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I was reading Constrained Clustering with Minkowski Weighted K-Means paper. In this paper, they are using 4 datasets and deriving 2 new datasets from each of the 4. So, total 12 datasets. The description for derivation is given like this:
"This dataset (Iris) contains solely numerical data, it has 150 entities over four features, partitioned into three clusters. From this the dataset we have derived two other with two and four extra noise features."

I understand how to add noise to the given data. However, I don't understand the meaning of adding two and four extra features. Does it mean that along with the original features, the author adds dummy features(noise added data)? Again, from where and how the author does that? Any help would be appreciated.

EDIT: The paper can be viewed here

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Methods like k-means rely on a distance measure like the euclidean distance. The intention of the authors was probably to make the clustering problem on somewhat trivial data sets like iris harder by adding additional features, as you correctly assumed, that are not very discriminative with respect to the actual cluster structure in the data.

How I understand it, the authors want to 'weaken' the notion of similarity that the distance measure provides by adding these unrelated features in order to be able to demonstrate the quality of their approach.
Sadly I cannot view the referenced paper, otherwise I could go into more detail. Personally I'm a bit surprised, because this is the first time I hear of such a procedure.


Edit: Regarding your question

when the author mentions two or four new noisy features, how to predict which of the original feature(s) he used to add noise ( uniformly random noise)?

I only skipped through the paper briefly, not seeing any indication that the noisy features are actually derived from existing features, merely that the additional data sets are derived from the original data set.
The only detail they give regarding that is

we have derived datasets from the four originals, containing features with uniformly random noise.

Which sounds to me like they just generated several random uniformly-distributed variables and added them as an additional feature. Given that the contribution of their approach is some kind of feature weighting, this probably serves to demonstrate that their method recognizes that these new features are just distracting and ignores it in the clustering process.

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  • $\begingroup$ You can view the same paper at dcs.bbk.ac.uk/~renato/WebFiles/Constraint_MWK.pdf as well :) $\endgroup$ – Baba Rocks Mar 21 '18 at 11:18
  • $\begingroup$ when the author mentions two or four new noisy features, how to predict which of the original feature(s) he used to add noise ( uniformly random noise)? $\endgroup$ – Baba Rocks Mar 21 '18 at 11:25
  • $\begingroup$ I added a reply to your comment to my answer $\endgroup$ – deemel Mar 21 '18 at 11:40
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    $\begingroup$ make sense! As cluster structure in a data set is often confined to a subset of features rather than the entire feature set. Adding other uniform noisy features can only obscure the discovery of the cluster structure by a regular K-means. $\endgroup$ – Baba Rocks Mar 21 '18 at 11:48
  • $\begingroup$ Exactly that was the author's intention, I suppose. In case that answered your question, please consider accepting my answer ;) $\endgroup$ – deemel Mar 21 '18 at 12:04

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