1. Introduction

People's Emotions Analysis while Watching YouTube Videos

Volodymyr Motyka

volodymyr.motyka@lpnu.ua 0

Yaroslav Stepaniak

yaroslav.stepaniak@lpnu.ua 0

Mariia Nasalska

mariia.nasalska@lpnu.ua 0

Victoria Vysotska

victoria.a.vysotska@lpnu.ua 0 1 0 Lviv Polytechnic National University , S. Bandera Street, 12, Lviv, 79013 , Ukraine 1 Osnabrück University , Friedrich-Janssen-Str. 1, Osnabrück, 49076 , Germany

For analysis, a dataset containing information about videos from video hosting YouTube is selected, namely: title, video category, channel (author), number of views, number of likes, number of dislikes, date of video release. The purpose of the study was to analyze the state of people while watching videos on this platform. For this, various methods of visualization and data processing, smoothing methods, correlation and cluster analysis are used.

1 Cluster analysis correlation smoothing YouTube like dislike emotion sentiment analysis

1. Introduction 2. Related works

Let's pay attention to the exact numbers and look at the statistics of the most popular social networks for July 2021. The data are taken from the resource [ 1 ] and shown in Fig. 1. The number of users is given in millions. As can be seen from the statistics, YouTube is the second most popular platform in the world after the social network Facebook. In addition, YouTube is the second most popular search engine after Google. More than two billion of its users, equivalent to nearly one-third of all Internet users, log in every month. However, that is not all. YouTube viewers watch more than a billion hours of video on its platform every day and are responsible for generating billions upon billions of views [ 2 ].

Let's look at how many more users have become in recent years:

One of the reasons for the jump in popularity was changing the interface and adding new functions and opportunities for users, for example, users could rate not only videos, but also entire playlists, and when choosing a video, they were immediately shown the number of video views and its duration. All this affects the emotional state of users. The reason for the jump in popularity in 2020 was the pandemic of the coronavirus disease, as an extremely large number of people around the world began to work, study at home. This increased the amount of free time people have and they started using social platforms like YouTube more [ 3-5 ]. It is impossible not to note the number of video views on YouTube. As can be seen from Figure 2, views more than once exceed the population of countries, so there is certain content that people are ready to view more than once and more than twice.

3. Methods and materials

We will use the methods of visual presentation of data, smoothing, correlation method to perform the tasks. Methods of visual presentation of data - methods of presenting data in the form of graphs, charts and/or other subtypes of them (histograms, pie charts, etc.), time series, etc. Depending on the specific task, a specific method of data presentation will be used. We will implement these methods using Microsoft Power BI and/or R tools. Smoothing methods are used to reduce the influence of the random component (random fluctuations) in time series. They make it possible to obtain more "pure" values, which consist only of deterministic components. Some of the methods are aimed at highlighting some components, for example, a trend [ 6-8 ]. We will implement these methods using Microsoft Excel, R and/or Microsoft Power BI. Correlation method (Correlation - analysis) - a method of studying the interdependence of characteristics in the general population, which are random variables with a normal distribution [ 9-13 ] for different NLP-talks based on emotions recognizing and analysis [ 14-23 ].

4. Experiments

The source of the selected dataset: https://www.kaggle.com/ahmedmohamedmahrous/youtubetextsentiment?select=USvideos.csv. Let's open the dataset using R Studio: selecting the views data column, which characterizes the number of views of the corresponding video, using R:  

Sample size – the number of units in the sample: sample_size<-nrow(videos)

Sample mean. We find using the built-in mean() method:

avg<-mean(videos$views, na.rm = FALSE)  The median of the sample is the number that "divides" "in half" the ordered set of all the values of the sample, that is, the average value of the changing characteristic, which is contained in the middle of the series, placed in the order of increasing or decreasing of the characteristic. For this, we will use the median() method: median_views<-median(videos$views, na.rm = FALSE)  Mode - the value that occurs most often in the sample. Since there is no built-in method for finding it in R, we will define our modes function: modes <-function(v) {## modes function uniqv <- unique(v) uniqv[which.max(tabulate(match(v, uniqv)))] } mode_views<-modes(videos$views)  Sample size – the difference between the maximum and minimum value of the sample. To find the maximum and minimum, use the built-in methods max() and min():

range_views<-max(videos$views)-min(videos$views)  Standard deviation - the amount of spread relative to the arithmetic mean. To find, we will use the built-in method sd(): standart_deviation<-sd(videos$views)  Coefficient of variation – an indicator that determines the percentage ratio of the average deviation to the average value:

variation_coef<-sd(videos$views)*100/mean(videos$views, na.rm = FALSE)  Asymmetry reflects the skewness of the distribution relative to the mode. Let's use the built-in h<-3.5*sd(videos$category_id)*(nrow(videos))^(-1/3) #Interval width

Construction of a histogram:

hist(videos$category_id, breaks = k, xlab = "Category", main = "Histogram of categories", xlim = c(0,8*10^5))

Construction of cumulata:

plot(ecdf(videos$category_id), main="Cumulate", xlab="Category", ylab = "Frequency")

Let's present the dataset in the form of a table: Number of likes and dislikes depending on video categories: Let's find the statistical parameters for the views attribute (Table 1). After executing the code, we have histograms and corresponding cumulates:

Smoothing methods are used to reduce the influence of the random component (random fluctuations) in time series. They make it possible to obtain more "pure" values, which consist only of deterministic components. Some of the methods are aimed at highlighting some components, for example, a trend.

Smoothing methods can be conventionally divided into two classes based on different approaches: analytical and algorithmic. The simplest method of forecasting is considered to be an approach that determines the forecast estimate from the actually achieved level using the average level, average growth, average growth rate. Extrapolation based on the average level of the series.

The resulting confidence interval takes into account the uncertainty hidden in the estimate of the average value. However, the assumption remains that the predicted indicator is equal to the sample mean, that is, this approach does not take into account the fact that individual values of the indicator have fluctuated around the average in the past, and this will happen in the future.

Analytical smoothing methods include regression analysis together with the method of least squares and its modifications. To identify the main trend by analytical method means to give the studied process the same development throughout the entire observation period. Therefore, for four of these methods, it is important to choose the optimal function of the deterministic trend (growth curve), which smoothes a number of observations.

Forecasting methods based on regression methods are used for short- and medium-term forecasting. They do not allow for adaptation: with the receipt of new data, the forecast construction procedure must be repeated from the beginning. The optimal length of the lead-up period is determined separately for each economic process, taking into account its statistical instability.

The most widely used are the methods of smoothing time series using moving averages.

