Visualization of Non-metric Relationships by Adaptive Learning Multiple Maps t-SNE Regularization

Known as phenotypic overlapping, some disease-related symptoms share a common pathological and physiological mechanism. Researchers attempt to visualize the phenotypic relationships between different human diseases from the perspective of machine learning, but traditional visualization methods may be subject to fundamental limitations of metric spaces. Multiple maps t-SNE regularization method, a probabilistic method for visualizing data points in multiple low-dimensional spaces has been proposed to address the limitation. However, the convergence speed is low when apply on the scale dataset. We use the RMSProp with Nesterov momentum method to learn the objective loss function. This method normalize the gradients by applying an exponential moving average of gradient magnitude for each iteration parameter and use Nesterov momentum to counterweigh too high velocities by "peeking ahead" actual objective values in the candidate search direction. This method convergent faster than the original method of convergence speed. Experiments results on several dataset shows that the proposed method outperforms the several version of mm-tSNE with or without regularization, as measured by the neighborhood preservation ratio and error rate. This suggests the modified mm-tSNE regularization can be applied directly in other domain including social, biological and microbiomic datasets.