Mgm Clustering Eval

mgm-clustering-eval

Multiscale Grassmann Manifolds for Single-Cell Data Analysis — Wang et al. (2025) (arXiv:2511.11717, 2025)

What this evaluates

Evaluates the ability of a multiscale Grassmann manifold framework to cluster single-cell RNA-seq data compared to standard dimensionality reduction and clustering baselines. It probes how well non-Euclidean subspace representations preserve cellular structure and handle varying noise levels across different dataset scales.

Datasets

• GSE75748time — total 758; splits: test (-1)
• GSE94820 — total 1140; splits: test (-1)
• GSE67835 — total 420; splits: test (-1)
• GSE75748cell — total 1018; splits: test (-1)
• GSE109979 — total 329; splits: test (-1)
• GSE84133human1 — total 1895; splits: test (-1)
• GSE84133human2 — total 1702; splits: test (-1)
• GSE84133human4 — total 1275; splits: test (-1)
• GSE57249 — total 49; splits: test (-1)

Metrics

• accuracy (ACC) (primary) — range: [0, 1]
  • Maximum accuracy over all permutations of predicted cluster labels to ground-truth classes, typically solved via the Hungarian algorithm.
• normalized mutual information (NMI) — range: [0, 1]
  • Mutual information between predictions and labels normalized by the geometric mean of their entropies.
• adjusted Rand index (ARI) — range: [0, 1]
  • Rand index adjusted for chance, measuring agreement between predicted and true clusterings.
• purity — range: [0, 1]
  • Proportion of cells in the most frequent cluster that belong to the same true class.

Input / output format

Input: Gene expression matrices (cells × genes) for single-cell RNA-seq datasets, typically normalized and log-transformed.

Output: Cluster assignment labels for each cell.

Scoring recipe

def compute_metrics(preds, gold):
    acc = max_accuracy(gold, preds)  # Hungarian algorithm for label matching
    nmi = normalized_mutual_info_score(gold, preds)
    ari = adjusted_rand_score(gold, preds)
    purity = sum(max(Counter(zip(preds, gold))[c] for c in set(preds))) / len(gold)
    return acc, nmi, ari, purity

Common pitfalls

• ACC requires optimal label matching (e.g., Hungarian algorithm) to avoid penalizing arbitrary cluster numbering.
• The paper uses different downstream clustering algorithms for the two setups (spectral clustering for noisy, k-means for refined), so cross-setup comparisons are invalid.
• Baseline metrics for NMF/rNMF in Setup II were copied from prior literature rather than re-run, potentially introducing slight evaluation inconsistencies.

Evidence (verbatim from paper)

Clustering performance was assessed using standard evaluation metrics: accuracy (ACC), normalized mutual information (NMI), adjusted Rand index (ARI), purity, and average purity (Avg-Purity).

Citation

@misc{wang2025mgm,
  title={Multiscale Grassmann Manifolds for Single-Cell Data Analysis},
  author={Wang et al. (2025)},
  year={2025},
  note={arXiv:2511.11717}
}

• arXiv: 2511.11717