  Dimensionality reduction (DR) is frequently used for analyzing and
visualizing high-dimensional data as it provides a good first glance of the
data. However, to interpret the DR result for gaining useful insights from the
data, it would take additional analysis effort such as identifying clusters and
understanding their characteristics. While there are many automatic methods
(e.g., density-based clustering methods) to identify clusters, effective
methods for understanding a cluster's characteristics are still lacking. A
cluster can be mostly characterized by its distribution of feature values.
Reviewing the original feature values is not a straightforward task when the
number of features is large. To address this challenge, we present a visual
analytics method that effectively highlights the essential features of a
cluster in a DR result. To extract the essential features, we introduce an
enhanced usage of contrastive principal component analysis (cPCA). Our method,
called ccPCA (contrasting clusters in PCA), can calculate each feature's
relative contribution to the contrast between one cluster and other clusters.
With ccPCA, we have created an interactive system including a scalable
visualization of clusters' feature contributions. We demonstrate the
effectiveness of our method and system with case studies using several publicly
available datasets.
