Applying clustering analysis for discovering time series heterogeneity using Saint Petersburg morbidity rate as an illustration

Abstract

One of the machine learning approaches for unsupervised learning is clustering. Clustering has the task of exploring the structure of data with the aim of assigning a set of objects in such a way that objects belonging to the same group are more similar to each other than the objects drawn from different groups. Determining the number of clusters in a data set, searching for stable clusters, selection of dissimilarity measure and algorithm are significant tasks of cluster analysis. Multidimentional clustering is often used when an object is characterized by a vector. A dissimilarity measure or distance is selected with respect to the purpose and features of a certain task. But there are also such fields as economics, geology, medicine, sociology that are often presented by time series. Time series are random processes but not a random vector. That is why it is important to construct such a similarity (or dissimilarity) measure which would take into consideration that data are time-dependent. The research of morbidity rate of Saint Petersburg from 1999 to 2014 years and clustering of 18 districts are conducted. Several different similarity measures are used for clustering. Besides, an interesting aspect is clustering of multidimentional time series. There are two approaches. The first concept is to split multidimentional time series into several univariate time series, whilst the second one is to consider it as a whole unit that preserves the influence of data interdependence. Research is made with application of TSclust, tseries packages in R and missed algorithms are realised there. As a result of clustering of Saint Petersburg districts applying several similarity measures three stable clusters are found out but seven districts do not belong to any cluster. Refs 10. Figs 2.

Tax Authority and Taxpayers: How Does Mutual Collecting of Information Affect the Effectiveness of Tax Control

“…Further research is based on a static model similar to the game-theoretic model of tax control (Bure and Kumacheva, 2010). Following (Chander and Wilde, 1998;Vasin and Morozov, 2005;Lamantia and Pezzino, 2021) and (Kumacheva et al, 2019), here and below we suppose that there are only two possible levels of income that can be earned.…”

“…Following (Chander and Wilde, 1998;Vasin and Morozov, 2005;Lamantia and Pezzino, 2021) and (Kumacheva et al, 2019), here and below we suppose that there are only two possible levels of income that can be earned. Without loss of generality, a larger number of income gradations can be considered, as it was done, for example, in (Bure and Kumacheva, 2005) or (Kumacheva, 2012). But the basic premises and way of reasoning will remain the same.…”

“…Considering the model represented in (Bure and Kumacheva, 2010) as a pattern of interaction between principal and risk-neutral agents, let's assume that there is a population of n taxpayers. Each of them can be characterized by her/his true income ξ and can declare income η, where η ≤ ξ.…”

“…Summarizing and simplifying the results obtained in (Bure and Kumacheva, 2010), we formulate that risk-neutral taxpayers decide whether to evade or not, depending on whether the actual probability P L of audit is greater or less the value…”

“…Therefore, the tax authority needs to find the way to optimize tax collections. One of such possible ways, the using an additional information about taxpayers, was mentioned in (Macho-Stadler and Perez-Castrillo, 2002) and studied further in (Bure and Kumacheva, 2005) and (Kumacheva, 2012). The issue of the exchange and dissemination of information on tax audits between taxpayers was also investigated in (Gubar et al, 2016;Gubar et al, 2017;Kumacheva et al, 2018) and (Gubar et al, 2019).…”