ArgMin

 

https://math.stackexchange.com/questions/227626/explanation-on-arg-min

 

arg min is argument of the minimum.

The simplest example is

argminxf(x)argminxf(x) is the value of xx for which f(x)f(x) attains it's minimum.

for your example

xnxn is known and depends on πnkπnk and kk equals to jj such that ∥xn−μj∥2‖xn−μj‖2 attains minimum among all values of μjμj and given xnxn.

hopefully is helped.

 

argmin(f(x))argmin⁡(f(x)) simply returns the value of xx which minimizes f(x)f(x) over the set of candidates for xx as opposed to the minimum value itself.

This arises, of course, in all kinds of statistical estimates of parameters when building models (like the LS situation alluded to in your example).

 

3 down vote

argminargmin (or argmaxargmax) return the input for minimum (or maximum) output. For example: The graph illustrat f(x)=(sin(x−0.5)+cos(x)2)∗2f(x)=(sin(x−0.5)+cos(x)2)∗2 The global minmum of f(x)f(x) is min(f(x))≈min(f(x))≈ -2, while the argmin(f(x))≈argmin(f(x))≈ 4.9 .