  Deep image clustering methods are typically evaluated on small-scale balanced
classification datasets while feature-based $k$-means has been applied on
proprietary billion-scale datasets. In this work, we explore the performance of
feature-based deep clustering approaches on large-scale benchmarks whilst
disentangling the impact of the following data-related factors: i) class
imbalance, ii) class granularity, iii) easy-to-recognize classes, and iv) the
ability to capture multiple classes. Consequently, we develop multiple new
benchmarks based on ImageNet21K. Our experimental analysis reveals that
feature-based $k$-means is often unfairly evaluated on balanced datasets.
However, deep clustering methods outperform $k$-means across most large-scale
benchmarks. Interestingly, $k$-means underperforms on easy-to-classify
benchmarks by large margins. The performance gap, however, diminishes on the
highest data regimes such as ImageNet21K. Finally, we find that non-primary
cluster predictions capture meaningful classes (i.e. coarser classes).
