Multimetric Autoencoder for Representing High-Dimensional and Incomplete Data

High-dimensional and incomplete (HDI) data commonly arise in many complex application scenarios, such as bioinformatics and recommender systems. Deep neural networks (DNNs) exhibit cutting-edge performance in representing HDI data due to their formidable capacity for nonlinear learning. However, previous research primarily concentrates on single-metric-focused models utilizing fixed and exclusive$L_{2}$-norm-based strategies for both loss and regularize terms. Such strategies limit the model’s ability to effectively learn from diverse and heterogeneous HDI data. Recognizing this limitation, this article presents the multimetric autoencoder (MMA) with the following twofold ideas: 1) utilizing multiple$L_{p}$-norms to create four distinct autoencoders, each defining a unique metric representation space with diverse regularize and loss characteristics; 2) integrating these four diverse autoencoders by using a customized, self-adjusting weighting strategy. This innovative approach enhances the model’s capacity to handle heterogeneous and inclusive HDI data effectively, addressing the limitations of previous studies. The theoretical analysis supports the effectiveness of the MMA in harnessing the benefits of diverse multimetric spaces. In the experiments, the MMA is evaluated on six real HDI datasets. The experimental results reveal that the MMA outperforms seven contemporary models in effectively representing HDI data.