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Unsupervised Learning: Difference between revisions
→Optimization
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&= \sum_{j=1}{k} \sum_{i\mid z(i)=j} \nabla \Vert x^{(i)} - \mu_{j} \Vert ^2\\ | &= \sum_{j=1}{k} \sum_{i\mid z(i)=j} \nabla \Vert x^{(i)} - \mu_{j} \Vert ^2\\ | ||
&= \sum_{j=1}{k} \sum_{i\mid z(i)=j} 2(x^{(i)} - \mu_{j})\\ | &= \sum_{j=1}{k} \sum_{i\mid z(i)=j} 2(x^{(i)} - \mu_{j})\\ | ||
\implies \mu_{j} &= (\sum_{i\mid z(i)=j} x^(i))/(\sum_{i\mid z(i)=j} 1) \quad \forall j | \implies \mu_{j} &= (\sum_{i\mid z(i)=j} x^{(i)})/(\sum_{i\mid z(i)=j} 1) \quad \forall j | ||
\end{align} | \end{align} | ||
</math> | </math> | ||