Deep Learning Approach for Matrix Completion Using Manifold Learning
This work offers an incremental improvement for matrix completion by combining linear and nonlinear modeling, which could benefit various applications relying on accurate data imputation.
This paper proposes a deep learning model for matrix completion that simultaneously addresses both linear and nonlinear relationships within data matrices, which existing methods often overlook. The model uses two neural network branches for rows and columns, combined with a multi-task learning approach where manifold learning acts as a regularizer to improve missing entry recovery and reduce overfitting. The method's effectiveness was validated on synthetic and real-world datasets against state-of-the-art methods.
Matrix completion has received vast amount of attention and research due to its wide applications in various study fields. Existing methods of matrix completion consider only nonlinear (or linear) relations among entries in a data matrix and ignore linear (or nonlinear) relationships latent. This paper introduces a new latent variables model for data matrix which is a combination of linear and nonlinear models and designs a novel deep-neural-network-based matrix completion algorithm to address both linear and nonlinear relations among entries of data matrix. The proposed method consists of two branches. The first branch learns the latent representations of columns and reconstructs the columns of the partially observed matrix through a series of hidden neural network layers. The second branch does the same for the rows. In addition, based on multi-task learning principles, we enforce these two branches work together and introduce a new regularization technique to reduce over-fitting. More specifically, the missing entries of data are recovered as a main task and manifold learning is performed as an auxiliary task. The auxiliary task constrains the weights of the network so it can be considered as a regularizer, improving the main task and reducing over-fitting. Experimental results obtained on the synthetic data and several real-world data verify the effectiveness of the proposed method compared with state-of-the-art matrix completion methods.