Abstract Pairwise learning is a specialized form of supervised learning that focuses on predicting outcomes for pairs of objects. In this paper, we formulate the pairwise learning problem as a difference of convex (DC) optimization problem using the Kronecker product kernel, $$\ell _1$$ ℓ 1 - and $$\ell _0$$ ℓ 0 -regularizations, and various, possibly nonsmooth, loss functions. Our aim is to develop an efficient learning algorithm, SparsePKL, that produces accurate predictions with the desired sparsity level. In addition, we propose a novel limited memory bundle DC algorithm (LMB-DCA) for large-scale nonsmooth DC optimization and apply it as an underlying solver in the SparsePKL. The performance of the SparsePKL-algorithm is studied in seven real-world drug-target interaction data and the results are compared with those of the state-of-art methods in pairwise learning.

Clustering is a crucial task in data mining and machine learning. In this paper, we propose an efficient algorithm, Big-Clust , for solving minimum sum-of-squares clustering problems in large and big datasets. We first develop a novel stochastic limited memory bundle algorithm ( SLMBA ) for large-scale nonsmooth finite-sum optimization problems and then formulate the clustering problem accordingly. The Big-Clust algorithm — a stochastic adaptation of the incremental clustering methodology — aims to find the global or a high-quality local solution for the clustering problem. It detects good starting points, i.e., initial cluster centers, for the SLMBA , applied as an underlying solver. We evaluate Big-Clust on several real-world datasets with numerous data points and features, comparing its performance with other clustering algorithms designed for large and big data. Numerical results demonstrate the efficiency of the proposed algorithm and the high quality of the found solutions on par with the best existing methods.

In this paper a new method of preprocessing incomplete data is introduced. The method is based on clusterwise linear regression and it combines two well-known approaches for missing value imputation: linear regression and clustering. The idea is to approximate missing values using only those data points that are somewhat similar to the incomplete data point. A similar idea is used also in clustering based imputation methods. Nevertheless, here the linear regression approach is used within each cluster to accurately predict the missing values, and this is done simultaneously to clustering. The proposed method is tested using some synthetic and real-world data sets and compared with other algorithms for missing value imputations. Numerical results demonstrate that this method produces the most accurate imputations in MCAR and MAR data sets with a clear structure and the percentages of missing data no more than 25 percent.