Social Trend Mining: Lead or Lag

: This research underscores the profound implications of Social Intelligence Mining, notably employing open access data and Google Search engine data for trend discernment. Utilizing advanced analytical methodologies, including wavelet coherence analysis and phase difference, hidden relationships and patterns within social data were revealed. These techniques furnish an enriched comprehension of social phenomena dynamics, bolstering decision-making processes. The study’s versatility extends across myriad domains, offering insights into public sentiment and the foresight for strategic approaches. The ﬁndings suggest immense potential in Social Intelligence Mining to inﬂuence strategies, foster innovation, and add value across diverse sectors.


Introduction
The importance of social trend mining lies in its ability to provide stakeholders with a deep understanding of user behavior, preferences, and sentiments.By leveraging the vast amount of data available from the internet including search engines, businesses gain real-time insights into market dynamics, consumer trends, and competitive intelligence.These data also have a high potential to inform research in the public interest.
Big Data Analytics using available information provided by various search engines (for instance, Google) has opened a new golden opportunity [1,2].In addition, such an approach can also be used to measure people's engagement, priority, and sentiment over time.For example, Google Trends [3] allows users to analyze the popularity of keywords and phrases on Google over time.It can be used for a variety of purposes, including analyzing public opinion, tracking the spread of information and news, and identifying trends in consumer behavior.Here are a few examples of studies that have used Google Trends data.For instance, Google Trends data has been used to predict the GDP growth in the United States [4]; Google Trends data was utilized to analyze tourism demand in various countries [5]; ref. [6] used Google Trends data to predict stock market returns in China; and [7] used Google Trends data to predict the spread of infectious diseases.These are just a few examples; there are many more studies and articles that have used Google Trends data in various ways (see, for example, [8][9][10][11][12][13][14][15][16][17]).
The landscape of online networks and interaction mediums has been significantly transformed by the advent of social media platforms.Unlike their predecessors, social media platforms exhibit distinctive characteristics such as openness, participatory dynamics, flexibility, robustness, and creativity.These platforms, akin to real-life social networks, establish virtual connections between individuals, giving rise to the small-world phenomena that characterize them (see, for instance, [18][19][20][21][22][23][24][25].Recent statistics reveal that the average social media user maintains 8.4 active accounts and dedicates around 145 min daily to engaging across various social media platforms.Amidst this vibrant virtual environment, numerous challenges have emerged concerning the extraction and analysis of content generation, modification, and dissemination across diverse topics on social media.This paper draws on a recent review [26] and various other sources [27][28][29][30][31][32][33] to delve into the multifaceted challenges inherent in social media mining and analysis, shedding light on the complexities of understanding and navigating this dynamic landscape.
The novelty of this paper lies in its innovative approach to social trend mining, which leverages open access data and Google Search engine data to provide comprehensive insights into user behavior, and trend identification.By integrating time series analysis and advanced analytical methods, this paper offers a fresh perspective on understanding and harnessing social data for decision making.Furthermore, this paper introduces the novel application of wavelet coherence analysis and phase difference to uncover hidden relationships and patterns within social data, enhancing our ability to identify leading and lagging trends.This unique combination of methodologies and its adaptability to various domains make the paper a pioneering contribution to the field of social trend mining.
The ability to identify leading and lagging trends, perform trend analysis, and differentiate noise from meaningful events provides organizations with a powerful tool for informed decision making, proactive strategy formulation, and effective risk management.
The next section presents the methodology, which consists of two subsections: trend extraction based on indexed time series and coherence analysis between two time series.These methodologies are employed to explore the applicability of the proposed approach using real data extracted from Google Search.
The first subsection focuses on trend extraction based on indexed time series.By utilizing indexed time series data, trends can be identified and analyzed.This approach allows for the examination of temporal patterns and variations in search interest over time.The indexed time series data, obtained from Google Search data, serve as a valuable resource for trend analysis and provide insights into societal interests and preferences.
The second subsection delves into coherence analysis between two time series.This analysis explores the association between two time series, considering both time and frequencies.By examining the coherence between the two series, it becomes possible to understand the degree of similarity and correlation between them.This analysis provides valuable information about the interconnectedness and potential causal relationships between different social phenomena.
To evaluate the proposed approach, real data extracted from Google searches are utilized.These data represent actual search queries made by individuals, reflecting their interests and concerns.By employing this real-world data, the applicability and effectiveness of the methodology can be assessed, providing valuable insights into social intelligence mining.

