth the speech behaviour classification algorithm for analysing the development tendency of public opinion. However, most of the research above observes netizens’ features only at the most recent fixed time interval (fixed temporal scale).

When making the management decisions on the policy-focused public opinion, it is necessary to consider not only the objective timeliness of public opinion data, but also the subjective attention of decision makers at special time points, like the promulgation of relevant policies (Zhang and He, 2023). Hence, this paper studies the feature identification problem of public opinion under a variable-scale observation perspective on the time dimension.

 Variable-Scale Clustering Methods

Decision hierarchy transformation is the most significant thinking feature of intelligent decision analysis, as well as one of the important ways to realize data granulation in the data space (Liu and Zhang, 2019; Leng et al., 2018). The variable scale data analysis theory (VSDA) establishes an automatic data analysis hierarchy (observation scale) transformation mechanism by simulating the decision analysis hierarchy transformation process of managers, so as to achieve the balance between the quality and efficiency of data analysis in the decision process (Wang et al., 2020).

As the time dimension is one of the most commonly utilized observation rulers for decision analysis process in both business and policy-making scenarios, previous studies build various scale space models with different characteristics to describe the time-related data observation scales for differentiated management demands.

Numerical scale space model of dimension (observation ruler) A λ .

For instance, considering the versatile materials inventory management context of aerospace project, Wang and Gao (2021b) propose the numerical scale space model (see Fig. 1) to represent the data feature that the latest period data earns more significance on the decision-making process, including the purchasing cycle, demand quantity, cost of sales observation ruler, etc. Fig. 1 depicts that with the increase of the time interval observation scales in the concept chain, the number of data observation scale value decreases gradually, which causes the value space to appear as a unimodal state of aggregation towards the nearest time point t n . Table 1 further shows the maximum data value of different types of material objects under the multiple observation scales, based on the numerical scale space model in Fig. 1, i.e. the numerical multi-scale data model. It can be seen that material objects could be divided into a smaller number of equivalence classes, following the scale up transformation of one observation ruler.

Multi-scale numerical data model.

Furthermore, Wang et al. (2022) also study the space-time scale transformation problem on the charging and discharging behaviours of electric vehicle owners for the digital vehicle-to-grid (V2G) platform. Taking EV owners’ different short-term demand response time intervals as temporal observation scales, as well as taking the distance intervals between EV owners to the target public charging pile at the V2G demand release time point as spatial observation scales, the space-time scale space model is established, where the value space shows the number of responses EV users provide under the fixed time and space observation scale. Although the space-time scale space model has paid attention to the importance of key time point and multiple time intervals when making scheduling strategies on EV owners, only one demand release time point is taken into consideration.

Therefore, this paper studies the netizens’ feature identification problem for public opinion management based on the variable-scale data analysis, under both of the observation requirements on the data timeliness, as well as key time points.

 Research Methods

Since the variable-scale data analysis theory (VSDA) has the advantage of modelling the multi-level decision analysis needs (Wang et al., 2022), this section studies the feature identification problem of policy-focused public opinion while considering different types of data.

In order to describe the relation between multiple observation time intervals and key time points simultaneously, the temporal scale space model is established in Definition 1.

(<italic>Temporal scale space model</italic>)<italic>.</italic>

Given a time series TS = ( v t 1 , v t 2 , … , v t n ) of observation ruler (dimension) A λ , and v t represents the value at time t, the temporal scale space model of A λ is Temporal-, where the concept chain C C = { CH k λ | 0 ⩽ k ⩽ m } and CH k λ is the kth observation scale of A λ , the value space VS = { V k t λ | V k t λ = f ( v ( t − k ) : ( t + k ) ) ∧ ( k + 1 ⩽ t ⩽ n − k ) }, if t is the policy time point (Observation time point); otherwise, V k t λ = f ( v ( t − k ) : t ) ∧ ( k + 1 ⩽ t ⩽ n ), f is the maximum information function, i.e. f ( v ( t − k ) : ( t + k ) ) means get the maximum value of TS in the time window [ t − k , t + k ].

According to Definition 1, the temporal scale space model has the following properties: (1) The lower level temporal observation scale in the concept chain is partially ordered at the higher level scale; (2) The scale values in value space follow the partial order relationship between the scale hierarchies to which they belong.

Taking the public opinion on the double-reduction education policy as an example, the data collection process is shown in Section 4.1 in detail. Since there was an influential double-reduction relevant policy promulgated in March 2023, the above policy time point gains more attention from policymakers and the public. Moreover, combining the data timeliness requirement (that the latest period data earns more significance on the decision-making process, Wang and Gao, 2021b), March and November are the two key observation time points for netizens’ feature identification. Hence, according to the Definition 1, the temporal scale space model could be built (see Fig. 2). It can be seen that with the increase of the time observation scale, the number of observation scale value in the value space becomes smaller and gathers two key points towards Mar. and Nov., showing a double-peak pattern.

