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Here, an algorithm is presented for solving the minimum sum-of-squares clustering problems using their difference of convex representations. The proposed algorithm is based on an incremental approach and applies the well known DC algorithm at each iteration. The proposed algorithm is tested and compared with other clustering algorithms using large real world data sets.

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Over five decades have passed since the first wave of robust optimization studies conducted by Soyster and Falk. It is outstanding that real-life applications of robust optimization are still swept aside; there is much more potential for investigating the exact nature of uncertainties to obtain intelligent robust models. For this purpose, in this study, we investigate a more refined description of the uncertain events including (1) event-driven and (2) attribute-driven. Classical methods transform convex programming classes of uncertainty sets. The structural properties of uncertain events are analyzed to obtain a more refined description of the uncertainty polytopes. Hence, tractable robust models with a decent degree of conservatism are introduced to avoid the over-protection induced by classical uncertainty sets.