Unsupervised Learning: Difference between revisions

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</math><br>
</math><br>
<math>
<math>
= \nabla \sum_{j=1}{k} \sum_{i\mid z(i)=j} \Vert x^{(i)} - \mu_{z^{(i)}} \Vert ^2
= \nabla \sum_{j=1}^{k} \sum_{i\mid z(i)=j} \Vert x^{(i)} - \mu_{z^{(i)}} \Vert ^2
</math><br>
</math><br>
<math>
<math>
= \nabla \sum_{j=1}{k} \sum_{i\mid z(i)=j} \Vert x^{(i)} - \mu_{j} \Vert ^2
= \nabla \sum_{j=1}^{k} \sum_{i\mid z(i)=j} \Vert x^{(i)} - \mu_{j} \Vert ^2
</math><br>
</math><br>
<math>
<math>
= \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
</math><br>
</math><br>
<math>
<math>
=  \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
</math><br>
</math><br>
<math>
<math>
=  \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})
</math><br>
</math><br>
<math>
<math>