Methodology and Methods
The methodology section of this paper briefly describes a trend extraction approach based on indexed time series and an approach to coherence analysis between two time series.By utilizing real data from Google Search, the proposed approach can be evaluated and its effectiveness in uncovering trends and associations can be assessed.These methodologies serve as powerful tools for exploring and analyzing social phenomena, offering valuable insights into the dynamics of our ever-evolving society.

Trend Analysis
Search engine trend analysis has emerged as a valuable technique for gaining insights into user behavior, sentiment analysis, and trend identification.Among various search engines, Google Trends stands out as a prominent platform that provides a vast amount of data, which can be utilized for time series analysis and opinion mining of individuals.
By monitoring the frequency of searches related to specific keywords over time, researchers can obtain valuable insights into the popularity and dynamics of various topics.This data can be leveraged for time series analysis techniques, such as trend identification, seasonality detection, and forecasting.The data extracted from Google Trends data provides not only quantitative information but also a glimpse into public sentiment and opinions.By analyzing the content of search queries and associated search results, re-searchers can gain insights into the preferences, concerns, and sentiments of individuals.Opinion mining techniques, such as sentiment analysis and topic modeling, can be applied to extract meaningful insights from this data, enabling a deeper understanding of public opinion on specific subjects.
To facilitate trend analysis and comparison across different topics, the concept of creating indices based on selected keywords can be used.These indices capture the relative popularity or interest in specific topics over time.The formula for creating indices can be adjusted based on the desired characteristics and data normalization techniques.Two common types of indices are: (a) Univariate Google Trend Index: This index represents the search interest for a single keyword or topic.It is calculated by normalizing the search volume or frequency for the chosen keyword over a specific time period.Normalization techniques, such as dividing by the maximum search volume or using z-scores, can be employed to standardize the data and make it comparable.
(b) Multivariate Google Trend Index: This index captures the comparative popularity of multiple keywords or topics.It involves selecting a set of keywords of interest and calculating the search volume or frequency for each keyword.
By utilizing these indices, researchers and practitioners can gain a comprehensive view of the relative popularity and trends associated with different keywords or topics over time.This enables them to identify emerging trends, track public sentiment, and compare the performance of various keywords or topics within their respective domains.

Lead and Lag Analysis
A wavelet transform is used to transform time series with complex periodic behavior to simplified signals, each of which has simple periodic behavior (with a single period).From a mathematical point of view, a wavelet transform is a generalization of Fourier transform.A Continuous Wavelet Transform, CWT, uses a mother wavelet function ψ(•) to transform a discrete-time time series {y t } n 1 to wavelet coefficients W ψ {y}(τ, s), for the time localizing parameter τ and the scale parameter s.

Univariate Case
The wavelet coefficients W ψ {y}(τ, s) are defined as a convolution of time series {y t } n 1 with the localized mother wavelet ψ(•) (named child wavelet), localized in time and frequency space by τ and s [34]: where ψ(•) is the complex conjugate of the mother wavelet ψ(•).The localization parameter τ exhibits periodic behavior over time, while the scale parameter s localizes the periodic behavior in the frequency domain.When the scale parameter s has larger values, this indicates long-term periodic behavior with low frequency.On the other hand, smaller values of the scale parameter s reveal details in short-term periodic patterns with higher frequencies.One commonly used choice for the mother wavelet is the Morlet wavelet [33], which is formulated as follows: where ω is the angular frequency, and κ ω and c ω are constants defined as: The ω = 6 is a proper choice for the angular frequency since it makes the Morlet wavelet approximately analytic.Large absolute values of W ψ {y}(τ, s) indicate powerful periodic patterns in time τ and period s.The wavelet coefficients can be used to construct the wavelet power spectrum of time series {y t } n 1 : The wavelet power spectrum, denoted as Power ψ {y}, is a valuable tool for mapping pe- riodic patterns in a given time series over time.To assess the significance of the wavelet power spectrum, it can be compared against the white noise spectrum using either the asymptotic chi-square statistic [34] or Monte Carlo simulation [35].The Monte Carlo simulation approach is employed for evaluating the significance of the wavelet power spectrum.