Example: The temporal scale space model.

According to the construction procedures of traditional scale space model (Wang and Gao, 2022), the temporal scale space model could be built mainly through three stages below.

On the first stage, determine all the candidate temporal scale hierarchies (time intervals) and clarify the key time points for the specific management scenario. For example, the basic (lowest) observation scale CH 0 λ in Fig. 2 is equal to the initial monthly interval in the double-reduction education policy case, while the adjacent higher scale CH 1 λ means the last two months.

On the second stage, correlate scale values according to the scale hierarchies from low to high, and follow the order of key time points within the same scale level, which could be broken down into three steps. (1) Extract the maximum value within the observation time interval at the latest time point, that is November in Fig. 2. (2) Extract the maximum value within the observation time interval at other key time points in a chronological order from far to near, that is March in Fig. 2. (3) Extract the maximum value within the observation time interval of the remaining time points in a chronological order from near to far.

At the last stage, reduce the current temporal scale space model from the high scale hierarchy to the low level, until its peak number is the same as the number of key time points.

Compared to the traditional numerical scale space model in the research of Wang and Gao (2021b), the proposed temporal scale space model keeps the scale hierarchies of the latest observation time intervals, while also emphasizes the influence of policy time points on netizens’ participation behaviour in the public opinion dissemination, which provides a kind of problem-solving space (Allen and Simon, 1972) for the subsequent variable scale data analysis process.

After establishing the temporal scale space model, the multi-scale temporal data model is proposed in Definition 2, in order to comprehensively present various netizens’ behaviour in the dissemination of public opinion under every temporal observation scale.

(<italic>Multi-scale temporal data model</italic>)<italic>.</italic>

Let Temporal- D S = ( U , A S , V S , f ) represent the multi-scale temporal data model, where U = { x 1 , x 2 , … , x p } is the object set (universe), A S = { A 1 , A 2 , … , A r } represents the observation attribute (observation ruler) set, where at least one attribute within A S has multiple temporal scales in its temporal scale space, i.e. ∃ A λ , C C ( A λ ) = ⟨ CH 0 λ , CH 1 λ , … , CH m λ ⟩ ( A λ ∈ A S ), f : U × A S → V S is the information function, and V S ∈ VS ( A λ ) , A λ ∈ A S .

Hence, compared to the traditional multi-scale numerical data model in Table 1, the multi-scale temporal data model could represent netizens’ different behaviour under every temporal observation scale (like the various behaviour features V 0 i λ ( i = 1 , 2 , … , 11 ) on the basic observation scale CH 0 λ in Fig. 2), instead of just keeping one maximum value of the original time series.

According to the temporal scale space model (Temporal-) and multi-scale temporal data model (Temporal- D S ), the mechanism of the temporal scale transformation (Temporal-ST) is proposed in Fig. 3.

The mechanism of the temporal scale transformation (Temporal-ST).

Temporal variable-scale clustering (policy time points, Temporal-, Temporal- D S , initial evaluation dimension A λ , public opinion content set) // Temporal- D S = ( U , A S , V S , f ) is the multi-scale temporal data model of all the netizens; Temporal- ( A λ ∈ A S ) are the temporal scale space model of netizens’ behaviour observation rulers (while the data collection process is shown in Section 4.1 in detail).

In order to achieve the public opinion management for different types of netizens, the temporal scale transformation mechanism starts with the initial clustering process on the basic temporal scale of Temporal- D S , which aims to obtain netizen clusters with similar behaviour feature. The measurement granular deviation GrD (see Eq. (1)) is utilized to evaluate whether the scale feature of each cluster satisfies decision requirements. According to the variable-scale data analysis theory (see Section 2.2), the satisfaction judgement standard of granular deviation is specified as the maximum granular deviation value of initial qualified clusters which are determined by decision makers. Hence, all the clusters with larger granular deviation are unqualified clusters and need further scale transformation.

For the scale transformation process, such as improving the scale hierarchy from the lower level to higher level, let different observation values of qualified objects’ equivalence classes on the target level be the equivalent interval (Wang and Gao, 2022) and replace it with the intermediate value. And then iteratively perform clustering for the remaining objects based on the Temporal-.

According to the temporal scale transformation mechanism Temporal-ST, a temporal variable-scale clustering method (T-VSC) is put forward, and the calculation steps are shown in Algorithm 1.

The time complexity of the method T-VSC is O ( t ( φ + p ) ), where t is the time complexity of the meta clustering method, φ = min ( p , m r ), p is the number of netizens, r is the number of observation rulers of netizens’ behaviour and m is the maximum number of temporal scale hierarchies in one ruler.