For moving average smoothing, we will use Kendel's formulas to calculate the lost levels at the beginning and end of the smoothed series. Let's prepare the data for using smoothing methods: dates<-seq(as.Date("2021-09-13"), as.Date("2021-10-22"), by="days") str1<-c("13/09/2021","14/09/2021","15/09/2021","16/09/2021","17/09/2021","18/09/2021", "19/09/2021","20/09/2021","21/09/2021","22/09/2021","23/09/2021","24/09/2021", "25/09/2021","26/09/2021","27/09/2021","28/09/2021","29/09/2021","30/09/2021", "01/10/2021","02/10/2021","03/10/2021","04/10/2021","05/10/2021","06/10/2021", "07/10/2021","08/10/2021","09/10/2021","10/10/2021","11/10/2021","12/10/2021", "13/10/2021","14/10/2021","15/10/2021","16/10/2021","17/10/2021","18/10/2021", "19/10/2021","20/10/2021","21/10/2021","22/10/2021") sums<-1:40 k<-1 sum<-0 for(i in 1:7998) { if(videos$date[i]==str1[k]){ videos$date[i]<-str1[k] sum<-sum+videos$views[i] }else if(videos$date[i]==str1[k+1]){ sums[k]<-sum sum<-0 k<-k+1 }

The method of smoothing according to Kendel's formulas: ma$ma1[ 1 ]<-(5*sums[ 1 ]+2*sums[ 2 ]-sums[ 3 ])/6 ma$ma1[40]<-(-sums[38]+2*sums[39]+5*sums[40])/6 ma$ma2[ 1 ]<-(3*sums[ 1 ]+2*sums[ 2 ]+sums[ 3 ]-sums[ 5 ])/5 ma$ma2[ 2 ]<-(4*sums[ 1 ]+3*sums[ 2 ]+2*sums[ 3 ]+sums[ 4 ])/10 ma$ma2[39]<-(4*sums[40]+3*sums[39]+2*sums[38]+sums[37])/10 ma$ma2[40]<-(-sums[36]+sums[38]+2*sums[39]+3*sums[40])/5 ma$ma3[ 1 ]<-(13*sums[ 1 ]+10*sums[ 2 ]+7*sums[ 3 ]+4*sums[ 4 ]+1*sums[ 5 ]-2*sums[ 6 ]-5*sums[ 7 ])/28 ma$ma3[ 2 ]<-(5*sums[ 1 ]+4*sums[ 2 ]+3*sums[ 3 ]+2*sums[ 4 ]+1*sums[ 5 ]+0*sums[ 6 ]-1*sums[ 7 ])/14 ma$ma3[ 3 ]<-(7*sums[ 1 ]+6*sums[ 2 ]+5*sums[ 3 ]+4*sums[ 4 ]+3*sums[ 5 ]+2*sums[ 6 ]+sums[ 7 ])/28 ma$ma3[38]<-(7*sums[34]+6*sums[35]+5*sums[36]+4*sums[37]+3*sums[38]+2*sums[39]+sums[40])/28 ma$ma3[39]<-(5*sums[40]+4*sums[39]+3*sums[38]+2*sums[37]+1*sums[36]+0*sums[35]+1*sums[34])/14 ma$ma3[40]<-(13*sums[40]+10*sums[39]+7*sums[38]+4*sums[37]+sums[36]-2*sums[35]-5*sums[34])/28 ma$ma4[ 1 ]<-(17*sums[ 1 ]+14*sums[ 2 ]+11*sums[ 3 ]+8*sums[ 4 ]+5*sums[ 5 ]+2*sums[ 6 ]-1*sums[ 7 ]-4*sums[ 8 ]-7*sums[ 9 ])/45 ma$ma4[ 2 ]<-(56*sums[ 1 ]+47*sums[ 2 ]+38*sums[ 3 ]+29*sums[ 4 ]+20*sums[ 5 ]+11*sums[ 6 ]+2*sums[ 7 ]-7*sums[ 8 ]-16*sums[ 9 ])/180 ma$ma4[ 3 ]<-(22*sums[ 1 ]+19*sums[ 2 ]+16*sums[ 3 ]+13*sums[ 4 ]+10*sums[ 5 ]+7*sums[ 6 ]+4*sums[ 7 ]+sums[ 8 ]-2*sums[ 9 ])/90 ma$ma4[ 4 ]<-(32*sums[ 1 ]+29*sums[ 2 ]+26*sums[ 3 ]+23*sums[ 4 ]+20*sums[ 5 ]+17*sums[ 6 ]+14*sums[ 7 ]+11*sums[ 8 ]+8*sums[ 9 ])/180 ma$ma4[37]<-(32*sums[40]+29*sums[39]+26*sums[38]+23*sums[37]+20*sums[36]+17*sums[35]+14*sums[34]+11*sums[33]+8*sums[32])/180 ma$ma4[38]<-(22*sums[40]+19*sums[39]+16*sums[38]+13*sums[37]+10*sums[36]+7*sums[35]+4*sums[34]+sums[33]-2*sums[32])/90 ma$ma4[39]<-(56*sums[40]+47*sums[39]+38*sums[38]+29*sums[37]+20*sums[36]+11*sums[35]+2*sums[34]-7*sums[33]-16*sums[32])/180 ma$ma4[40]<-(17*sums[40]+14*sums[39]+11*sums[38]+8*sums[37]+5*sums[36]+2*sums[35]-1*sums[34]-4*sums[33]-7*sums[32])/45 ma$ma5[ 1 ]<-(7*sums[ 1 ]+6*sums[ 2 ]+5*sums[ 3 ]+4*sums[ 4 ]+3*sums[ 5 ]+2*sums[ 6 ]+1*sums[ 7 ]+0*sums[ 8 ]-1*sums[ 9 ]-2*sums[ 10 ]-3*sums[ 11 ])/22 ma$ma5[ 2 ]<-(15*sums[ 1 ]+13*sums[ 2 ]+11*sums[ 3 ]+9*sums[ 4 ]+7*sums[ 5 ]+5*sums[ 6 ]+3*sums[ 7 ]+1*sums[ 8 ]-1*sums[ 9 ]-3*sums[ 10 ]-5*sums[ 11 ])/55 ma$ma5[ 3 ]<-(25*sums[ 1 ]+22*sums[ 2 ]+19*sums[ 3 ]+16*sums[ 4 ]+13*sums[ 5 ]+10*sums[ 6 ]+7*sums[ 7 ]+4*sums[ 8 ]+sums[ 9 ]-2*sums[ 10 ]-5*sums[ 11 ])/110 ma$ma5[ 4 ]<-(10*sums[ 1 ]+9*sums[ 2 ]+8*sums[ 3 ]+7*sums[ 4 ]+6*sums[ 5 ]+5*sums[ 6 ]+4*sums[ 7 ]+3*sums[ 8 ]+2*sums[ 9 ]+1*sums[ 10 ]+0*sums[ 11 ])/55 ma$ma5[ 5 ]<-(15*sums[ 1 ]+14*sums[ 2 ]+13*sums[ 3 ]+12*sums[ 4 ]+11*sums[ 5 ]+10*sums[ 6 ]+9*sums[ 7 ]+8*sums[ 8 ]+7*sums[ 9 ]+6*sums[ 10 ]+5*sums[ 11 ])/110 ma$ma5[36]<-(15*sums[40]+14*sums[39]+13*sums[38]+12*sums[37]+11*sums[37]+10*sums[36]+9*sums[35]+8*sums[34]+7*sums[33]+6*sums[32]+5*sums[31])/110 ma$ma5[37]<-(10*sums[40]+9*sums[39]+8*sums[38]+7*sums[37]+6*sums[37]+5*sums[36]+4*sums[35]+3*sums[34]+2*sums[33]+1*sums[32]+0*sums[31])/55 ma$ma5[38]<-(25*sums[40]+22*sums[39]+19*sums[38]+16*sums[37]+13*sums[37]+10*sums[36]+7*sums[35]+4*sums[34]+sums[33]-2*sums[32]-5*sums[31])/110 ma$ma5[39]<-(15*sums[40]+13*sums[39]+11*sums[38]+9*sums[37]+7*sums[37]+5*sums[36]+3*sums[35]+1*sums[34]-1*sums[33]-3*sums[32]-5*sums[31])/55 ma$ma5[40]<-(7*sums[40]+6*sums[39]+5*sums[38]+4*sums[37]+3*sums[37]+2*sums[36]+1*sums[35]+0*sums[34]-1*sums[33]-2*sums[32]-3*sums[31])/22 ma$ma6[ 1 ]<-(25*sums[ 1 ]+22*sums[ 2 ]+19*sums[ 3 ]+16*sums[ 4 ]+13*sums[ 5 ]+10*sums[ 6 ]+7*sums[ 7 ]+4*sums[ 8 ]+1*sums[ 9 ]-2*sums[ 10 ]-5*sums[ 11 ]-8*sums[ 12 ]-11*sums[ 13 ])/91 ma$ma6[ 2 ]<-(44*sums[ 1 ]+39*sums[ 2 ]+34*sums[ 3 ]+29*sums[ 4 ]+24*sums[ 5 ]+19*sums[ 6 ]+14*sums[ 