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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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.
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.