Bivariate Case
Let us now consider the time series {x t } n 1 and {y t } n 1 as the bivariate case.A crosswavelet transform can be used to investigate the relationship between {x t } n 1 and {y t } n 1 [34]: where W denotes a complex conjugate and W ψ {x}(τ, s) and W ψ {y}(τ, s) are the wavelet coefficients in CWT of {x t } n 1 and {y t } n 1 , respectively.The wavelet cross power spectrum, as modulus of wavelet coefficients, can be used to map the similarities between two time series' periodic behavior: The Power ψ {xy}(τ, s), like covariance, depends on the underlying time series' unit of measurement and may not properly interpret the degree of association between two series.Wavelet coherence between two time series {x t } n 1 and {y t } n 1 is defined as the local crosscorrelation between the series, localized at time τ and scale s: 2 sPower ψ {x}(τ, s).sPower ψ {y}(τ, s) , where prefix s behind W ψ and Power ψ indicates smoothing is required.Similar to the power spectrum, the wavelet coherence between two series can also be examined using Monte Carlo simulation [36][37][38][39].Monte Carlo simulation provides a robust approach for testing the significance of wavelet coherence and assessing the presence of coherent relationships between the two series under investigation.The Continuous Wavelet Transform (CWT) reveals localized periodic patterns in a given time series {y t } n 1 .The wavelet phase indicates the local displacement of the periodic behavior relative to the localization parameter τ, which is shifted across the time domain when τ is set as the origin.The wavelet phase is typically represented as an angle within the interval [−π, π].
where Im(.) and Re(.) are imaginary and real parts of the wavelet coefficient W ψ {y}(τ, s).
Using the cross-wavelet coefficients, one can calculate the difference between wavelet phases from two time series (which is actually the difference between two phases): where Angle ψ {xy}(τ, s) represents the phase difference between two time series {x t } n 1 and {y t } n 1 .Angle ψ {xy}(τ, s) can be used to determine which time series starts the periodic pattern first and which one is following, for a given time and frequency interval.Figure 1 shows the simplified interpretation of the phase difference between time series {x t } n 1 and {y t } n 1 .
Using the cross-wavelet coefficients, one can calculate the difference between wavelet phases from two time series (which is actually the difference between two phases): where   ,  represents the phase difference between two time series  and  .  ,  can be used to determine which time series starts the periodic pattern first and which one is following, for a given time and frequency interval.Figure 1 shows the simplified interpretation of the phase difference between time series  and  .Various social phenomena can exhibit cyclical patterns [33].By applying wavelet analysis to the social data, we can uncover the underlying periodic patterns in these phenomena.For example, analyzing people's interest in a subject through chat discussions or online searches can reveal if there are cycles where this subject becomes popular in society.Similarly, examining the number of participants in a social activity can expose the cycles of outbursts in that particular activity.
Furthermore, by utilizing a wavelet coherence analysis and phase difference, we can examine the correlation between two social phenomena, even if it was only for a brief period.This analysis can help determine which phenomenon had a leading role if such a relationship existed.The presence of coherency and phase difference between two social phenomena could indicate a causal relationship, where events from the leading series influence events in the lagging series.Alternatively, it could suggest that both series are influenced by another common social phenomenon.These findings serve as powerful tools for generating hypotheses about social events, trends, and their interrelations.