7 ]+9*sums[ 8 ]+4*sums[ 9 ]-1*sums[ 10 ]-6*sums[ 11 ]-11*sums[ 12 ]-15*sums[ 13 ])/182 ma$ma6[ 3 ]<-(19*sums[ 1 ]+17*sums[ 2 ]+15*sums[ 3 ]+13*sums[ 4 ]+11*sums[ 5 ]+9*sums[ 6 ]+7*sums[ 7 ]+5*sums[ 8 ]+3*sums[ 9 ]+1*sums[ 10 ]-1*sums[ 11 ]-3*sums[ 12 ]-5*sums[ 13 ])/91 ma$ma6[ 4 ]<-(32*sums[ 1 ]+29*sums[ 2 ]+26*sums[ 3 ]+23*sums[ 4 ]+20*sums[ 5 ]+17*sums[ 6 ]+14*sums[ 7 ]+11*sums[ 8 ]+8*sums[ 9 ]+5*sums[ 10 ]+2*sums[ 11 ]-1*sums[ 12 ]-4*sums[ 13 ])/182 ma$ma6[ 5 ]<-(13*sums[ 1 ]+12*sums[ 2 ]+11*sums[ 3 ]+10*sums[ 4 ]+9*sums[ 5 ]+8*sums[ 6 ]+7*sums[ 7 ]+6*sums[ 8 ]+5*sums[ 9 ]+4*sums[ 10 ]+3*sums[ 11 ]+2*sums[ 1 2 ]+1*sums[ 13 ])/91 ma$ma6[ 6 ]<-(20*sums[ 1 ]+19*sums[ 2 ]+18*sums[ 3 ]+17*sums[ 4 ]+16*sums[ 5 ]+15*sums[ 6 ]+14*sums[ 7 ]+13*sums[ 8 ]+12*sums[ 9 ]+11*sums[ 10 ]+10*sums[ 11 ]+9*sums[ 12 ]+8*sums[ 13 ])/182 ma$ma6[40]<-(25*sums[40]+22*sums[39]+19*sums[38]+16*sums[37]+13*sums[36]+10*sums[35]+7*sums[34]+4*sums[33]+1*sums[32]-2*sums[31]-5*sums[30]-8*sums[29]11*sums[28])/91 ma$ma6[39]<-(44*sums[40]+39*sums[39]+34*sums[38]+29*sums[37]+24*sums[36]+19*sums[35]+14*sums[34]+9*sums[33]+4*sums[32]-1*sums[31]-6*sums[30]-11*sums[29]15*sums[28])/182 ma$ma6[38]<-(19*sums[40]+17*sums[39]+15*sums[38]+13*sums[37]+11*sums[36]+9*sums[35]+7*sums[34]+5*sums[33]+3*sums[32]+1*sums[31]-1*sums[30]-3*sums[29]-5*sums[28])/91 ma$ma6[37]<-(32*sums[40]+29*sums[39]+26*sums[38]+23*sums[37]+20*sums[36]+17*sums[35]+14*sums[34]+11*sums[33]+8*sums[32]+5*sums[31]+2*sums[30]-1*sums[29]4*sums[28])/182 ma$ma6[36]<-(13*sums[40]+12*sums[39]+11*sums[38]+10*sums[37]+9*sums[36]+8*sums[35]+7*sums[34]+6*sums[33]+5*sums[32]+4*sums[31]+3*sums[30]+2*sums[29]+1*sums[28])/91 ma$ma6[35]<(20*sums[40]+19*sums[39]+18*sums[38]+17*sums[37]+16*sums[36]+15*sums[35]+14*sums[34]+13*sums[33]+12*sums[32]+11*sums[31]+10*sums[30]+9*sums[29]+8*sums[28])/182 ma$ma7[ 1 ]<-(29*sums[ 1 ]+26*sums[ 2 ]+23*sums[ 3 ]+20*sums[ 4 ]+17*sums[ 5 ]+14*sums[ 6 ]+11*sums[ 7 ]+8*sums[ 8 ]+5*sums[ 9 ]+2*sums[ 10 ]-1*sums[ 11 ]-4*sums[ 12 ]-7*sums[ 13 ]10*sums[ 14 ]-13*sums[ 15 ])/120 ma$ma7[ 2 ]<-(91*sums[ 1 ]+82*sums[ 2 ]+73*sums[ 3 ]+64*sums[ 4 ]+55*sums[ 5 ]+46*sums[ 6 ]+37*sums[ 7 ]+28*sums[ 8 ]+19*sums[ 9 ]+10*sums[ 10 ]+1*sums[ 11 ]-8*sums[ 12 ]-17*sums[ 13 ]26*sums[ 14 ]-35*sums[ 15 ])/420 ma$ma7[ 3 ]<-(161*sums[ 1 ]+146*sums[ 2 ]+131*sums[ 3 ]+116*sums[ 4 ]+101*sums[ 5 ]+86*sums[ 6 ]+71*sums[ 7 ]+56*sums[ 8 ]+41*sums[ 9 ]+26*sums[ 10 ]+11*sums[ 11 ]-4*sums[ 12 ]-19*sums[ 13 ]34*sums[ 14 ]-49*sums[ 15 ])/840 ma$ma7[ 4 ]<-(35*sums[ 1 ]+32*sums[ 2 ]+29*sums[ 3 ]+26*sums[ 4 ]+23*sums[ 5 ]+20*sums[ 6 ]+17*sums[ 7 ]+14*sums[ 8 ]+11*sums[ 9 ]+8*sums[ 10 ]+5*sums[ 11 ]+2*sums[ 12 ]-1*sums[ 13 ]4*sums[ 14 ]-7*sums[ 15 ])/210 ma$ma7[ 5 ]<(119*sums[ 1 ]+110*sums[ 2 ]+101*sums[ 3 ]+92*sums[ 4 ]+83*sums[ 5 ]+74*sums[ 6 ]+65*sums[ 7 ]+56*sums[ 8 ]+47*sums[ 9 ]+38*sums[ 10 ]+29*sums[ 11 ]+20*sums[ 12 ]+11*sums[ 13 ]+2*sums[ 14 ]7*sums[ 15 ])/840 ma$ma7[ 6 ]<(49*sums[ 1 ]+46*sums[ 2 ]+43*sums[ 3 ]+40*sums[ 4 ]+37*sums[ 5 ]+34*sums[ 6 ]+31*sums[ 7 ]+28*sums[ 8 ]+25*sums[ 9 ]+22*sums[ 10 ]+19*sums[ 11 ]+1 6*sums[ 12 ]+13*sums[ 13 ]+10*sums[ 14 ]+7*su ms[ 15 ])/420 ma$ma7[ 7 ]<(77*sums[ 1 ]+74*sums[ 2 ]+71*sums[ 3 ]+68*sums[ 4 ]+65*sums[ 5 ]+62*sums[ 6 ]+59*sums[ 7 ]+56*sums[ 8 ]+53*sums[ 9 ]+52*sums[ 10 ]+49*sums[ 11 ]+46*sums[ 12 ]+43*sums[ 13 ]+40*sums[ 14 ]+37*s ums[ 15 ])/840 ma$ma7[40]<-(29*sums[40]+26*sums[39]+23*sums[38]+20*sums[37]+17*sums[36]+14*sums[35]+11*sums[34]+8*sums[33]+5*sums[ 2 ]+2*sums[ 10 ]-1*sums[ 9 ]-4*sums[ 12 ]-7*sums[ 13 ]10*sums[ 14 ]-13*sums[ 15 ])/120 ma$ma7[39]<-(91*sums[40]+82*sums[39]+73*sums[38]+64*sums[37]+55*sums[36]+46*sums[35]+37*sums[34]+28*sums[33]+19*sums[32]+10*sums[31]+1*sums[30]-8*sums[29]17*sums[28]-26*sums[27]-35*sums[26])/420 ma$ma7[38]<-(161*sums[40]+146*sums[39]+131*sums[38]+116*sums[37]+101*sums[36]+86*sums[35]+71*sums[34]+56*sums[33]+41*sums[32]+26*sums[31]+11*sums[30]-4*sums[29]19*sums[28]-34*sums[27]-49*sums[26])/840 ma$ma7[37]<-(35*sums[40]+32*sums[39]+29*sums[38]+26*sums[37]+23*sums[36]+20*sums[35]+17*sums[34]+14*sums[33]+11*sums[32]+8*sums[31]+5*sums[30]+2*sums[29]1*sums[28]-4*sums[27]-7*sums[26])/210 ma$ma7[36]<(119*sums[40]+110*sums[39]+101*sums[38]+92*sums[37]+83*sums[36]+74*sums[35]+65*sums[34]+56*sums[33]+47*sums[32]+38*sums[31]+29*sums[30]+20*sums[29]+11*sums[28]+2*su ms[27]-7*sums[26])/840 ma$ma7[35]<(49*sums[40]+46*sums[39]+43*sums[38]+40*sums[37]+37*sums[36]+34*sums[35]+33*sums[34]+30*sums[33]+27*sums[32]+24*sums[31]+21*sums[30]+18*sums[29]+15*sums[28]+12*sums [27]+9*sums[26])/420 ma$ma7[34]<(77*sums[40]+74*sums[39]+71*sums[38]+68*sums[37]+65*sums[36]+61*sums[35]+58*sums[34]+55*sums[33]+52*sums[32]+49*sums[31]+46*s ums[30]+43*sums[29]+40*sums[28]+37*sums [27]+34*sums[26])/840

