Effects of loss function and data sparsity on smooth manifold extraction with deep model

• Proper loss function selection improves smoothness better than the reduction of data sparsity. The less sensitive a deep model is to sparsity, smoother extracted manifold is. Simply stacking hidden layers in does not significantly improve smoothness. Deep useful tool that can extract smooth from data. As computationally intensive method, however, parameters and sparsity are common factors likely cause uncertainty consequently affect result. Thus, it challenge design an effective for extraction without prior knowledge target datasets, which usually sparse many real-world applications. In this paper, we proposed based on Brenier theorem manifold. Beyond design, several experiments both simulated datasets were conducted explore three scientific questions: 1) How or select appropriate neural network fit data, will be helpful manifold? 2) model’s sensitivity extraction? And 3) What relative importance these improving Results showed our outperformed state-of-the-art models metrics, such as computational error. demonstrated extract. Our finding indicated by dependent layout functions, means simply stack way extraction. addition, exploration also suggested functions carries more weights investing effort overcoming