Non-Linear Matrix Completion

Current methods for predicting missing values in datasets often rely on simplistic approaches such as taking median value of attributes, limiting their applicability. Real-world observations can be diverse, taking stock price as example, ranging from prices post-IPO to values before a company’s collapse, or instances where certain data points are missing due to stock suspension. In this paper, we propose a novel approach using Nonlinear Matrix Completion (NIMC) and Deep Matrix Completion (DIMC) to predict associations, and conduct experiment on financial data between dates and stocks. Our method leverages various types of stock observations to capture latent factors explaining the observed date-stock associations. Notably, our approach is nonlinear, making it suitable for datasets with nonlinear structures, such as the Russell 3000. Unlike traditional methods that may suffer from information loss, NIMC and DIMC maintain nearly complete information, especially in high-dimensional parameters. We compared our approach with state-of-the-art linear methods, including Inductive Matrix Completion, Nonlinear Inductive Matrix Completion, and Deep Inductive Matrix Completion. Our findings show that the nonlinear matrix completion method is particularly effective for handling nonlinear structured data, as exemplified by the Russell 3000. Additionally, we validate the information loss of the three methods across different dimensionalities.