Dimensionality Reduction Method for Manifold Learning Based on Variational Autoencoder

Given the rapidly growing scale and complexity of scientific datasets, existing dimensionality reduction methods suffer from the “crowding problem” and the inability to embed new samples. A data dimensionality reduction method based on variational autoencoder uniform manifold approximation and projection (VAE-UMAP) has been proposed. First, to reduce the coupling between the high-dimensional data, the data is compressed into latent variables using a variational autoencoder (VAE). Then, the uniform manifold approximation and projection (UMAP) is used to further reduce the dimensionality of the latent variables, so that the low-dimensional embedding better maintains the similarity relationship within the original data. Finally, the proposed method is fitted with a training set and embedded in an out-of-sample test set to evaluate the generalization ability to the new data. Experimental results show that on the MNIST and Fashion-MNIST datasets, compared to four prominent dimensionality reduction methods UMAP, DensMAP, VAE and AE, the proposed method achieved trustworthiness scores of 0.994 4 and 0.993 9, surpassing the best current method UMAP by 0.031 6 and 0.014 1, respectively. Additionally, there were significant improvements in visualization, Kendall rank correlation coefficient, and classification accuracy metrics.