# Argmax là gì

\$\$pi_nk=left{eginarraycl1& extrmif k=argmin_jleftVertloginar.netbf x_n-mu_j ightVert^2\0& extrmotherwiseendarray ight..\$\$

Especially the \$argmin\$ part.Quý khách hàng vẫn xem: Argmin là gì

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

\$argmin\$ is argument of the minimum.

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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\$and \$k\$ equals lớn \$j\$ such that \$eginVmatrixx_n-mu_jendVmatrix^2\$ attains minimum aý muốn all values of \$mu_j\$ & given \$x_n\$.

hopefully that helps.

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 (lượt thích the LS situation alluded khổng lồ in your example).

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