Simulation of Territorial Development Based on Fiscal Policy Tools

Table 2

Distances measures among objects (regions).

Distances measure among objects	Calculated formula	Conditions of using
The common Mahalanobis distance	𝑑𝑖𝑗=𝑋𝑖−𝑋𝑗^′Λ^′𝑆^−1Λ𝑋𝑖−𝑋𝑗, where 𝑑𝑖𝑗 is the distance between 𝑖th and 𝑗th regions (or objects); Х𝑖,𝑋𝑗 are the value vectors of the SETD indicators for 𝑖th and 𝑗th objects; 𝑆 is the common covariation matrix; Λ is the matrix of weighting coefficients	Is used in case of dependent vector components  𝑥1,𝑥2,…,𝑥𝑛 and their different significance at classification
Euclidean’s distance	𝑑𝑖𝑗=∑^𝑚𝑘=1𝑥𝑖𝑘−𝑥𝑗𝑘^2, where 𝑥𝑖𝑘,𝑥𝑗𝑘 are the values for 𝑘th indicator, respectively, for 𝑖th and 𝑗th objects	Is used in case if the vector observation components  𝑋 are homogeneous by physical sense and are equally important for classification
Weighted Euclidean’s distance	𝑑𝑖𝑗=∑^𝑚𝑘=1𝑤𝑘𝑥𝑖𝑘−𝑥𝑗𝑘^2, where 𝑤𝑘 is the weight, which can be used for 𝑘th indicator	Is used in case when for each vector component 𝑋 can be used as a weight, which is proportional for a degree of a sign important 0≤𝑤𝑘≤1
Hamming’s distance	𝑑𝑖𝑗=∑^𝑚𝑘=1𝑥𝑖𝑘−𝑥𝑗𝑘	Is used as a difference measure of the objects, which can be defined by dichotomous signs