  Dimensionality reduction (DR) techniques inherently distort the original
structure of input high-dimensional data, producing imperfect low-dimensional
embeddings. Diverse distortion measures have thus been proposed to evaluate the
reliability of DR embeddings. However, implementing and executing distortion
measures in practice has so far been time-consuming and tedious. To address
this issue, we present ZADU, a Python library that provides distortion
measures. ZADU is not only easy to install and execute but also enables
comprehensive evaluation of DR embeddings through three key features. First,
the library covers a wide range of distortion measures. Second, it
automatically optimizes the execution of distortion measures, substantially
reducing the running time required to execute multiple measures. Last, the
library informs how individual points contribute to the overall distortions,
facilitating the detailed analysis of DR embeddings. By simulating a real-world
scenario of optimizing DR embeddings, we verify that our optimization scheme
substantially reduces the time required to execute distortion measures.
Finally, as an application of ZADU, we present another library called ZADUVis
that allows users to easily create distortion visualizations that depict the
extent to which each region of an embedding suffers from distortions.
