Argmin là gì

$$pi_nk=left{eginarraycl1& extrmif k=argmin_jleftVertcortua.combf x_n-mu_j ightVert^2\0& extrmotherwiseendarray ight..$$

Especially the $argmin$ part.

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(It"s from the $k$-means algorithm.)



$argmin$ is argument of the minimum.

The simplest example is

$argmin _x f(x)$ is the value of $x$ for which $f(x)$ attains its minimum.

for your example

$x_n$ is known & depends on $pi_nk$và $k$ equals to lớn $j$ such that $eginVmatrixx_n-mu_jendVmatrix^2$ attains minimum aước ao all values of $mu_j$ and given $x_n$.

hopefully that helps.



$arg min$ (or $arg max$) return the đầu vào for minimum (or maximum) output.

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For example:

The graph illustrat $f(x)=(sin(x-0.5)+cos(x)^2)*2$

The global minmum of $f(x)$ is $min(f(x)) approx$ -2, while the $arg min(f(x)) approx$ 4.9 .



$operatornameargmin(f(x))$ simply returns the value of $x$ which minimizes $f(x)$ over the set of candidates for $x$ 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 lớn in your example).

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