The objective of this study is to reveal the COVID19 characteristics of the countries by using time series clustering. Up to now, various studies have been conducted for similar objectives. But, it has been observed that these studies belong to early time of pandemic and are involved limited number of countries. To analyze the characteristic of COVID19 more, this study has considered 111 countries and time period between the 4th of April 2020 and the 1st of January 2021. Fuzzy K-Medoid (FKM) is preferred as clustering method due to its three abilities: i) FKM enables to determine the similarities and differences between the countries in more detail by utilizing the membership degrees, ii) In FKM, cluster centers are selected among from objects in the data set. Thus, it has the ability of detecting the countries which represent the behavior of all countries, iii) FKM is a robust method against to outliers. Thanks to this ability, FKM prevents that the countries exhibiting abnormal behavior negatively affect to the clustering results. At the results of the analyses, it is observed that 111 countries have three different behaviors in terms of confirmed cases and five different behaviors in terms of deaths.
ÖZBu çalışmanın amacı Türkiye'de PM10 ve SO2 kirleticileri konsantrasyonları bakımından benzer davranışa sahip hava kirliliği izleme istasyonlarını belirlemek ve böylece izleme maliyetini ve bilgi fazlalığını azaltmaktır. Bu amaca yönelik olarak, otoregresif modele dayanan Bulanık k-Medoidler (BKM) algoritması kullanılmıştır. Yapılan analizler sonucunda, izleme istasyonlarındaki bilgi fazlalılığının ve bununla birlikle izleme maliyetinin PM10 hava kirleticisi için yaklaşık olarak %78.5, SO2 hava kirleticisi için %73.5 azaltılabileceği sonucunda ulaşılmıştır.Anahtar Kelimeler: otoregresif model, bulanık k-medoid kümeleme, hava kalitesi izleme istasyonları Time Series Clustering's application to identifying of information redundancy at air pollution monitoring stations in Turkey ABSTRACTThe aim of study is to determine the monitoring stations having similar behavior with respect to PM10 and SO2 concentrations and thus decrease monitoring cost and information redundancy. For this purpose, autoregressive model based Fuzzy K-medoids algorithm is used. At the results of analyses, it has been concluded that information redundancy in monitoring stations and thus monitoring cost can be decreased approximately 78.5% for PM10 air pollutant, 73.5% for SO2 air pollutant.
Reliability is the probability that a system or a product fulfills its intended function without failure over a period of time and it is generally used to determine the reliability, release and testing stop time of the system. The primary objective of this study is to predict and forecast COVID19 reliabilities of the countries by utilizing this definition of the reliability. To our knowledge, this study is the first carried out in the direction of this objective. The major contribution of this study is to model the COVID19 data by considering the intensity functions with different types of functional shapes, including geometric, exponential, Weibull, gamma and identifying best fit (BF) model for each country, separately. To achieve the objective determined, cumulative number of confirmed cases are modelled by eight Non-Homogenous Poisson Process (NHPP) models. BF models are selected based on three comparison criteria, including Root Mean Square Error (RMSE), Normalized Root Mean Square Error (NRMSE), and Theil Statistics (TS). The results can be summarized as follows: S-shaped models provide better fit for 56 of 70 countries. Current outbreak may continue in 43 countries and a new outbreak may occur in 27 countries. 50 countries have the reliability smaller than 75%, 9 countries between 75% and 90%, and 11 countries a 90% or higher on 11 August 2021. Supplementary Information The online version contains supplementary material available at 10.1007/s00354-022-00183-1.
This study proposes a new time series prediction method that combines Fuzzy Time Series (FTS) based on fuzzy clustering and Maximal Overlap Discrete Wavelet Transform (MODWT). Time series generally consist of subseries, each of which reflects the different behavior of the time series and using of a single prediction method for all subseries can be negatively impacted the prediction and forecasting accuracy. Proposed method is based on decomposing of time series into sub-time series through MODWT and predicting an FTS model for each sub-time series separately. Besides, time series can contain noise, outlier or unwanted data points and these points can hide the actual behavior of the time series. MODWT has the ability of eliminating negative effects of these kind of data points on the predictions. Besides, proposed method has also all advantages of FTS methods. The main objective of this study based on these advantages is to improve the prediction and forecasting performance of existing FTS methods based on fuzzy clustering. In order to show the performance of proposed method, three FTS methods based on fuzzy clustering and wavelet-based versions of them are applied to eight real time series and experimental results clearly showed that proposed method achieves the best prediction and forecasting results.
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