Nonlinear expression and visualization of nonmetric relationships in genetic diseases and microbiome data

The traditional methods of visualizing high-dimensional data objects in low-dimensional metric spaces are subject to the basic limitations of metric space. These limitations result in multidimensional scaling that fails to faithfully represent non-metric similarity data.

Multiple maps t-SNE (mm-tSNE) has drawn much attention due to the construction of multiple mappings in low-dimensional space to visualize the non-metric pairwise similarity to eliminate the limitations of a single metric map. mm-tSNE regularization combines the intrinsic geometry between data points in a high-dimensional space. The weight of data points on each map is used as the regularization parameter of the manifold, so the weights of similar data points on the same map are also as close as possible. However, these methods use standard momentum methods to calculate parameters of gradient at each iteration, which may lead to erroneous gradient search directions so that the target loss function fails to achieve a better local minimum. In this article, we use a Nesterov momentum method to learn the target loss function and correct each gradient update by looking back at the previous gradient in the candidate search direction. By using indirect second-order information, the algorithm obtains faster convergence than the original algorithm. To further evaluate our approach from a comparative perspective, we conducted experiments on several datasets including social network data, phenotype similarity data, and microbiomic data.

The experimental results show that the proposed method achieves better results than several versions of mm-tSNE based on three evaluation indicators including the neighborhood preservation ratio (NPR), error rate and time complexity.