Uniform Manifold Approximation and Projection (UMAP) is a dimensionality reduction method that has been shown to have advantages over other methods such as principal component analysis (PCA),...Show moreUniform Manifold Approximation and Projection (UMAP) is a dimensionality reduction method that has been shown to have advantages over other methods such as principal component analysis (PCA), multidimensional scaling (MDS), and t-distributed stochastic neighbour embedding (t-SNE) for data visualization. Although valuable, previous comparisons between these methods have not been done with data from Likert scales. Likert scales are common in psychological research and often cause data to contain ties. This study therefore compared UMAP to PCA, MDS, and t-SNE for three datasets varying in feature types. We included a dataset that was used in previous research (MNIST), a dataset containing Likert scales (CCAM), and a simulated personality dataset to confirm findings. The latter two datasets were edited into two versions that did contain ties and did not. Comparisons were done mainly on local and global structure preservation between visual embeddings of the respective methods. Additionally, we inspected what advantages the different dimensionality reduction methods provided. For datasets without ties, UMAP and t-SNE performed similarly in local structure preservation. However, UMAP showed arguably better global structure preservation than t-SNE. Valuable global structure could also be achieved with t-SNE but this was at the cost of a higher runtime. UMAP and t-SNE both arguably showed a better clustered structure in embeddings compared to PCA and MDS. On the other hand, PCA embeddings provided insights into feature relationships that UMAP did not provide. For datasets with ties, UMAP and t-SNE both suffered in terms of local and global structure. Embeddings were substantially different compared to the embeddings from data without ties. In some cases, UMAP showed a clustered structure arguably worse than PCA. We conclude that UMAP is recommended over t-SNE for data visualization if a clustered structure can be assumed in data since it provides similar local structure but better global structure. This is however only true for data without ties. Therefore we recommend dealing with ties before using UMAP and t-SNE. Finally, PCA is still recommended when the interpretability of feature relationships is concerned.Show less
