Explainable and cohesive clustering of embeddings with InfoClus Dashboard

Developing an understanding of the top-level structure of high-dimensional data can be facilitated by visualizing that data using a dimensionality reduction method. However, low-dimensional embeddings are often not so straightforward to interpret. To alleviate this problem, we introduce a method for clustering with explanations that partitions the data on the embedding into groups that each have a sparse explanation. Our objective function uses information theory to measure how much we learn from the explanations of the data partitioning, and also how complex the explanations are. This combination yields a tunable optimization objective. To optimize this objective, we employ hierarchical clustering to narrow the search space, and show the objective can then be effectively optimized using greedy search, resulting in a scalable algorithm. We conduct a qualitative and quantitative analysis of InfoClus on three data sets, and find the method efficiently yields useful insights. We contrast the results on the cytometry data with its associated published manual analysis. This comparison highlights that a thresholding procedure used in the manual analysis may lead to false negatives, unlike in the bottom-up analysis using t-SNE and InfoClus. Empirical scalability results for InfoClus show close to linear scaling in number of data points and dimensions. We conclude that InfoClus can automatically create good starting points for the analysis of dimensionality-reduction-based scatter plots.