  Deep clustering, a method for partitioning complex, high-dimensional data
using deep neural networks, presents unique evaluation challenges. Traditional
clustering validation measures, designed for low-dimensional spaces, are
problematic for deep clustering, which involves projecting data into
lower-dimensional embeddings before partitioning. Two key issues are
identified: 1) the curse of dimensionality when applying these measures to raw
data, and 2) the unreliable comparison of clustering results across different
embedding spaces stemming from variations in training procedures and parameter
settings in different clustering models. This paper addresses these challenges
in evaluating clustering quality in deep learning. We present a theoretical
framework to highlight ineffectiveness arising from using internal validation
measures on raw and embedded data and propose a systematic approach to applying
clustering validity indices in deep clustering contexts. Experiments show that
this framework aligns better with external validation measures, effectively
reducing the misguidance from the improper use of clustering validity indices
in deep learning.
