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I came across the post here which mentioned the following:

k-means assumes the variance of the distribution of each attribute (variable) is spherical

I wanted to understand what does it mean by "variance of the distribution is spherical". Could anyone please help me understand this?

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    $\begingroup$ stats.stackexchange.com/… turns up explanations. The first I found is at stats.stackexchange.com/a/144896/919. $\endgroup$
    – whuber ♦
    Commented Jun 8, 2022 at 16:30
  • $\begingroup$ Thanks for the reference @whuber. Is there a less mathy and more intuitive approach to understand the meaning of variance of distribution being spherical? $\endgroup$
    – Curious
    Commented Jun 10, 2022 at 10:48
  • $\begingroup$ Yes: this is techno-speak for assuming the attributes (modeled as random variables) are uncorrelated and share a common variance. That's all. When the joint distribution is Normal, isocontours of the density are indeed (hyper)spheres. That's relevant to k-means because it implies any cluster created through joint random variation around a single point would have a ball shape rather than a strongly ellipsoidal shape. $\endgroup$
    – whuber ♦
    Commented Jun 10, 2022 at 12:52

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