Carina Moreira Costa The minimum sum-of-squares clustering problem is a very important problem in data mining and machine learning with very many applications in, e.g., medicine or social sciences. However, it is known to be NP-hard in all relevant cases and to be notoriously hard to be solved to global optimality in practice. In this paper, we develop … Read more
Cardinality-constrained optimization problems are notoriously hard to solve both in theory and practice. However, as famous examples such as the sparse portfolio optimization and best subset selection problems show, this class is extremely important in real-world applications. In this paper, we apply a penalty alternating direction method to these problems. The key idea is to … Read more
k-means clustering is a classic method of unsupervised learning with the aim of partitioning a given number of measurements into k clusters. In many modern applications, however, this approach suffers from unstructured measurement errors because the k-means clustering result then represents a clustering of the erroneous measurements instead of retrieving the true underlying clustering structure. … Read more