A novel deep quantile matrix completion model for top-N recommendation[Formula presented]

Matrix completion models have been receiving keen attention due to their wide applications in science and engineering. However, the majority of these models assumes a symmetric noise distribution in their completion processes and uses conditional mean to characterize data distribution in a data set, the assumption of which incurs noticeable bias toward outliers. Recognizing the fact that noise distribution tends to be asymmetric in the real-world, this paper proposes a novel Deep Quantile Matrix Completion model, abbreviated as DQMC, which aims to accurately capture noise distribution in a data set by modeling conditional quantile of the data set instead of its conditional mean as traditionally handled by many state-of-the-art methods. Implemented via a deep computing paradigm, the newly proposed model maps a data set from its input space to the latent spaces through a two-branched deep autoencoder network. Such a mapping can effectively capture complex information latent in the data set. The proposed model is empowered by two key designed elements, including: (1) its two-branched deep autoencoder network that provides a flexible computing pathway to attain completion results with a high quality; (2) the introduction of a quantile loss function in combination with the proposed deep network, leading to a new unsupervised learning algorithm for tackling the matrix completion tasks with a superior capability. Comparative experimental results consistently demonstrate the superiority of the proposed DQMC model in conducting the top-N recommendation tasks involving both explicit and implicit rating data sets with respect to a series of state-of-the-art recommendation algorithms.