Explain what a local optimum is and why it is important in a specific context, such as K-means clustering. What are specific ways of determining if you have a local optimum problem? What can be done to avoid local optima?

A solution that is optimal in within a neighboring set of candidate solutions. In contrast with global optimum: the optimal solution among all others.

K-means clustering context:

It's proven that the objective cost function will always decrease until a local optimum is reached.
Results will depend on the initial random cluster assignment.

Determining if you have a local optimum problem:

  • Tendency of premature convergence
  • Different initialization induces different optima


Avoid local optima in a K-means context: repeat K-means and take the solution that has the lowest cost.

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