Technical confounding

Acquisition artifacts

Is clustering tracking biology, or something technical -- clinical site, scanner, staining batch? For PathMNIST, this is directly testable using its real NCT-CRC-HE-100K vs. CRC-VAL-HE-7K site split. This analysis may matter more than any headline clustering score (Section 18 of the project scope).

Representation	Cramer's V vs. label	Cramer's V vs. site	Site association detected	Site stronger than label
PCA on pixels	0.443	0.272	yes	no
Handcrafted color/texture	0.373	0.140	yes	no
HOG	0.272	0.146	yes	no
ResNet50 (ImageNet-supervised)	0.542	0.162	yes	no
DINO ViT-S/16	0.670	0.160	yes	no
DINOv2 ViT-S/14	0.699	0.135	yes	no

Computed on the union of PathMNIST's train (NCT-CRC-HE-100K) and test (CRC-VAL-HE-7K) subsamples, clustered jointly at k = number of annotated tissue classes. Cramer's V measures association strength (0 = none, 1 = perfect); p-value is from a chi-squared test of independence between cluster assignment and the site variable. This axis is not available for BloodMNIST -- no site/scanner metadata is exposed in its public release (see Datasets).

Does clustering input choice change the answer?

Hypothesis H4: clustering directly on 2D UMAP coordinates should recover meaningfully less external structure than clustering on full (or PCA-reduced) feature space. This table runs the identical clustering pipeline on three different inputs derived from the same features.

Dataset	Representation	Clustering input	Dimensions	External ARI	External NMI
pathmnist	PCA on pixels	full feature space	50	0.240	0.411
pathmnist	PCA on pixels	pca 10d	10	0.224	0.408
pathmnist	PCA on pixels	umap 2d used as clustering input	2	0.250	0.431
pathmnist	Handcrafted color/texture	full feature space	56	0.183	0.288
pathmnist	Handcrafted color/texture	pca 10d	10	0.183	0.288
pathmnist	Handcrafted color/texture	umap 2d used as clustering input	2	0.159	0.267
pathmnist	HOG	full feature space	1296	0.076	0.153
pathmnist	HOG	pca 10d	10	0.088	0.203
pathmnist	HOG	umap 2d used as clustering input	2	0.051	0.110
pathmnist	ResNet50 (ImageNet-supervised)	full feature space	2048	0.345	0.513
pathmnist	ResNet50 (ImageNet-supervised)	pca 10d	10	0.345	0.509
pathmnist	ResNet50 (ImageNet-supervised)	umap 2d used as clustering input	2	0.513	0.638
pathmnist	DINO ViT-S/16	full feature space	384	0.525	0.669
pathmnist	DINO ViT-S/16	pca 10d	10	0.549	0.676
pathmnist	DINO ViT-S/16	umap 2d used as clustering input	2	0.577	0.724
pathmnist	DINOv2 ViT-S/14	full feature space	384	0.550	0.685
pathmnist	DINOv2 ViT-S/14	pca 10d	10	0.555	0.666
pathmnist	DINOv2 ViT-S/14	umap 2d used as clustering input	2	0.592	0.735
bloodmnist	PCA on pixels	full feature space	50	0.330	0.430
bloodmnist	PCA on pixels	pca 10d	10	0.306	0.406
bloodmnist	PCA on pixels	umap 2d used as clustering input	2	0.285	0.378
bloodmnist	Handcrafted color/texture	full feature space	56	0.103	0.224
bloodmnist	Handcrafted color/texture	pca 10d	10	0.103	0.224
bloodmnist	Handcrafted color/texture	umap 2d used as clustering input	2	0.138	0.208
bloodmnist	HOG	full feature space	1296	0.226	0.339
bloodmnist	HOG	pca 10d	10	0.204	0.328
bloodmnist	HOG	umap 2d used as clustering input	2	0.227	0.333
bloodmnist	ResNet50 (ImageNet-supervised)	full feature space	2048	0.172	0.281
bloodmnist	ResNet50 (ImageNet-supervised)	pca 10d	10	0.180	0.285
bloodmnist	ResNet50 (ImageNet-supervised)	umap 2d used as clustering input	2	0.242	0.344
bloodmnist	DINO ViT-S/16	full feature space	384	0.315	0.441
bloodmnist	DINO ViT-S/16	pca 10d	10	0.277	0.408
bloodmnist	DINO ViT-S/16	umap 2d used as clustering input	2	0.481	0.572
bloodmnist	DINOv2 ViT-S/14	full feature space	384	0.202	0.269
bloodmnist	DINOv2 ViT-S/14	pca 10d	10	0.184	0.254
bloodmnist	DINOv2 ViT-S/14	umap 2d used as clustering input	2	0.297	0.383

A detected site association is not an error

If a representation clusters partly along acquisition site, that is a real property of the representation and the data, not a bug in this analysis. It means some fraction of latent structure reflects technical variation rather than tissue biology -- exactly the kind of finding a benchmark like this exists to surface.