MMA: Multi-Metric-Autoencoder for Analyzing High-Dimensional and Incomplete Data

Abstract

High-dimensional and incomplete (HDI) data usually arise in various complex applications, e.g., bioinformatics and recommender systems, making them commonly heterogeneous and inclusive. Deep neural networks (DNNs)-based approaches have provided state-of-the-art representation learning performance on HDI data. However, most prior studies adopt fixed and exclusive $L_2$ -norm-oriented loss and regularization terms. Such a single-metric-oriented model yields limited performance on heterogeneous and inclusive HDI data. Motivated by this, we propose a Multi-Metric-Autoencoder (MMA) whose main ideas are two-fold: 1) employing different $L_p$ -norms to build four variant Autoencoders, each of which resides in a unique metric representation space with different loss and regularization terms, and 2) aggregating these Autoencoders with a tailored, self-adaptive weighting strategy. Theoretical analysis guarantees that our MMA could attain a better representation from a set of dispersed metric spaces. Extensive experiments on four real-world datasets demonstrate that our MMA significantly outperforms seven state-of-the-art models. Our code is available at the link https://github.com/wudi1989/MMA/