Zebrafish Sctrans Eval

zebrafish-sctrans-eval

Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomics — Lin (2022) (arXiv:2204.14048, 2022)

What this evaluates

Evaluates the ability of topological data analysis methods to capture developmental transitions and cell lineage dynamics in single-cell RNA sequencing time-series data. It specifically tests whether higher-order simplicial complexity can outperform conventional topological invariants like Betti numbers in identifying critical biological stages.

Datasets

• Farrell et al. (2018) zebrafish scRNA-seq — total 38731; splits: time_step_1 (2225), time_step_2 (200), time_step_3 (1158), time_step_4 (1467), time_step_5 (5716), time_step_6 (1026), time_step_7 (4101), time_step_8 (6178), time_step_9 (5442), time_step_10 (5200), time_step_11 (1614), time_step_12 (4404)

Metrics

• normalized simplicial complexity (primary) — range: other
  • Ratio of the number of n-simplices discovered in the actual data to the number discovered in a corresponding null model.
• Betti numbers — range: other
  • Topological invariants counting the number of n-dimensional holes in the data complex, used here as clustering features.

Input / output format

Input: Standardized gene expression profiles (103 dimensions) for each single cell, grouped by developmental time steps.

Output: Summary statistics (Betti numbers, normalized simplicial complexity) and topological visualizations (persistent diagrams, simplicial networks).

Scoring recipe

def compute_normalized_simplicial_complexity(data, null_data, dim):
    n_simplices_data = count_n_simplices(data, dim)
    n_simplices_null = count_n_simplices(null_data, dim)
    return n_simplices_data / n_simplices_null

Common pitfalls

• Dataset is highly imbalanced across time steps, requiring fixed witness sampling (200 points) to ensure comparability.
• Evaluation relies on comparison to null models rather than ground-truth labels, making traditional accuracy metrics inapplicable.

Evidence (verbatim from paper)

The normalized simplicial complexity (computed as the ratio of the number of simplicial complexes discovered within the data over the number of those discovered within the null model) suggests an abundance of high-dimensional simplices over the null models.

Citation

@misc{lin2022topological,
  title={Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomics},
  author={Lin (2022)},
  year={2022},
  note={arXiv:2204.14048}
}

• arXiv: 2204.14048