Data visualization:

ma %>% gather(metric, sums, ma1:ma7) %>% ggplot(aes(dates,sums, color = metric)) + geom_line(size=1)

Visualization of the moving average at k=5: ggplot(viewh,mapping= aes(x=dates)) + geom_line(mapping= aes(y=likes, col="Real"),lwd=1.5) + geom_line(mapping= aes(y=ma$ma2, col="ma2"),lwd=1.5)+scale_color_manual(values= c("Real"="blue","ma2"="red"))+ theme(legend.title = element_blank()) + labs(x="",y="Likes")

Finding turning points:

tp1 <- turnpoints(ma$ma1) summary(tp1) tp2 <- turnpoints(ma$ma2)

Visualization of turning points: We are looking for the correlation coefficients of the smoothed values with the original ones, taking into account the fact that with each smoothing we subtract rows :

cor(viewh$views,ma$ma7)

Similarly, we do research for likes and dislikes. To implement Pollard's formula, we will use the built-in method wma(): wma <- viewh %>% select(dates, views) %>% mutate(wma1 = WMA(views, n = 3, wts = 1:3), wma2 = WMA(views, n = 5, wts = 1:5), wma3 = WMA(views, n = 7, wts = 1:7), wma4 = WMA(views, n = 9, wts = 1:9), wma5 = WMA(views, n = 11, wts = 1:11), wma6 = WMA(views, n = 13, wts = 1:13), wma7 = WMA(views, n = 15, wts = 1:15))