Applied Methodology: Real Data Implementation and Analysis
In this section, we focus on the application of social trend mining to several dimensions of human security including food, water, and energy security.These three dimensions of human security correspond to three UN Sustainable Development Goals (SDGs)-SDG 2, SDG 6, and SDG 7, respectively.Let us now provide a brief overview of three SDGs utilized in this paper.
Sustainable Development Goal 2 is about creating a world free of hunger by 2030.In 2020, between 720 million and 811 million persons worldwide were suffering from hunger, roughly 161 million more than in 2019.Also in 2020, a staggering 2.4 billion people, or above 30 percent of the world's population, were moderately or severely food insecure, lacking regular access to adequate food.The figure increased by nearly 320 million people Various social phenomena can exhibit cyclical patterns [33].By applying wavelet analysis to the social data, we can uncover the underlying periodic patterns in these phenomena.For example, analyzing people's interest in a subject through chat discussions or online searches can reveal if there are cycles where this subject becomes popular in society.Similarly, examining the number of participants in a social activity can expose the cycles of outbursts in that particular activity.
Furthermore, by utilizing a wavelet coherence analysis and phase difference, we can examine the correlation between two social phenomena, even if it was only for a brief period.This analysis can help determine which phenomenon had a leading role if such a relationship existed.The presence of coherency and phase difference between two social phenomena could indicate a causal relationship, where events from the leading series influence events in the lagging series.Alternatively, it could suggest that both series are influenced by another common social phenomenon.These findings serve as powerful tools for generating hypotheses about social events, trends, and their interrelations.