 Results and Discussion Experiment Design and Data Collection

The double-reduction policy, that aims to reduce students’ homework burden and off-campus training burden, has attracted wide attention since it was first put forward in July 2021 (Li et al., 2022a). Several new social phenomena caused by the implementation process of the double-reduction policy has become hot topics of online public opinion. Timely and accurately identifying the core demands of different types of netizens through online public opinion could support policymaking in the next stage.

Numerical experiments in this section aim to verify the effectiveness of the proposed temporal variable-scale clustering method (T-VSC) on the feature identification scenarios for the policy public opinion management.

Since the year 2023 is a crucial phase for the implementation of the double-reduction education policy, we collect relevant public opinion data from January 2023 to November 2023 from the Sina Weibo social network platform on the monthly basic observation scale, and obtain a total of 48552 raw data.

In order to reflect the behaviour feature of netizens, the frequency of original content publishing ( A 1 ), frequency of forwarding and commenting ( A 2 ), as well as frequency of being liked ( A 3 ) are taken as observation rulers. For the temporal scale space model of each observation ruler, the temporal observation scale CH 0 1 , CH 1 1 and CH 2 1 are, respectively, the latest one month, the latest two months, the latest three months. March is the first policy time point t I due to the promulgation of the double-reduction related policy. Moreover, considering the data timeliness requirement, the last month November is regarded as the second observation time point t II .

 Experiment Results and Discussion

According to the temporal variable-scale clustering method (T-VSC) in Algorithm 1, we identify netizens’ feature from the behaviour and demand – two aspects, through the collected raw public opinion data on the double-reduction education policy (see Section 4.1). During the data preprocessing, we track the raw data of 2292 netizen users, who have passed the identity authentication by the platform, as well as participated in the dissemination of public opinion throughout January until November 2023.

Fig. 4 shows the temporal scale transformation process by the proposed method T-VSC. In Fig. 4, the height of rectangles represents the granular deviation value (GrD) of every netizen cluster, while the width of rectangles represents the scale hierarchy of temporal observation rulers and higher observation scales have larger width; the dotted line means the satisfaction judgement standard of GrD, and the broken line is the number of netizens in every cluster. It can be seen that all netizens are divided into eight clusters with satisfied scale feature through performing the scale up transformation twice.

The temporal scale transformation process on the behaviour feature identification.

Comparative experiments are conducted between the traditional single scale clustering method (SSC) (Wang and Gao, 2022) and the proposed T-VSC, and the evaluation results are shown in Table 2 in detail. It can be seen that although the granular deviation evaluation results of the SSC become smaller as the scale hierarchy increases, the average and maximum evaluation results of the SSC are still larger than the proposed T-VSC, which further verifies the efficiency of the T-VSC method.

Comparative experimental results between the proposed T-VSC and the traditional single scale clustering method SSC.

Evaluation results of granular deviation index SSC T-VSC
Observation scale CH 0 1 Observation scale CH 1 1 Observation scale CH 2 1
Netizen Cluster X 1 1.5149 0.0000 0.0000 1.8998
X 2 1.5802 1.0943 1.0729 0.9737
X 3 1.7756 1.6132 1.1415 1.2471
X 4 1.7810 1.7899 1.2923 1.5701
X 5 1.9934 1.8002 1.4431 0.2556
X 6 2.0012 1.8898 1.4709 1.1842
X 7 2.2319 2.1090 1.9806 1.0492
X 8 2.2857 2.1864 2.0617 0.4718
Average evaluation result 1.8955 1.5604 1.3079 1.0814
Maximum evaluation result 2.2857 2.1864 2.0617 1.8998

Experiment results of netizens’ behaviour feature obtained by the proposed method T-VSC.

Netizen cluster X 1 X 2 X 3 X 4    X 5 X 6 X 7 X 8
Scale hierarchy Observation scale CH 0 1 Observation scale CH 1 1 Observation scale CH 2 1
Netizens’ behaviour feature under variable time intervals A 1 : Frequency of original content publishing max 75 449 141 25 16 14 18 40
min 0 0 0 3 1 1 0 0
avg 25.91 112.18 54.73 10.36 3.82 3.82 2.27 8.45
std 20.96 130.01 56.43 5.73    4.45 3.64 5.05 11.3
A 2 : Frequency of forwarding and commenting max 0 19 34 5 1 12 18 4
min 0 1 0 0 0 1 0 0
avg 0 3.09 3.82 0.45 0.09 2.73 2.18 0.73
std 0 5.07 9.59 1.44    0.29 3.02 5.08 1.21
A 3 : Frequency of being liked max 43 120946 6255 2 127207 80445 1755 200268
min 23 110946 76 0 125909 127 1755 199743
avg 36.33 117606 2142 0.67 126774.33 53506 1755 200093
std 9.43 4709.34 2908 0.94    611.88 37745 0 247.49

Moreover, Tables 3 and 4 further describes the behaviour and demand feature of every netizen cluster under certain temporal observation scales, as well as observation time points.

