# Kriteriji kompleksnosti za k-means algoritam

Šeperić, Stela (2014) Kriteriji kompleksnosti za k-means algoritam. Diploma thesis, Faculty of Science > Department of Mathematics.

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In this thesis, we have studied method for determining $k$ in k-means algorithm, which is a well known problem. It is shown that the objective function coverges. Furthermore, a couple of lemmas proved that, if data follow a uniform distribution, then the objective function behaves as $C\cdot\frac{1}{k^2}$. Assumption about data is not as strong as assumption in G-means algorithm which requires normal distribution of data. We have shown that with relatively limited assumptions, we can neatly describe behaviour of the objective function with respect to $k$ - the number of clusters. Finally, a series of tests on simulated data sets confirmed our theoretical results about behaviour of the objective function.