Applied Methodology: Real Data Implementation and Analysis
In this section, we focus on the application of social trend mining to several dimensions of human security including food, water, and energy security.These three dimensions of human security correspond to three UN Sustainable Development Goals (SDGs)-SDG 2, SDG 6, and SDG 7, respectively.Let us now provide a brief overview of three SDGs utilized in this paper.
Sustainable Development Goal 2 is about creating a world free of hunger by 2030.In 2020, between 720 million and 811 million persons worldwide were suffering from hunger, roughly 161 million more than in 2019.Also in 2020, a staggering 2.4 billion people, or above 30 percent of the world's population, were moderately or severely food insecure, lacking regular access to adequate food.The figure increased by nearly 320 million people in just one year.Globally, 149.2 million children under 5 years of age, or 22.0 percent, were suffering from stunting (low height for their age) in 2020, a decrease from 24.4 percent in 2015.
SDG 6 is about ensuring access to water and sanitization for all.Access to safe water, sanitation, and hygiene is the most basic human need for health and well-being.Billions of people will lack access to these basic services in 2030 unless progress quadruples.Demand for water is rising owing to rapid population growth, urbanization, and increasing water needs from the agriculture, industry, and energy sectors.
To reach universal access to drinking water, sanitation, and hygiene by 2030, the current rates of progress would need to increase fourfold.Achieving these targets would save 829,000 people annually, who die from diseases directly attributable to unsafe water, inadequate sanitation, and poor hygiene practices.
SDG 7 is about ensuring access to clean and affordable energy, which is key to the development of agriculture, business, communications, education, healthcare, and transportation.The lack of access to energy hinders economic and human development.
The latest data suggest that the world continues to advance towards sustainable energy targets.Nevertheless, the current pace of progress is insufficient to achieve Goal 7 by 2030.Huge disparities in access to modern sustainable energy persist.
It should be mentioned that significant challenges remain at the global level in terms of achieving these SDGs.This assessment is true for most of the world's major regions, while recent trends are mainly stagnating (in lower-income countries) or moderately increasing (in higher-income countries).
The actual or perceived lack of food, water, or energy security could be a source of social instability.In addition to the indicators describing the actual availability, accessibility, and affordability of food, water, and energy, such as prices and use, indicators describing people's perceptions provide important input for policy makers.Google Search data can inform such indicators which could be made available to policy makers almost in real time.
Figure 2, as an example, depicts the Google Search hits for the keywords "Food Security", "Energy Security", and "Water Security" over the past five years.These three concepts-food, energy, and water security-are important dimensions of human security.However, when comparing the search hits for the three subsets, it is evident that the search interest in food security is significantly higher than that for water security and energy security.The search interest in energy security is lower than the other two dimensions although only slightly lower than the search interest in water security.
in just one year.Globally, 149.2 million children under 5 years of age, or 22.0 percent, were suffering from stunting (low height for their age) in 2020, a decrease from 24.4 percent in 2015.
SDG 6 is about ensuring access to water and sanitization for all.Access to safe water, sanitation, and hygiene is the most basic human need for health and well-being.Billions of people will lack access to these basic services in 2030 unless progress quadruples.Demand for water is rising owing to rapid population growth, urbanization, and increasing water needs from the agriculture, industry, and energy sectors.
To reach universal access to drinking water, sanitation, and hygiene by 2030, the current rates of progress would need to increase fourfold.Achieving these targets would save 829,000 people annually, who die from diseases directly attributable to unsafe water, inadequate sanitation, and poor hygiene practices.
SDG 7 is about ensuring access to clean and affordable energy, which is key to the development of agriculture, business, communications, education, healthcare, and transportation.The lack of access to energy hinders economic and human development.
The latest data suggest that the world continues to advance towards sustainable energy targets.Nevertheless, the current pace of progress is insufficient to achieve Goal 7 by 2030.Huge disparities in access to modern sustainable energy persist.
It should be mentioned that significant challenges remain at the global level in terms of achieving these SDGs.This assessment is true for most of the world's major regions, while recent trends are mainly stagnating (in lower-income countries) or moderately increasing (in higher-income countries).
The actual or perceived lack of food, water, or energy security could be a source of social instability.In addition to the indicators describing the actual availability, accessibility, and affordability of food, water, and energy, such as prices and use, indicators describing people's perceptions provide important input for policy makers.Google Search data can inform such indicators which could be made available to policy makers almost in real time.
Figure 2, as an example, depicts the Google Search hits for the keywords "Food Security", "Energy Security", and "Water Security" over the past five years.These three concepts-food, energy, and water security-are important dimensions of human security.However, when comparing the search hits for the three subsets, it is evident that the search interest in food security is significantly higher than that for water security and energy security.The search interest in energy security is lower than the other two dimensions although only slightly lower than the search interest in water security.Let us now explore the periodic behavior in the search interests for "Food Security" and "Water Security".Figure 3 displays the wavelet power spectrum for both series.Let us now explore the periodic behavior in the search interests for "Food Security" and "Water Security".Figure 3 displays the wavelet power spectrum for both series.As depicted in Figure 3 (top panel), the interest in "Food Security" has exhibited significant low and mid-frequency behaviors over the past five years.Note that low-frequency cycles are cycles with long periods, for example, longer than 32 weeks period in this data.
Mid-frequency cycles are cycles with mid-range periods, for example, around a 16week period in this data.The significance test, conducted using Monte Carlo simulation with 5000 sample paths, confirms this observation.However, in recent years (i.e., after 19-Apr-2020), the power spectrum has shown an increase, with a focus on mid-range periods (around 16 and 32 weeks) and long-range periods (above 32 weeks).This indicates that the search frequency for the keyword "Food Security" has become more frequent over time.
In the middle panel of Figure 3, the power spectrum for "Water Security" displays significant patterns mostly concentrated on the right side of the timeline (approximately after 15-Nov-2020).The most powerful periodic patterns occur within the 16 to 32-week period range.In other words, approximately after 15-Nov-2020, there has been a periodic pattern in people's interest in the "Water Security" keyword.The length of each periodic As depicted in Figure 3 (top panel), the interest in "Food Security" has exhibited significant low and mid-frequency behaviors over the past five years.Note that lowfrequency cycles are cycles with long periods, for example, longer than 32 weeks period in this data.
Mid-frequency cycles are cycles with mid-range periods, for example, around a 16-week period in this data.The significance test, conducted using Monte Carlo simulation with 5000 sample paths, confirms this observation.However, in recent years (i.e., after 19-Apr-2020), the power spectrum has shown an increase, with a focus on mid-range periods (around 16 and 32 weeks) and long-range periods (above 32 weeks).This indicates that the search frequency for the keyword "Food Security" has become more frequent over time.
In the middle panel of Figure 3, the power spectrum for "Water Security" displays significant patterns mostly concentrated on the right side of the timeline (approximately after 15-Nov-2020).The most powerful periodic patterns occur within the 16 to 32-week period range.In other words, approximately after 15-Nov-2020, there has been a periodic pattern in people's interest in the "Water Security" keyword.The length of each periodic pattern (the beginning of one surge of interest to the beginning of the next one) mostly includes periods below 16 to periods above 32 weeks.