Using Kendel's formulas: sums<-views wma$wma1[ 1 ]<-(5*sums[ 1 ]+2*sums[ 2 ]-sums[ 3 ])/6 wma$wma1[ 2 ]<-(-sums[38]+2*sums[39]+5*sums[40])/6 wma$wma2[ 1 ]<-(3*sums[ 1 ]+2*sums[ 2 ]+sums[ 3 ]-sums[ 5 ])/5 wma$wma2[ 2 ]<-(4*sums[ 1 ]+3*sums[ 2 ]+2*sums[ 3 ]+sums[ 4 ])/10 wma$wma2[ 3 ]<-(4*sums[40]+3*sums[39]+2*sums[38]+sums[37])/10 wma$wma2[ 4 ]<-(-sums[36]+sums[38]+2*sums[39]+3*sums[40])/5 wma$wma3[ 1 ]<-(13*sums[ 1 ]+10*sums[ 2 ]+7*sums[ 3 ]+4*sums[ 4 ]+1*sums[ 5 ]-2*sums[ 6 ]-5*sums[ 7 ])/28 wma$wma3[ 2 ]<-(5*sums[ 1 ]+4*sums[ 2 ]+3*sums[ 3 ]+2*sums[ 4 ]+1*sums[ 5 ]+0*sums[ 6 ]-1*sums[ 7 ])/14 wma$wma3[ 3 ]<-(7*sums[ 1 ]+6*sums[ 2 ]+5*sums[ 3 ]+4*sums[ 4 ]+3*sums[ 5 ]+2*sums[ 6 ]+sums[ 7 ])/28 wma$wma3[ 4 ]<-(7*sums[34]+6*sums[35]+5*sums[36]+4*sums[37]+3*sums[38]+2*sums[39]+sums[40])/28 wma$wma3[ 5 ]<-(5*sums[40]+4*sums[39]+3*sums[38]+2*sums[37]+1*sums[36]+0*sums[35]+1*sums[34])/14 wma$wma3[ 6 ]<-(13*sums[40]+10*sums[39]+7*sums[38]+4*sums[37]+sums[36]-2*sums[35]-5*sums[34])/28 wma$wma4[ 1 ]<-(17*sums[ 1 ]+14*sums[ 2 ]+11*sums[ 3 ]+8*sums[ 4 ]+5*sums[ 5 ]+2*sums[ 6 ]-1*sums[ 7 ]-4*sums[ 8 ]-7*sums[ 9 ])/45 wma$wma4[ 2 ]<-(56*sums[ 1 ]+47*sums[ 2 ]+38*sums[ 3 ]+29*sums[ 4 ]+20*sums[ 5 ]+11*sums[ 6 ]+2*sums[ 7 ]-7*sums[ 8 ]-16*sums[ 9 ])/180 wma$wma4[ 3 ]<-(22*sums[ 1 ]+19*sums[ 2 ]+16*sums[ 3 ]+13*sums[ 4 ]+10*sums[ 5 ]+7*sums[ 6 ]+4*sums[ 7 ]+sums[ 8 ]-2*sums[ 9 ])/90 wma$wma4[ 4 ]<-(32*sums[ 1 ]+29*sums[ 2 ]+26*sums[ 3 ]+23*sums[ 4 ]+20*sums[ 5 ]+17*sums[ 6 ]+14*sums[ 7 ]+11*sums[ 8 ]+8*sums[ 9 ])/180 wma$wma4[ 5 ]<-(32*sums[40]+29*sums[39]+26*sums[38]+23*sums[37]+20*sums[36]+17*sums[35]+14*sums[34]+11*sums[33]+8*sums[32])/180 wma$wma4[ 6 ]<-(22*sums[40]+19*sums[39]+16*sums[38]+13*sums[37]+10*sums[36]+7*sums[35]+4*sums[34]+sums[33]-2*sums[32])/90 wma$wma4[ 7 ]<-(56*sums[40]+47*sums[39]+38*sums[38]+29*sums[37]+20*sums[36]+11*sums[35]+2*sums[34]-7*sums[33]-16*sums[32])/180 wma$wma4[ 8 ]<-(17*sums[40]+14*sums[39]+11*sums[38]+8*sums[37]+5*sums[36]+2*sums[35]-1*sums[34]-4*sums[33]-7*sums[32])/45 wma$wma5[ 1 ]<-(7*sums[ 1 ]+6*sums[ 2 ]+5*sums[ 3 ]+4*sums[ 4 ]+3*sums[ 5 ]+2*sums[ 6 ]+1*sums[ 7 ]+0*sums[ 8 ]-1*sums[ 9 ]-2*sums[ 10 ]-3*sums[ 11 ])/22 wma$wma5[ 2 ]<-(15*sums[ 1 ]+13*sums[ 2 ]+11*sums[ 3 ]+9*sums[ 4 ]+7*sums[ 5 ]+5*sums[ 6 ]+3*sums[ 7 ]+1*sums[ 8 ]-1*sums[ 9 ]-3*sums[ 10 ]-5*sums[ 11 ])/55 wma$wma5[ 3 ]<-(25*sums[ 1 ]+22*sums[ 2 ]+19*sums[ 3 ]+16*sums[ 4 ]+13*sums[ 5 ]+10*sums[ 6 ]+7*sums[ 7 ]+4*sums[ 8 ]+sums[ 9 ]-2*sums[ 10 ]-5*sums[ 11 ])/110 wma$wma5[ 4 ]<-(10*sums[ 1 ]+9*sums[ 2 ]+8*sums[ 3 ]+7*sums[ 4 ]+6*sums[ 5 ]+5*sums[ 6 ]+4*sums[ 7 ]+3*sums[ 8 ]+2*sums[ 9 ]+1*sums[ 10 ]+0*sums[ 11 ])/55 wma$wma5[ 5 ]<-(15*sums[ 1 ]+14*sums[ 2 ]+13*sums[ 3 ]+12*sums[ 4 ]+11*sums[ 5 ]+10*sums[ 6 ]+9*sums[ 7 ]+8*sums[ 8 ]+7*sums[ 9 ]+6*sums[ 10 ]+5*sums[ 11 ])/110 wma$wma5[ 6 ]<-(15*sums[40]+14*sums[39]+13*sums[38]+12*sums[37]+11*sums[37]+10*sums[36]+9*sums[35]+8*sums[34]+7*sums[33]+6*sums[32]+5*sums[3 1])/110 wma$wma5[ 7 ]<-(10*sums[40]+9*sums[39]+8*sums[38]+7*sums[37]+6*sums[37]+5*sums[36]+4*sums[35]+3*sums[34]+2*sums[33]+1*sums[32]+0*sums[31])/5 5 wma$wma5[ 8 ]<-(25*sums[40]+22*sums[39]+19*sums[38]+16*sums[37]+13*sums[37]+10*sums[36]+7*sums[35]+4*sums[34]+sums[33]-2*sums[32]-5*sums[31])/110 wma$wma5[ 9 ]<-(15*sums[40]+13*sums[39]+11*sums[38]+9*sums[37]+7*sums[37]+5*sums[36]+3*sums[35]+1*sums[34]-1*sums[33]-3*sums[32]-5*sums[31])/55 wma$wma5[ 10 ]<-(7*sums[40]+6*sums[39]+5*sums[38]+4*sums[37]+3*sums[37]+2*sums[36]+1*sums[35]+0*sums[34]-1*sums[33]-2*sums[32]-3*sums[31])/22 wma$wma6[ 1 ]<-(25*sums[ 1 ]+22*sums[ 2 ]+19*sums[ 3 ]+16*sums[ 4 ]+13*sums[ 5 ]+10*sums[ 6 ]+7*sums[ 7 ]+4*sums[ 8 ]+1*sums[ 9 ]-2*sums[ 10 ]-5*sums[ 11 ]-8*sums[ 12 ]-11*sums[ 13 ])/91 wma$wma6[ 2 ]<-(44*sums[ 1 ]+39*sums[ 2 ]+34*sums[ 3 ]+29*sums[ 4 ]+24*sums[ 5 ]+19*sums[ 6 ]+14*sums[ 7 ]+9*sums[ 8 ]+4*sums[ 9 ]-1*sums[ 10 ]-6*sums[ 11 ]-11*sums[ 12 ]-15*sums[ 13 ])/182 wma$wma6[ 3 ]<-(19*sums[ 1 ]+17*sums[ 2 ]+15*sums[ 3 ]+13*sums[ 4 ]+11*sums[ 5 ]+9*sums[ 6 ]+7*sums[ 7 ]+5*sums[ 8 ]+3*sums[ 9 ]+1*sums[ 10 ]-1*sums[ 11 ]-3*sums[ 12 ]-5*sums[ 13 ])/91 wma$wma6[ 4 ]<-(32*sums[ 1 ]+29*sums[ 2 ]+26*sums[ 3 ]+23*sums[ 4 ]+20*sums[ 5 ]+17*sums[ 6 ]+14*sums[ 7 ]+11*sums[ 8 ]+8*sums[ 9 ]+5*sums[ 10 ]+2*sums[ 11 ]-1*sums[ 12 ]-4*sums[ 13 ])/182 wma$wma6[ 5 ]<-(13*sums[ 1 ]+12*sums[ 2 ]+11*sums[ 3 ]+10*sums[ 4 ]+9*sums[ 5 ]+8*sums[ 6 ]+7*sums[ 7 ]+6*sums[ 8 ]+5*sums[ 9 ]+4*sums[ 10 ]+3*sums[ 11 ]+2*sums[ 1 2 ]+1*sums[ 13 ])/91 wma$wma6[ 6 ]<-(20*sums[ 1 ]+19*sums[ 2 ]+18*sums[ 3 ]+17*sums[ 4 ]+16*sums[ 5 ]+15*sums[ 6 ]+14*sums[ 7 ]+13*sums[ 8 ]+12*sums[ 9 ]+11*sums[ 10 ]+10*sums[ 11 ]+9 *sums[ 12 ]+8*sums[ 13 ])/182 wma$wma6[ 7 ]<-(25*sums[40]+22*sums[39]+19*sums[38]+16*sums[37]+13*sums[36]+10*sums[35]+7*sums[34]+4*sums[33]+1*sums[32]-2*sums[31]-5*sums[30]-8*sums[29]11*sums[28])/91 wma$wma6[ 8 ]<-(44*sums[40]+39*sums[39]+34*sums[38]+29*sums[37]+24*sums[36]+19*sums[35]+14*sums[34]+9*sums[33]+4*sums[32]-1*sums[31]-6*sums[30]-11*sums[29]15*sums[28])/182 wma$wma6[ 9 ]<-(19*sums[40]+17*sums[39]+15*sums[38]+13*sums[37]+11*sums[36]+9*sums[35]+7*sums[34]+5*sums[33]+3*sums[32]+1*sums[31]-1*sums[30]-3*sums[29]5*sums[28])/91 wma$wma6[ 10 ]<-(32*sums[40]+29*sums[39]+26*sums[38]+23*sums[37]+20*sums[36]+17*sums[35]+14*sums[34]+11*sums[33]+8*sums[32]+5*sums[31]+2*sums[30]-1*sums[29]4*sums[28])/182 wma$wma6[ 11 ]<(13*sums[40]+12*sums[39]+11*sums[38]+10*sums[37]+9*sums[36]+8*sums[35]+7*sums[34]+6*sums[33]+5*sums[32]+4*sums[31]+3*sums[30] +2*sums[29]+1*sums[28])/91 wma$wma6[ 12 ]<(20*sums[40]+19*sums[39]+18*sums[38]+17*sums[37]+16*sums[36]+15*sums[35]+14*sums[34]+13*sums[33]+12*sums[32]+11*sums[31]+10*sums[ 30]+9*sums[29]+8*sums[28])/182 wma$wma7[ 1 ]<-(29*sums[ 1 ]+26*sums[ 2 ]+23*sums[ 3 ]+20*sums[ 4 ]+17*sums[ 5 ]+14*sums[ 6 ]+11*sums[ 7 ]+8*sums[ 8 ]+5*sums[ 9 ]+2*sums[ 10 ]-1*sums[ 11 ]-4*sums[ 12 ]-7*sums[ 13 ]10*sums[ 14 ]-13*sums[ 15 ])/120 wma$wma7[ 2 ]<-(91*sums[ 1 ]+82*sums[ 2 ]+73*sums[ 3 ]+64*sums[ 4 ]+55*sums[ 5 ]+46*sums[ 6 ]+37*sums[ 7 ]+28*sums[ 8 ]+19*sums[ 9 ]+10*sums[ 10 ]+1*sums[ 11 ]-8*sums[ 12 ]-17*sums[ 13 ]26*sums[ 14 ]-35*sums[ 15 ])/420 wma$wma7[ 3 ]<-(161*sums[ 1 ]+146*sums[ 2 ]+131*sums[ 3 ]+116*sums[ 4 ]+101*sums[ 5 ]+86*sums[ 6 ]+71*sums[ 7 ]+56*sums[ 8 ]+41*sums[ 9 ]+26*sums[ 10 ]+11*sums[ 11 ]-4*sums[ 12 ]19*sums[ 13 ]-34*sums[ 14 ]-49*sums[ 15 ])/840 wma$wma7[ 4 ]<-(35*sums[ 1 ]+32*sums[ 2 ]+29*sums[ 3 ]+26*sums[ 4 ]+23*sums[ 5 ]+20*sums[ 6 ]+17*sums[ 7 ]+14*sums[ 8 ]+11*sums[ 9 ]+8*sums[ 10 ]+5*sums[ 11 ]+2*sums[ 12 ]-1*sums[ 13 ]4*sums[ 14 ]-7*sums[ 15 ])/210 wma$wma7[ 5 ]<(119*sums[ 1 ]+110*sums[ 2 ]+101*sums[ 3 ]+92*sums[ 4 ]+83*sums[ 5 ]+74*sums[ 6 ]+65*sums[ 7 ]+56*sums[ 8 ]+47*sums[ 9 ]+38*sums[ 10 ]+29*sums[ 11 ]+20*sums[ 12 ]+11*sums[ 13 ]+2*sums[ 14 ]7*sums[ 15 ])/840 wma$wma7[ 6 ]<(49*sums[ 1 ]+46*sums[ 2 ]+43*sums[ 3 ]+40*sums[ 4 ]+37*sums[ 5 ]+34*sums[ 6 ]+31*sums[ 7 ]+28*sums[ 8 ]+25*sums[ 9 ]+22*sums[ 10 ]+19*sums[ 11 ]+1 6*sums[ 12 ]+13*sums[ 13 ]+10*sums[ 14 ]+7*su ms[ 15 ])/420 wma$wma7[ 7 ]<(77*sums[ 1 ]+74*sums[ 2 ]+71*sums[ 3 ]+68*sums[ 4 ]+65*sums[ 5 ]+62*sums[ 6 ]+59*sums[ 7 ]+56*sums[ 8 ]+53*sums[ 9 ]+52*sums[ 10 ]+49*sums[ 11 ]+46*sums[ 12 ]+43*sums[ 13 ]+40*sums[ 14 ]+37*s ums[ 15 ])/840 wma$wma7[ 8 ]<-(29*sums[40]+26*sums[39]+23*sums[38]+20*sums[37]+17*sums[36]+14*sums[35]+11*sums[34]+8*sums[33]+5*sums[ 2 ]+2*sums[ 10 ]-1*sums[ 9 ]-4*sums[ 12 ]-7*sums[ 13 ]10*sums[ 14 ]-13*sums[ 15 ])/120 wma$wma7[ 9 ]<-(91*sums[40]+82*sums[39]+73*sums[38]+64*sums[37]+55*sums[36]+46*sums[35]+37*sums[34]+28*sums[33]+19*sums[32]+10*sums[31]+1*sums[30]-8*sums[29]17*sums[28]-26*sums[27]-35*sums[26])/420 wma$wma7[ 10 ]<-(161*sums[40]+146*sums[39]+131*sums[38]+116*sums[37]+101*sums[36]+86*sums[35]+71*sums[34]+56*sums[33]+41*sums[32]+26*sums[31]+11*sums[30]-4*sums[29]19*sums[28]-34*sums[27]-49*sums[26])/840 wma$wma7[ 11 ]<-(35*sums[40]+32*sums[39]+29*sums[38]+26*sums[37]+23*sums[36]+20*sums[35]+17*sums[34]+14*sums[33]+11*sums[32]+8*sums[31]+5*sums[30]+2*sums[29]1*sums[28]-4*sums[27]-7*sums[26])/210 wma$wma7[ 12 ]<(119*sums[40]+110*sums[39]+101*sums[38]+92*sums[37]+83*sums[36]+74*sums[35]+65*sums[34]+56*sums[33]+47*sums[32]+38*sums[31]+29*sums[30]+20*sums[29]+11*sums[28]+2*su ms[27]-7*sums[26])/840 wma$wma7[ 13 ]<(49*sums[40]+46*sums[39]+43*sums[38]+40*sums[37]+37*sums[36]+34*sums[35]+33*sums[34]+30*sums[33]+27*sums[32]+24*sums[31]+21*sums[30]+18*sums[29]+15*sums[28]+12*sums [27]+9*sums[26])/420 wma$wma7[ 14 ]<(77*sums[40]+74*sums[39]+71*sums[38]+68*sums[37]+65*sums[36]+61*sums[35]+58*sums[34]+55*sums[33]+52*sums[32]+49*sums[31]+46*sums[30]+43*sums[29]+40*sums[28]+37*sums [27]+34*sums[26])/840

