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.