As shown in the bottom panel, the significant "Energy Security" power spectrum also is mostly concentrated on low and mid frequencies (i.e., long periods in which the time from one surge of interest in "Energy Security" is between 32 to 64 weeks and mid-ranged periods which the time from one surge of interest in "Energy Security" is between 16 to 32 weeks).Periodic behavior of interest in the "Energy Security" keyword has become more powerful after 13-Jun-2021.Furthermore, the periodic behavior of interest in "Energy Security" includes shorter periods (higher frequency) as well.In other words, the power spectrum of interest in "Energy Security" shows that the interest in "Energy Security" has increased and the search for "Energy Security" has become more frequent.
These findings suggest that the interest in "Food Security", "Water Security", and "Energy Security" has increased in the last three years (after 14-Apr-2020), and searching for these keywords has become more frequent.Furthermore, it can be seen the increased interest in these keywords started with "Food Security" and, as the top panel shows an increased power spectrum at higher frequencies sooner.In other words, after 14-Apr-2020, the search for "Food Security" became more frequent, then the search for "Water Security", and, finally, "Energy Security".
Additionally, in recent years (especially after 13-Jun-2021) the periodic behavior of interest in these keywords demonstrates mid-range periodic patterns (with period lengths between 16 and 32 weeks.),which suggests that it takes 16 to 32 weeks (almost 4 to 8 months) form one surge of interest in these keywords to the next one.
In order to examine the relationship between interest in "Food Security" and "Water Security", the wavelet coherence analysis is applied to two series.The results are given in Figure 4.In order to analyze the coherence between each two of these three time series, only the time intervals and periods in which the coherence of the two series is significant, and their power spectrum will be considered.Furthermore, in order to avoid overestimating the number of cyclical patterns, the results are presented for time intervals and periods whose length is not shorter than half of their period and at least 5 weeks apart.
The coherence analysis between "Food Security" and "Water Security" (top panel in As previously mentioned, wavelet coherence and phase difference analysis are valuable tools for examining the relationship between two time series signals, such as food security and water security, in both the time and frequency domains.These techniques provide insights into the similarity, coherence, and phase relationship between the two signals at different scales or frequencies, over time.
Wavelet coherence quantifies the correlation between the two signals as a function of both time and frequency.It reveals the level of similarity or shared variability between the two time series across different frequency components.Higher coherence values indicate a stronger relationship, while lower coherence values suggest a weaker or non-existent relationship.
On the other hand, phase difference captures the phase lag or lead between the two signals.It indicates the relative timing or synchronization between the peaks and troughs of the two time series.A phase difference of zero denotes perfect synchronization, implying that the peaks and troughs of the two signals align precisely.Non-zero phase difference values indicate a lag or lead between the two signals, with the peaks and troughs occurring at different times.
By employing wavelet coherence and phase difference analysis, we can gain a deeper understanding of the relationship between food security and water security, uncovering their coherence and phase synchronization characteristics across different frequencies and over time.
In order to analyze the coherence between each two of these three time series, only the time intervals and periods in which the coherence of the two series is significant, and their power spectrum will be considered.Furthermore, in order to avoid overestimating the number of cyclical patterns, the results are presented for time intervals and periods whose length is not shorter than half of their period and at least 5 weeks apart.
The coherence analysis between "Food Security" and "Water Security" (top panel in Figure 4) reveals that the two series exhibit significant coherence mostly in mid-range periods, i.e., 15.45-week and 25.11-week periods, and long periods, i.e., 32-week, 38.1-week, 43.71-week, and 64-week periods (see Table A1 in Appendix A for more details).In other words, significant cyclical patterns are evident in both series and demonstrate a significant coherence between them, suggesting that they behave similarly, possibly with a time delay.It also can be seen that during the time, the frequencies in which two series have become coherent are increased (the length of periods is decreased).For instance, before the end of 2020, coherence between two series existed mostly at 43.71-week and 64-week periods ( 1 43.71 = 0.02287806 and 1 64 = 0.015625 frequencies, respectively) while after June 2022, the coherence between the two series has occurred mostly in 25.11-week and 15.45-week periods ( 115.45 = 0.06472492 and 1 25.11 = 0.03982477 frequencies, respectively).The middle panel in Figure 4 shows significant coherency between "Food Security" and "Energy Security".Coupling these results with the power spectrum results (Figure 3) reveals that the two series exhibit significant coherence mostly in mid-range periods, i.e., 18.38-week and 25.11-week periods, and longer periods, i.e., 34.3-week and 39.4-week periods (see Table A2 for more details).This means there are significant cyclical patterns in both series with these periods in which they behave similarly in a time interval, possibly with a time delay.For instance, between 13-Feb-2022 and 3-Jul-2022, both series demonstrate a significant cyclical pattern in which it would take 25.11 weeks from one surge of interest in keywords to the next one, and two series have almost the same behavior possibly with a time delay.
Significant coherence between "Water Security" and "Energy Security" is presented in the bottom panel of Figure 4. Overlapping significant coherence areas (inside white contours) with "Water Security" and "Energy Security" power spectrums (Figure 3) shows that two series have significant coherence, mostly in mid-range periods (i.e., 17.15-week and 25.11-week periods) and very long period, i.e., 84.45-week period (see Table A3 for details).
The arrows displayed in above mentioned periods indicate the angular phase difference between the two series during each period.To convert these angular phase differences into a time unit (weeks), the following formulation can be utilized.
where Phase.dif f ψ {xy}(τ, s) is the phase difference between two series, measured by time unit (which is "week" in our data), l p is the period length and Angle ψ {xy}(τ, s) is angular phase difference measured in radians.For instance, in weekly data, the angular phase difference between two series for a 25.11-week period converts to phase difference in weeks as: Tables A1-A3 in Appendix A illustrate the phase difference and leading time series in each of the time intervals and periods discussed above.According to Tables A1-A3, all three time series have significant cyclical behavior with a 25.11-week period at some point over the time and each time series has significant coherence with another one.For instance, between 15-Apr-2022 and 3-Jul-2022, there is significant coherence between all pairs of time series, i.e., in the "Food Security"-"Water Security" pair, in the "Food Security"-"Energy Security" pair, and in "Water Security-Energy Security".In other words, in this short time interval, all three time series have a cyclical pattern in which the surge of interest in any one keyword to the next surge of interest in that keyword takes almost 25.11 weeks.Furthermore, the cyclical pattern is similar in all three time series, except for possible time delay.However, the cyclical pattern and coherence for each pair of time series may exceed this time interval differently.Phase difference analysis shows that between 15-Apr-2022 and 3-Jul-2022, in a cyclical pattern with a 25.11-week period, interest in "Food Security" leads both "Water Security" and "Energy Security" (with different phase difference values) and interest in "Energy Security" leads interest in "Water Security".These results imply that there is a cyclical pattern with a 25.11-week period length, between 15-Apr-2022 and 3-Jul-2022, in which the surge of interest in keywords first comes to "Food Security" and then "Energy Security" and, finally, "Water Security".

