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In the following article, one of the statement is as follows:

The K-means algorithm is effective only for spherical datasets

What does spherical dataset mean?

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    $\begingroup$ In this context it means the clusters are spherical in shape. $\endgroup$
    – Emre
    Sep 6 '17 at 18:06
  • $\begingroup$ Second what Emre said, k-means is (more) effective for spherical clusters, not spherical datasets. The paper may be wrong or just not very precisely worded. By the way: sufficiently high-dimensional datasets tends to have some surprising distance properties: stats.stackexchange.com/questions/99171/… $\endgroup$
    – Alex I
    Dec 7 '18 at 19:02
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In this case, a picture is a worth a thousand words. They literally mean data whose distribution on X,Y is roughly a sphere. Different clustering algorithms work better on different distributions. For example, K means does poorly on the arrangement in the first two rows but OK on the last row.

enter image description here

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spherical dataset is basically a form of non-linear dataset in which observational data are modeled by a function which is a non-linear combination of the model parameters and depends on one or more independent variables.

If your dataset has high variance , you need to reduce the number of features and add more dataset. After that you can then use non-linear methods for classification.

Also, Non-linear methods typically involves applying some type of transformation to your input dataset. After the transformation, many techniques can then try to use a linear method for classification.

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