Assessing Inhomogeneous
Indicator-Related Typologies Through
the Reverse Clustering Approach
Jan W. Owsi ´
nski, Jarosław Sta ´
nczak, Sławomir Zadro¨ zny,
and Janusz Kacprzyk
1 Introduction
The paper addresses the following pragmatic problem: We are given a typology of
spatial units (here: Polish municipalities, close to 2500 in number), elaborated for
definite planning purposes (see ´
Sleszy´ nski and Komornicki 2016). The typology
resulted from a complex procedure, involving a number of indicators. Moreover,
the set of indicators used was not uniform across all (types of) municipalities, for
the procedure had a “branching” character, implying different subsets of features for
particular types. At the same time, the number of types had to be kept “reasonable”
for pragmatic purposes. This gives rise to several questions, not only on the
“validity” of the typology, but also its “meaning”, and, last but not least, “intuitive
appeal”, so important from the policy making standpoint.
In view of these questions a study was performed, aimed at (1) providing
a comparative material for the typology elaborated, (2) basing this comparative
material on a uniform set of data (variables, indicators), (3) identifying the effects of
inhomogeneity of the original criteria and use of incommensurable variables, hard
to express on a par with the others.
This exercise was based on the “reverse clustering” approach, developed by the
authors (Owsi´ nski et al. 2017a, b; 2021). This approach consists in attempting to
recreate a given partition, P A , of a set of n objects, on the basis of a set of data on
these objects, X, composed of vectors x i , x i = [x i1 , . . . ,x im ]. We wish to obtain a
partition P B of the analysed set of objects that is as close to P A as possible (e.g. in
terms of the Rand index), by applying an optimisation procedure, described in the
references mentioned.
J. W. Owsi´ nski () · J. Sta´ nczak · S. Zadro¨ zny · J. Kacprzyk
Systems Research Institute, Polish Academy of Sciences, Warszawa, Poland
e-mail: owsinski@ibspan.waw.pl; Jaroslaw.Stanczak@ibspan.waw.pl; zadrozny@ibspan.waw.pl;
Janusz.Kacprzyk@ibspan.waw.pl
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_3
31
Indicator-Related Typologies Through
the Reverse Clustering Approach
Jan W. Owsi ´
nski, Jarosław Sta ´
nczak, Sławomir Zadro¨ zny,
and Janusz Kacprzyk
1 Introduction
The paper addresses the following pragmatic problem: We are given a typology of
spatial units (here: Polish municipalities, close to 2500 in number), elaborated for
definite planning purposes (see ´
Sleszy´ nski and Komornicki 2016). The typology
resulted from a complex procedure, involving a number of indicators. Moreover,
the set of indicators used was not uniform across all (types of) municipalities, for
the procedure had a “branching” character, implying different subsets of features for
particular types. At the same time, the number of types had to be kept “reasonable”
for pragmatic purposes. This gives rise to several questions, not only on the
“validity” of the typology, but also its “meaning”, and, last but not least, “intuitive
appeal”, so important from the policy making standpoint.
In view of these questions a study was performed, aimed at (1) providing
a comparative material for the typology elaborated, (2) basing this comparative
material on a uniform set of data (variables, indicators), (3) identifying the effects of
inhomogeneity of the original criteria and use of incommensurable variables, hard
to express on a par with the others.
This exercise was based on the “reverse clustering” approach, developed by the
authors (Owsi´ nski et al. 2017a, b; 2021). This approach consists in attempting to
recreate a given partition, P A , of a set of n objects, on the basis of a set of data on
these objects, X, composed of vectors x i , x i = [x i1 , . . . ,x im ]. We wish to obtain a
partition P B of the analysed set of objects that is as close to P A as possible (e.g. in
terms of the Rand index), by applying an optimisation procedure, described in the
references mentioned.
J. W. Owsi´ nski () · J. Sta´ nczak · S. Zadro¨ zny · J. Kacprzyk
Systems Research Institute, Polish Academy of Sciences, Warszawa, Poland
e-mail: owsinski@ibspan.waw.pl; Jaroslaw.Stanczak@ibspan.waw.pl; zadrozny@ibspan.waw.pl;
Janusz.Kacprzyk@ibspan.waw.pl
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_3
31