There are three qualified netizen clusters (that is X 1 , X 2 , X 3 ) obtained by the T-VSC on the basic observation scale the latest one month. Among them, cluster X 2 earns the most frequency of original content publishing, reaching 499 in one month, but its standard deviation is also relatively large as 130.01. That means the publishing behaviour of X 2 stays in a highly fluctuating state. Referring to the demand feature in Table 4, netizens in X 2 mostly care about the international school education and head training institutions at observation time point t I . Gradually, their attention has shifted to new regulations of Beijing high school entrance examination and ways of physical training over time. The above features indicate that although number of netizens in X 2 is small, they are relatively sensitive to education policies. Netizen cluster X 3 owns the maximum frequency of forwarding and commenting, while only cluster X 1 has never forwarded or commented any content during the whole time span. But both of them care about the qualification of training institutions at t I shown in Table 4.

Experiment results of netizens’ demand feature obtained by the proposed method T-VSC.

Netizen cluster GrD Number of netizens Scale hierarchy Netizens’ demand feature at policy time points
Observation time point t I Observation time point t II
X 1 1.8998 350 Observation scale CH 0 1 Qualification of training institutions After-school service design; Teachers’ competence and teaching skills
X 2 0.9737 61 International school education New regulations of Beijing high school entrance examination; Ways of physical training
Head training institutions
X 3 1.2471 76 Qualification of training institutions; Education bureau Transformation of learning machine market
X 4 1.5701 407 Observation scale CH 1 1 Homework design; Teaching effect of in-school courses Teachers’ workload; Students’ examination scores
X 5 0.2556 270 Pre-charge phenomenon of training courses Regulation of teachers’ flexible working schedule
X 6 1.1842 152 Observation scale CH 2 1 Science and technology training programs; Homework design Students’ career planning; Students’ learning interest
X 7 1.0492 850 Art training programs; Teachers’ competence and teaching skills After-school service design; Off-campus training course management
X 8 0.4718 126 Students’ sleep and eyesight protection; English training Youth employment problem; Students’ self-confidence

Taking the satisfaction judgement standard R 0 as the maximum GrD of the initial three clusters that is 1.8998 (shown in Fig. 4), the first scale up transformation process obtains two qualified netizen clusters X 4 and X 5 . The standard deviation of three behaviour dimensions of cluster X 4 is all at a low level, which implies the behaviour feature of X 4 is relatively stable. And the demands of the second largest cluster X 4 are also quite consistent at two time points, including teaching effect of in-school courses, students’ examination scores, homework design, etc. Cluster X 5 with the smallest behavioural granular deviation pays close attention to the pre-charge phenomenon of training courses at t I and regulation of teachers’ flexible working schedule at t II .

Finally, three netizen clusters (i.e. X 6 , X 7 , X 8 ) are obtained on the latest three months observation scale. Cluster X 6 and X 7 , respectively, get the largest and smallest standard deviation on the frequency of being liked, while cluster X 8 gets the most likes, exceeding two hundred thousand. According to Table 4, most of them care about the science and technology training programs, art training programs, students’ career planning and employment related issues. These netizens’ features could be applied to build the timely and efficient digital public dialogue mechanism.

 Conclusions

In this paper, we address the feature identification problem for the management of policy-focused public opinion. According to the variable-scale data analysis theory, the research starts from establishing the temporal scale space model considering the influence of the data timeliness and key observation time points on netizens’ feature identification process. The multi-scale temporal data model is established with the aim to represent netizens’ different behaviours in the dissemination of public opinion on the basis of the temporal scale space model.

After proposing the temporal scale transformation mechanism, a temporal variable-scale clustering method (T-VSC) is put forward. Compared to the traditional numerical variable-scale clustering method, the proposed T-VSC enables to combine the subjective attention of decision-makers and objective timeliness of public opinion data together during the scale transformation process. The efficiency of the proposed method T-VSC is verified by 48552 real public opinion data on the double-reduction education policy from the Sina Weibo platform. Experimental results indicate that the proposed T-VSC method could divide netizens that participating in the dissemination of policy-focused public opinion into clusters with low behavioural granularity deviation on the satisfied observation time scales, and identify the differentiated demand feature of each netizen cluster at policy time points.

In the future, we will keep studying the real-time decision-making constraint in intelligent management scenarios on the mechanism of temporal scale transformation process.

 Acknowledgements

The research was supported by China Postdoctoral Science Foundation (2021M700390), National Natural Science Foundation of China (71272161), China Scholarship Council (201906460087), and the Fundamental Research Funds for the Central Universities, China Grand number: FRF-TP-22-132A1.

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