Deep Clustering Evaluation: How to Validate Internal Clustering Validation Measures

Deep clustering partitions complex high-dimensional data using deep neural networks for clustering. It involves projecting data into lower-dimensional embeddings before partitioning, which embarks unique evaluation challenges. Traditional clustering validation measures, designed for low-dimensional spaces, are problematic for deep clustering for two reasons: 1) the curse of dimensionality when applied to the high-dimensional input data, and 2) unreliable comparison of clustering results when applied to embedded data from different embedding spaces, owing to variations in training procedures and model parameter settings. This paper addresses these unresolved and often overlooked challenges in evaluating clustering within deep learning. We propose a systematic evaluation framework for internal clustering validation measures that: (1) theoretically establishes why traditional measures are ineffective when applied to input data or across disparate embedding spaces paired with partitioning outcomes; (2) identifies embedding spaces that endorse reliable evaluations by detecting groups with high agreement in ranking partitioning outcomes; and (3) develops a stable and robust scoring scheme by weighting index values computed across these identified embedding spaces. Experiments show that this new framework aligns better with external measures, effectively reducing the misguidance from the improper use of internal validation measures in deep clustering evaluation.