Search Engine: Comparative Analysis
Table 1 presents a comparative analysis of the trend extraction features offered by three prominent search engines: Google, Bing, and Yahoo.It serves as a valuable reference for users and decision makers seeking to understand the capabilities of these search engines in extracting and analyzing trending data.
In the table, various key features are assessed, including data accessibility, trend analysis tools, real-time data availability, geographic specificity, data visualization options, API support, and customization capabilities.
Google stands out with its extensive data accessibility, strong trend analysis tools, and real-time data availability, making it a robust choice for users interested in tracking and analyzing trends.Bing offers decent trend analysis capabilities and some customization options, making it a suitable alternative.Yahoo, on the other hand, offers limited data accessibility and trend analysis tools, making it less suited for in-depth trend extraction and analysis tasks.
Overall, this comparative analysis provides insights into the strengths and weaknesses of these search engines concerning trend extraction, enabling users to make informed choices based on their specific data analysis needs and preferences.

Discussion
This paper delves into the concept of Social Intelligence Mining, highlighting the importance of leveraging open access data and Google Search engine data for trend analysis.This approach offers several notable advantages for both researchers and practitioners.
Firstly, the analysis of Google Search data as a time series provides a powerful tool for trend identification.By examining search queries over time, researchers can pinpoint emerging trends, recognize seasonality patterns, and even make predictions about future developments.This temporal perspective is invaluable for staying ahead in rapidly evolving fields and industries.
Furthermore, the application of opinion mining techniques to search queries offers a more profound understanding of public sentiment and preferences.This sentiment analysis adds a layer of nuance to the data, enabling decision makers to make informed choices regarding strategy formulation and risk management.In sum, Social Intelligence Mining, driven by open access data and Google Search engine data, equips organizations with comprehensive insights into user behavior, sentiment analysis, and trend identification.
This approach facilitates competitive advantages, informed decision making, and meaningful engagement with target audiences.As technology and data continue to evolve, the potential of Social Intelligence Mining for shaping strategies, driving innovation, and creating value across diverse domains remains substantial.
Additionally, the paper highlights the utility of wavelet coherence analysis and phase difference in uncovering hidden relationships and patterns within social data.These techniques offer a more profound understanding of the dynamics between social phenomena.By identifying leading and lagging trends, researchers and practitioners can make well-informed decisions based on a more comprehensive view of the data.
The specific case study presented in the paper on "Food Security", "Energy Security", and "Water Security" serves as an illustrative example.However, the methodology outlined can be applied to a wide range of domains and topics.Open access data sources like Google Trends offer valuable insights into public sentiment, emerging trends, and proactive strategy development.
Looking ahead, further research in this field should consider expanding the analysis to encompass additional relevant social phenomena.This expansion will allow for the exploration of more complex relationships and patterns.Additionally, incorporating data from social media and news sources can provide a more comprehensive understanding of social dynamics.
Addressing the challenges associated with data quality, privacy, and bias is also crucial for ensuring the reliability and validity of results in Social Intelligence Mining.As this field continues to evolve, these challenges must be carefully addressed to maintain the integrity of the research and its practical applications.

