High-Dimensional and Incomplete (HDI) data are frequently found in various industrial applications with complex interactions among numerous nodes, which are commonly non-negative for representing the inherent non-negativity of node interactions. A Non-negative Latent Factor (NLF) model is able to extract intrinsic features from such data efficiently. However, existing NLF models all adopt a static divergence metric like Euclidean distance or {\alpha}-\b{eta} divergence to build its learning objective, which greatly restricts its scalability of accurately representing HDI data from different domains. Aiming at addressing this issue, this study presents an Adaptive Divergence-based Non-negative Latent Factor (ADNLF) model with three-fold ideas: a) generalizing the objective function with the {\alpha}-\b{eta}-divergence to expand its potential of representing various HDI data; b) adopting a non-negative bridging function to connect the optimization variables with output latent factors for fulfilling the non-negativity constraints constantly; and c) making the divergence parameters adaptive through particle swarm optimization, thereby facilitating adaptive divergence in the learning objective to achieve high scalability. Empirical studies are conducted on four HDI datasets from real applications, whose results demonstrate that in comparison with state-of-the-art NLF models, an ADNLF model achieves significantly higher estimation accuracy for missing data of an HDI dataset with high computational efficiency.

Adversarial Optimization (AO) provides a reliable, practical way to match two implicitly defined distributions, one of which is usually represented by a sample of real data, and the other is defined by a generator. Typically, AO involves training of a high-capacity model on each step of the optimization. In this work, we consider computationally heavy generators, for which training of high-capacity models is associated with substantial computational costs. To address this problem, we introduce a novel family of divergences, which varies the capacity of the underlying model, and allows for a significant acceleration with respect to the number of samples drawn from the generator. We demonstrate the performance of the proposed divergences on several tasks, including tuning parameters of a physics simulator, namely, Pythia event generator.