Visualization of all graphs:

wma %>% gather(metric, views, views:wma7) %>% ggplot(aes(dates, views, color = metric)) + geom_line(size=1)

Graph visualization of real data and weighted data:

ggplot(viewh,mapping= aes(x=dates)) + geom_line(mapping= aes(y=views, col="Real"),lwd=1.5) + geom_line(mapping= aes(y=wma$wma2, col="ma2"),lwd=1.5)+ scale_color_manual(values= c("Real"="blue","ma2"="red"))+ theme(legend.title = element_blank()) + labs(x="",y="Likes")

Turning points: tp1 <- turnpoints(wma$wma1) summary(tp1) tp2 <- turnpoints(wma$wma2) summary(tp2) tp3 <- turnpoints(wma$wma3) summary(tp3) tp4 <- turnpoints(wma$wma4) summary(tp4) tp5 <- turnpoints(wma$wma5) summary(tp5) tp6 <- turnpoints(wma$wma6) summary(tp6) tp7 <- turnpoints(wma$wma7) summary(tp7)

Visualization of turning points:

plot(wma$wma1, type = "l") lines(tp1)

Correlation coefficients of weighted smoothed data with the original: cor(wma$views,wma$wma1) cor(wma$views,wma$wma2) cor(wma$views,wma$wma3) cor(wma$views,wma$wma4) cor(wma$views,wma$wma5) cor(wma$views,wma$wma6) cor(wma$views,wma$wma7)

Exponential smoothing: alpha<-0.1 sums<-views exp_smooth<-1:40 exp_smooth[ 1 ]<-sums[ 1 ] for(i in 2:40){

exp_smooth[i]<-sums[i]*alpha +(1-alpha)*exp_smooth[i-1] } viewh<-data.frame(dates,sums,exp_smooth) #save date into structure

Visualization:

ggplot(viewh,mapping= aes(x=dates)) + geom_line(mapping= aes(y=sums, col="Real"),lwd=1.5) + geom_line(mapping= aes(y=exp_smooth, col="es"),lwd=1.5)+ scale_color_manual(values= c("Real"="blue","es"="red"))+ labs(x="",y="Views",title ="alpha = 0.3")+ theme(legend.title = element_blank(),plot.title = element_text(hjust = 0.5))

Turning points:

tp_es<-turnpoints(exp_smooth) summary(tp_es)

Visualization of turning points:

plot(views, type = "l") lines(tp_es)

Correlation coefficient of smoothed and real values: cor(views,exp_smooth) Median filtering

med_fil<-1:40 med_fil[ 1 ]<-(5*sums[ 1 ]+2*sums[ 2 ]-sums[ 3 ])/6 med_fil[40]<-(-sums[38]+2*sums[39]+5*sums[40])/6 for(i in 2:39){med_fil[i]<-max(min(sums[i-1],sums[i]),min(sums[i],sums[i+1]),min(sums[i-1],sums[i+1]))} viewh<-data.frame(dates,views,med_fil)

Visualization:

ggplot(viewh,mapping= aes(x=dates)) + geom_line(mapping= aes(y=views, col="Real"),lwd=1.5) + geom_line(mapping= aes(y=med_fil, col="Median"),lwd=1.5)+ scale_color_manual(values= c("Real"="blue","Median"="red"))+ labs(x="",y="Views",title ="Median filter")+ theme(legend.title = element_blank(),plot.title = element_text(hjust = 0.5))

Turning points:

tp_mf<-turnpoints(med_fil) summary(tp_mf) plot(views, type = "l") lines(tp_mf)

Visualization of turning points: Correlation coefficient: cor(views,med_fil)

In general, correlation can be described as any statistical relationship of data. Correlation allows us to see the trends of changes in the average values of the functions depending on the parameter changes. Correlation can be positive or negative. Negative correlation is a correlation in which an increase in one variable is associated with a decrease in another, and the correlation coefficient is negative. Positive correlation is a correlation in which an increase in one variable is associated with an increase in another, and the correlation coefficient is positive.