Conclusions
In conclusion, this paper underscores the pivotal role of Social Intelligence Mining, accentuating the utility of open access data and Google Search engine data for in-depth trend analysis.Harnessing these resources, coupled with sophisticated analytical methods, empowers organizations to secure a competitive advantage, make evidence-based decisions, and more effectively engage their target demographics.
Our findings spotlight the efficacy of wavelet coherence analysis and phase difference in elucidating concealed relationships and patterns within social datasets.Such techniques facilitate a more profound grasp of social phenomena dynamics, subsequently refining decision-making protocols.
However, this research is not without its limitations.The focus on a singular case study, albeit comprehensive, may not capture the entire spectrum of possibilities within Social Intelligence Mining.Looking forward, the versatility of the presented methodology suggests its applicability across diverse domains and subjects.Still, future research should venture into investigating intricate relationships and broaden its analytical scope to encapsulate various social phenomena.Integrating data from diverse platforms, such as social media and news outlets, will enrich the analysis.Addressing pressing concerns of data integrity, privacy, and potential biases will be paramount to buttress the dependability of subsequent Social Intelligence Mining endeavors.
To encapsulate, Social Intelligence Mining stands poised to redefine strategy formulation, spur innovation, and offer unparalleled value across sectors.Its sustained evolution augurs well for refining both decision-making paradigms and the comprehension of intricate social dynamics.

Figure 1 .
Figure 1.Interpretation of phase difference between signals x and y [32].

Figure 1 .
Figure 1.Interpretation of phase difference between signals x and y [32].

Figure 2 .
Figure2.The Google Search hits for the keywords "Food Security", "Energy Security", and "Water Security" over the last 5 years.

Figure 2 .
Figure2.The Google Search hits for the keywords "Food Security", "Energy Security", and "Water Security" over the last 5 years.

Figure 3 .
Figure 3. Wavelet power spectrum for "Food Security", "Water Security", and "Energy Security" Google Trends.White contours show significant powers at  = 0.1 significance level.

Figure 3 .
Figure 3. Wavelet power spectrum for "Food Security", "Water Security", and "Energy Security" Google Trends.White contours show significant powers at α = 0.1 significance level.

24 Figure 4 .
Figure 4. Wavelet coherence and phase difference angles (arrows) for "Food Security", "Water Security", and "Energy Security" interests.White contours show significant powers at  = 0.1 significance level (90% confidence level).Phase difference angles are only presented for locations with significant coherence.

Figure 4 .
Figure 4. Wavelet coherence and phase difference angles (arrows) for "Food Security", "Water Security", and "Energy Security" interests.White contours show significant powers at α = 0.1 significance level (90% confidence level).Phase difference angles are only presented for locations with significant coherence.

Table 1 .
Comparison of trend extraction features in popular search engines.

Table A2 .
The phase difference and leading time series for "Food Security"-"Energy Security" pair.