The K-means algorithm, routinely used in many scientific fields, generates clustering solutions that depend on the initial cluster coordinates. The number of solutions may be large, which can make locating the global minimum challenging. Hence, the topography of the cost function surface is crucial to understanding the performance of the algorithm. Here, we employ the energy landscape approach to elucidate the topography of the K-means cost function surface for Fisher’s Iris dataset. For any number of clusters, we find that the solution landscapes have a funneled structure that is usually associated with efficient global optimization. An analysis of the barriers between clustering solutions shows that the funneled structures result from remarkably small barriers between almost all clustering solutions. The funneled structure becomes less well-defined as the number of clusters increases, and we analyze kinetic analogs to quantify the increased difficulty in locating the global minimum for these different landscapes.

Rotamers, namely amino acid side chain conformations common to many different peptides, can be compiled into libraries. These rotamer libraries are used in protein modeling, where the limited conformational space occupied by amino acid side chains is exploited. Here, we construct a sequence-dependent rotamer library from simulations of all possible tripeptides, which provides rotameric states dependent on adjacent amino acids. We observe significant sensitivity of rotamer populations to sequence and find that the library is successful in locating side chain conformations present in crystal structures. The library is designed for applications with basin-hopping global optimization, where we use it to propose moves in conformational space. The addition of rotamer moves significantly increases the efficiency of protein structure prediction within this framework, and we determine parameters to optimize efficiency.