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# A comparison of different approaches to hierarchical clustering of ordinal data

Author: Aleš Žiberna; Nataša Kejžar; Petra Golob Article : English Metodološki zvezki, Letn. 1, št. 1 (2004), str. 57-73 WorldCat The paper tries to answer the following question: ĆHow should we treat ordinal data in hierarchical clustering? The question is strongly connected to the use of questionnaires with ordinal scales in the social sciences. The results could help to differentiate among answers to the questions from questionnaires that could be considered as scale variables, those it would be better to convert to ranks and those that should be treated as nominal variables. To make the results general several two-dimensional combinations of group sizes, shapes and differences between their centers were used as well as one three-dimensional combination. Each combination was simulated both withand without unessential variables. All datasets consisted of 3 groups, each with its own multivariate distribution (2 or 3 variables) with known means and covariances. From each design several datasets were simulated. Each variable was cut and recoded to achieve an ordinal scale. Different cutting schemes were used (the intervals were of equal size, either increasing/decreasing from the lowest to the highest value or decreasing from the mean to both extremes). These new variables were then treated as interval, converted to ranks and treated as nominal. Then hierarchical clustering algorithms were used. Ward's algorithm with Squared Euclidean distance was used when data were considered interval or converted to ranks, and Ward's algorithm with matching coefficient as dissimilarity measure was used when they were considered nominal. The quality of the results was assessed by comparing the gained partitions with the three original groups. Wealso compared results from clustering the original (uncut) data with the three original groups for comparison. The comparison was made using Corrected Rand Index. The results indicate that in most cases treating the data as interval or converting them to ranks yields better results than treating them as nominal, but the differences are sometimes diminished when cutting into a smaller number of intervals.  Read more... (not yet rated) 0 with reviews - Be the first. Search this publication for other articles with the following words:

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Material Type: Internet resource Article, Internet Resource Aleš Žiberna; Nataša Kejžar; Petra Golob Find more information about: Aleš Žiberna Nataša Kejžar Petra Golob 1854-0023 442365010 str. 57-73 : Graf. prikazi. Aleš Žiberna, Nataša Kejžar, and Petra Golob.

### Abstract:

The paper tries to answer the following question: ĆHow should we treat ordinal data in hierarchical clustering? The question is strongly connected to the use of questionnaires with ordinal scales in the social sciences. The results could help to differentiate among answers to the questions from questionnaires that could be considered as scale variables, those it would be better to convert to ranks and those that should be treated as nominal variables. To make the results general several two-dimensional combinations of group sizes, shapes and differences between their centers were used as well as one three-dimensional combination. Each combination was simulated both withand without unessential variables. All datasets consisted of 3 groups, each with its own multivariate distribution (2 or 3 variables) with known means and covariances. From each design several datasets were simulated. Each variable was cut and recoded to achieve an ordinal scale. Different cutting schemes were used (the intervals were of equal size, either increasing/decreasing from the lowest to the highest value or decreasing from the mean to both extremes). These new variables were then treated as interval, converted to ranks and treated as nominal. Then hierarchical clustering algorithms were used. Ward's algorithm with Squared Euclidean distance was used when data were considered interval or converted to ranks, and Ward's algorithm with matching coefficient as dissimilarity measure was used when they were considered nominal. The quality of the results was assessed by comparing the gained partitions with the three original groups. Wealso compared results from clustering the original (uncut) data with the three original groups for comparison. The comparison was made using Corrected Rand Index. The results indicate that in most cases treating the data as interval or converting them to ranks yields better results than treating them as nominal, but the differences are sometimes diminished when cutting into a smaller number of intervals.

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