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This article is cited in 2 scientific papers (total in 2 papers)
General numerical methods
Inductive matrix completion with feature selection
M. Burkinaa, I. Nazarovb, M. Panovb, G. Fedoninacd, B. Shirokikhabc a Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, Russia
b Skolkovo Institute of Science and Technology (Skoltech), 121205, Moscow, Russia
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051, Moscow, Russia
d Central Research Institute of Epidemiology, 111123, Moscow, Russia
Abstract:
We consider the problem of inductive matrix completion, i.e., the reconstruction of a matrix using side features of its rows and columns. In numerous applications, however, side information of this kind includes redundant or uninformative features, so feature selection is required. An approach based on matrix factorization with group LASSO regularization on the coefficients of the side features is proposed, which combines feature selection with matrix completion. It is proved that the theoretical sample complexity for the proposed approach is lower than for methods without sparsifying. A computationally efficient iterative procedure for simultaneous matrix completion and feature selection is proposed. Experiments on synthetic and real-world data demonstrate that, due to the feature selection procedure, the proposed approach outperforms other methods.
Key words:
inductive matrix completion, group sparsity, sample complexity.
Received: 19.03.2020 Revised: 29.12.2020 Accepted: 14.01.2021
Citation:
M. Burkina, I. Nazarov, M. Panov, G. Fedonin, B. Shirokikh, “Inductive matrix completion with feature selection”, Zh. Vychisl. Mat. Mat. Fiz., 61:5 (2021), 744–758; Comput. Math. Math. Phys., 61:5 (2021), 719–732
Linking options:
https://www.mathnet.ru/eng/zvmmf11235 https://www.mathnet.ru/eng/zvmmf/v61/i5/p744
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