There are some samples which have feature vector(the feature vector is ordinal data), I want to perform cluster on these samples based on the ordinal data. For example, a institute have done some questionnaire asking people in the different country what aspect is your concern when talking about life satisfaction and make a rank. After got a plenty of questionnaire each one has a ordinal vector, how can we cluster these questionnaire to find the difference and similarity in and between country? In other word the researcher want to cluster these sample to find which country is same.Many thanks for your answer!
You can use Kendalls' concordance as a comparison metric between rankings:
https://en.wikipedia.org/wiki/Kendall%27s_W
Ordinal data can be considered as categorical data (with some additional properties). Hence the techniques of clustering categorical data apply.
Eugene Veniaminovich Lutsenko
As a method of the research we used Automated system-cognitive analysis (ASC-analysis), which is a new innovative method of artificial intelligence: it also has its own software tool – an intelligent system called "Eidos" (open source software) [1, 2, 3].
The Eidos-X++ system differs from other artificial intelligence systems in the following parameters:
- was developed in a universal setting, independent of the subject area. Therefore, it is universal and can be applied in many subject areas (http://lc.kubagro.ru/aidos/index.htm);
- is in full open free access (http://lc.kubagro.ru/aidos/_Aidos-X.htm), and with the relevant source texts (http://lc.kubagro.ru/__AIDOS-X.txt);
- is one of the first domestic systems of artificial intelligence of the personal level, i.e. it does not take special training in the field of technologies of artificial intelligence from the user (there is an act of introduction of system "Eidos" of 1987) (http://lc.kubagro.ru/aidos/aidos02/PR-4.htm);
- provides stable identification in a comparable form of strengh and direction of cause-effect relationships in incomplete noisy interdependent (nonlinear) data of very large dimension of numerical and non-numerical nature, measured in different types of scales (nominal, ordinal and numerical) and in different units of measurement (i.e. does not impose strict requirements to the data that can not be performed, and processes the data that is) [12];
- contains a large number of local (supplied with the installation) and cloud educational and scientific applications (currently 31 and 152, respectively) (http://lc.kubagro.ru/aidos/Presentation_Aidos-online.pdf);
- provides multilingual interface support in 44 languages. Language databases are included in the installation and can be replenished automatically;
- supports on-line environment of knowledge accumulation and is widely used all over the world (http://aidos.byethost5.com/map5.php);
- the most time-consuming computationally, the operations of the synthesis models and implements recognition by using graphic processing unit (GPU) that some tasks can only support up to the solution of these tasks is several thousand times that really provides intelligent processing of big data, big information and big knowledge;
- provides transformation of the initial empirical data into information, and its knowledge and solution using this knowledge of classification problems, decision support and research of the subject area by studying its system-cognitive model, generating a very large number of tabular and graphical output forms (development of cognitive graphics), many of which have no analogues in other systems (examples of forms can be found in: http://lc.kubagro.ru/aidos/aidos18_LLS/aidos18_LLS.pdf);
- well imitates the human style of thinking: gives the results of the analysis, understandable to experts on the basis of their experience, intuition and professional competence.
Li Guohui ,
By "what aspect is your concern" do you mean that the aspects are predefined and the task is to order them or rank (e.g. by "a star", "like/dislike", etc.)? If yes, do any of the aspects form categories or depend on each other so that if one gets a low rank than the other also gets a low rank, or vice versa? I think it would be important to know, because you can simplify your data model and leave only the most influential aspects. I would then calculate average, or median, or mode values for each aspect depending on your data, for each country. For example, you can consider it important that in country Z the majority of your respondents ranked aspect 3 as number 6 among all other aspects. Or you can come up with your own metric. As the result, you get a list of countries, where each country corresponds to a vector of the weighted values. Now, you can choose whatever clustering method fits your aim of research. In any case, you will either need to know the number of clusters, or distance between them.
Good luck!
First you need to metrize nominal scales (binary, linguistic) to the level of numeric scales, and then work with them as numeric scales
Article METRIZATION OF MEASURING SCALES OF DIFFERENT TYPES AND JOINT...
The article considers measuring scales as a tool for creating formal models of real objects and a tool for increasing the degree of formalization of these models to a level sufficient to implement them on computers. It also describes the different types of measuring scales, allowing to create models of varying degrees of formalization; lists the types of transformation valid during the processing of empirical data obtained with scales of different types; develops the task of metrization of the scales, i.e. conversion to the most formalized mind; it proposes 7 ways of metrization of all the types of scales, providing a joint comparable quantitative processing of heterogeneous factors measured in different units of measure due to the conversion of all scales to one universal unit of measurement in which the measurement number of information is selected. All of these methods of metrization have been implemented in the system-cognitive analysis and in the Eidos intellectual system
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