Abstract
The objective function, which is the main subject of this volume, has the following general form
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Notes
- 1.
At this point a remark is due on the sometimes voiced argument that by minimising the function like CD(P) for k-means-type algorithms, one maximises, at the same time, the respective inter-cluster distance measure, and so, by this means, the “bi-partiality” is secured. Such an argument is, of course, void, since the “other side” has to be maximised simultaneously, and not “by implication”, for otherwise, as already noted, we end up with the trivial solution for P, namely p = n.
- 2.
This particular (“leading”) concrete formulation is considered at greater length, due to its intuitive appeal, significance regarding the possibility of constructing the sub-optimising algorithm and some essential “historical” references, later on in this volume, especially in Sect. 5.1, in Chap. 6 and at the beginning of Chap. 7.
- 3.
Conform to the proposition that the entire problem of clustering is formulated according to the levels of perception, also the aspect of scale appears at such various levels. Here it was illustrated for the level of objects, but it might be also reasonable to consider it for the level of entire clusters, distances and proximities d and s being appropriately replaced by the functions D and S.
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Owsiński, J.W. (2020). The General Formulation of the Objective Function. In: Data Analysis in Bi-partial Perspective: Clustering and Beyond. Studies in Computational Intelligence, vol 818. Springer, Cham. https://doi.org/10.1007/978-3-030-13389-4_3
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DOI: https://doi.org/10.1007/978-3-030-13389-4_3
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