A Fast Nonnegative Autoencoder-Based Approach to Latent Feature Analysis on High-Dimensional and Incomplete Data

High-Dimensional and Incomplete (HDI) data are frequently encountered in various Big Data-related applications. Despite its incompleteness, an HDI data repository contains rich knowledge and patterns concerning the complex interactions among numerous nodes. Recently, a Neural Network (NN)-based approach to Latent Feature Analysis (LFA) model becomes popular owing to its strong representation learning ability to HDI data. Nevertheless, existing NN-based LFA models neglect the inherent nonnegativity in most HDI data, resulting in representation accuracy loss. Motivated by this discovery, this study innovatively proposes a <bold> F</bold>ast <bold> N</bold>onnegative <bold> A</bold>uto<bold> E</bold>ncoder (FNAE)-based approach to LFA on HDI data, whose ideas are three-fold: a) constructing a multilayered autoencoder subject to nonnegativity constraints for high representation learning ability; b) incorporating the data density-oriented modeling mechanism into FNAE's input and output layers for high computational and storage efficiency; and c) implementing an Adam-based single latent factor-dependent, nonnegative and multiplicative update algorithm for efficient model training as well as fulfilling the nonnegativity constraints. Experimental results on eight commonly-adopted HDI matrices from industrial applications demonstrate that the proposed FNAE significantly outperforms several state-of-the-art NN-based LFA models in both estimation accuracy for missing links of an HDI matrix and computational efficiency.