Limited memory bundle DC algorithm for sparse pairwise kernel learning

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, $$\ell _1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> - and $$\ell _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> -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.