Construction of the correlation field (plot)

plot(dt$likes, dt$dislikes, main="Correlation field",xlab="Likes", ylab="Dislikes") Correlation coefficient: cor(dt$views, dt$dislikes)

Correlation relation:

ggscatter(dt, x = 'likes', y = 'dislikes', add = "reg.line", conf.int = TRUE, cor.coef = TRUE, cor.method = "pearson", xlab = "Likes", ylab = "Dislikes")

Construction of graphs of autocorrelation functions:

data <- cbind(dt$likes, dt$dislikes) colnames(data) <- c("Likes", "Dislikes") autocorelation <- acf(data, lag.max = 1,type = c("correlation"), plot = TRUE, xlab="Likes", ylab="Dislikes")

Separation of data into 3 parts:

part1 <- dt$likes[1:2666] part2 <- dt$likes[2667:5332] part3 <- dt$likes[5333:7998]

A correlation matrix was constructed for the parts (rcorr): Finding multiple correlation coefficients:

mydata.rcorr = rcorr(as.matrix(cbind(part1, part2, part3))) numericData <- cbind(dt$id, dt$views, dt$likes, dt$dislikes, dt$category_id, dt$comment_total) chart.Correlation(numericData, histogram=TRUE, pch=19)

Cluster analysis itself is not a separate algorithm, but a general task that needs to be solved. Therefore, this general task consists in grouping objects in such a way that the grouped objects are more similar to each other compared to other grouped objects, and the given groups are called clusters, and to conduct an analysis of these clusters through experiments. This analysis can be carried out with the help of different algorithms, although the concept of a "cluster" and how to find it can differ greatly between these algorithms, it is the understanding of the cluster model of this or that algorithm that is the key stage to a successful research analysis. Construction of a graphical representation of clustering:

K-means clustering and clustering matrix:

set.seed(55) cluster <- kmeans(cbind(dt$channel_title, dt$dislikes), 4, nstart = 20) cluster table(cluster$cluster, dt$category_id)

Construction of a dendrogram:

rdata <- cbind(dt$category_id) rdata <- na.omit(rdata) data.hclust = hclust(dist(rdata), method = "single") plot(data.hclust, labels = FALSE, hang = -1)

5. Results Display likes and dislikes on a graph over time:

From the graph, you can already see a slight dependence between the number of likes and dislikes. Using Kendel's formulas, we obtained initial and final values that were lost in the calculation of averages, depending on the average by which we calculate the data. It can be noted that ma4, ma5, ma6, ma7 are not very suitable for identifying trends, since we do not have a large date interval, only 40 days.

For more accurate detection of trends, it is advisable to take ma1, ma2 or ma3.

This graph clearly shows when we have a trend change. The correlation coefficients are quite large and positive, which is logical, since they directly depend on the data.

It can be noted that ma4, ma5, ma6, ma7 are not very suitable for identifying trends, since we do not have a large date interval, only 40 days. For more accurate detection of trends, it is advisable to take ma1, ma2 or ma3.

The number of turning points allows better analysis of trends. As we can see, the trends of the views attribute are best viewed. This is due to the peculiarity of the data. Correlation coefficients are close to 1 and decrease as the step increases, as less and less data will affect the average. As in the case of a simple moving average, for our data it is better not to use averages with a step greater than 7 to get more accurate information. We can notice a noticeable difference between the graphs of the simple moving average and the weighted moving average. This is due to the fact that the weighted moving average reacts to changes more quickly than the simple moving average. This may allow us to predict, although the results will be quite imprecise, as smoothing methods are not designed to predict.

Compared to a simple moving average chart, we can say that the weighted moving average is more suitable for spotting trends in a time series.

As the step increases, the correlation coefficient decreases, since the values have less influence on the average. Exponential smoothing directly depends on the latest data, i.e. how the weighted average will react quickly to changes.

Median smoothing completely removes single extreme or anomalous values of levels that are separated from each other by at least half of the smoothing interval; preserves sharp changes in the trend (moving average and exponential smoothing smooth them); effectively removes single levels with very large or very small values that are random in nature and stand out sharply from other levels.

As can be seen from fig. 31-33, median filtering eliminated random levels that are random in nature.

As a result, we have a more stable schedule.

Note that the correlation is high, because the median filtering does not calculate, does not generalize, but shows the median on a certain interval. That is why median filtering is very effective when studying time series.

This value shows us a rather obvious influence of the number of views on the number of dislikes of videos on the YouTube platform.

Thanks to this correlation graph, we can observe that with a rapid increase in the number of likes, the number of dislikes also increases, albeit slightly.

From this visualization, it is possible to conclude that our board is stationary, and since the data on any interval are not equal to zero, their regularity follows. We can conclude that the attribute by which the matrix is built is quite homogeneous, which is logical, because this attribute is likes.

From this visualization, we can see that there are quite strong relationships between attributes, but there are also negative correlation coefficient results.

Again, as it was proven before, as the number of likes increases, the number of views increases. Although the clusters on the visualization are quite difficult to distinguish, it is possible to generally identify two clusters, namely, light blue spots - the relationship of a high number of views and likes, dark blue spots - a small number of these attributes.

According to this matrix, it is difficult to determine which cluster is built and according to which parameter, that is, there are no clear boundaries.

The dendrogram was constructed without labels, in order to facilitate the understanding of the number of levels of clustering between categories of video content on the YouTube platform, sacrificing, unfortunately, the hierarchical relationship between objects.

6. Discussion

For a better analysis of the categories, let's find out the names of the categories that correspond to the identifiers: 1 - movies and cartoons, 10 - music, 15 - pets and animals, 17 - sports, 19 - travel, 20 games, 22 - people and blogs, 23 - humor, 24 - entertainment, 25 - news and politics, 26 - style, 27 education, 28 - science and technology, 29 - non-profit and activism.

It can be seen from the histogram that the most popular categories are categories with identifiers 24, 10, 22, 28, that is, people are most interested in watching thoughtful videos or other people.

This graph clearly shows when we have a change in the viewing trend. A simple moving average got rid of the noise, but you have to take into account that the platform must be in trend.

Another method is median smoothing with the size of the smoothing interval w = 3.

We can note that the general trends in the above graphs (Figs. 42-44) are practically identical, which makes both methods suitable for working with the selected dataset.

Thanks to the correlation relationship, we can observe that with a rapid increase in the number of likes, the number of dislikes also increases, albeit slightly. Analyzing other graphs, we can conclude that when the number of views increases, the number of likes increases, and therefore the number of dislikes increases.

Thanks to this correlation graph, we can observe that with a rapid increase in the number of likes, the number of dislikes also increases, albeit slightly.

7. Conclusions

A simple moving average is suitable for identifying trends in the past, which will help us predict the future with less error. However, for such a large and popular platform as YouTube, it is necessary to analyse the latest events. To do this, they need methods that quickly respond to the latest data. During the calculation and graphic work on such methods, we studied the weighted moving average smoothing method and exponential smoothing. Analysing this dataset, we learned that people like to watch videos from the categories "Music", "Entertainment" or "People and blogs" the most. These categories account for the largest number of likes and views. At the same time, the most dislikes fell on the "People and blogs" category. This can be explained by the fact that people often differ in their opinions and they simply do not agree with what was said in the video. It is also worth noting that the relationship between the number of likes, dislikes and the number of views was investigated. There is a direct relationship between them, so when one of these attributes increases, the others will also increase. It turned out to be an interesting fact that topics related to science and technology have recently become more and more popular. However, the difference between likes and dislikes is significantly in favour of likes, which means that people are mostly happy when they consume YouTube content. 8. References

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