FindVar

A TDA-Based Cancer Biomarker Discovery Pipeline

FindVar is a project that applies Topological Data Analysis (TDA) to TCGA-BRCA RNA-seq data to identify cancer-associated biomarker gene sets that cannot be discovered through conventional Euclidean statistical methods. The project ultimately identifies the H2C Gene Panel, a topology-driven biomarker signature with strong predictive power.

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Key Findings

Finding	Description
H1 Loop Structures	Tumor samples exhibit 2.5× more H1 loops than normal samples (p < 0.001).
0% Gene Overlap	The top 200 genes identified by TDA and Euclidean statistics are completely disjoint.
H2C Gene Panel	A set of 37 genes, all statistically non-significant under Euclidean analysis (p > 0.05), achieves AUC = 0.993.
Pathway Orthogonality	TDA highlights cell invasion and cytoskeletal pathways, whereas Euclidean methods identify metabolic and ion-channel pathways, with zero pathway overlap.

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Project Structure

FindVar/
├── README.md                                ← This document
├── plan.md                                  ← Overall analysis plan
├── result.md                                ← Consolidated results (for manuscript preparation)
│
├── phase1_tda_setup/                        ← Phase 1: Exploratory TDA analysis
│   ├── verify_install.py                    │  Library installation verification
│   ├── explore_ph.py                        │  Persistent Homology exploration
│   ├── PHASE1_REPORT.md                     │  Analysis report
│   └── results/
│       ├── ph_comparison_summary.csv        │  PH comparison summary table
│       ├── ph_diagram_*.png                 │  Persistence diagrams (5 settings)
│       └── distance_comparison.png          │  Wasserstein/Bottleneck comparison
│
├── phase2_persistent_homology/              ← Phase 2: Statistical validation
│   ├── analyze_ph.py                        │  Permutation tests + bootstrap analysis
│   ├── PHASE2_REPORT.md                     │  Analysis report
│   └── results/
│       ├── permutation_test_results.csv     │  Permutation p-values
│       ├── h1_count_test_results.csv        │  H1 count test (key result)
│       ├── bootstrap_stability_results.csv  │  Bootstrap stability analysis
│       ├── permutation_null_distributions.png
│       ├── h1_count_comparison.png          │  ★ H1 count: Tumor vs Normal
│       ├── observed_vs_null_comparison.png
│       └── bootstrap_stability.png
│
├── phase3_gene_traceback/                   ← Phase 3: Gene attribution
│   ├── traceback_genes.py                   │  Decoder Jacobian-based gene tracing
│   ├── PHASE3_REPORT.md                     │  Analysis report
│   └── results/
│       ├── gene_importance_full.csv         │  Full ranking of 20,876 genes
│       ├── gene_importance_top100.csv       │  Detailed Top 100 genes
│       ├── tda_only_genes.csv               │  200 TDA-exclusive genes
│       ├── both_methods_genes.csv           │  Genes identified by both methods (0 genes)
│       ├── latent_dimension_analysis.csv    │  Analysis of 32 latent dimensions
│       ├── top30_genes.png                  │  Top 30 gene importance chart
│       ├── tda_vs_euclidean_rank.png        │  ★ TDA vs Euclidean scatter plot
│       ├── discovery_comparison.png         │  Gene discovery Venn diagram
│       ├── latent_dimension_importance.png
│       └── latent_pca.png
│
├── phase4_biological_interpretation/        ← Phase 4: Pathway analysis and validation
│   ├── pathway_and_validation.py            │  GO/KEGG enrichment + classification
│   ├── PHASE4_REPORT.md                     │  Analysis report
│   └── results/
│       ├── enrichment_tda_top200.csv        │  TDA pathway enrichment
│       ├── enrichment_euclidean_top200.csv  │  Euclidean pathway enrichment
│       ├── classification_results.csv       │  Classification performance
│       ├── pathway_overlap_summary.csv      │  Pathway overlap summary
│       ├── classification_comparison.png    │  ★ Classification comparison
│       └── pathway_comparison.png           │  ★ Pathway comparison
│
└── phase5_visualization_paper/              ← Phase 5: Publication-ready figures
    ├── generate_figures.py                  │  Figure generation script
    └── figures/
        ├── fig2_persistence_diagrams.pdf    │  Persistence diagrams
        ├── fig3_statistical_validation.pdf  │  Statistical validation
        ├── fig4_gene_discovery.pdf          │  Gene discovery
        ├── fig5_pathway_comparison.pdf      │  Pathway comparison
        ├── fig6_classification.pdf          │  Classification performance
        ├── fig7_latent_space.pdf            │  Latent space visualization
        ├── summary_figure.pdf               │  Overall summary figure
        └── *.png                            │  PNG versions

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Analysis Pipeline

TCGA-BRCA RNA-seq (1,215 samples × 20,862 genes)
  │
  ├─ [Preprocessing] log1p → GPU ComBat → Gene Filtering
  │
  ├─ [TAE] Topological Autoencoder (32-dimensional cosine latent space)
  │
  ├─ [Phase 1] Persistent Homology Exploration
  │       → Detect topological differences between tumor and normal samples
  │
  ├─ [Phase 2] Size-Matched Permutation Testing
  │       → H1 loop enrichment (p < 0.001)
  │
  ├─ [Phase 3] Decoder Jacobian Analysis
  │       → Gene attribution and traceback
  │       → 0% overlap between TDA and Euclidean discoveries
  │
  ├─ [Phase 4] Pathway Enrichment + Classification Validation
  │       → H2C Panel achieves AUC = 0.993
  │
  └─ [Phase 5] Publication-Ready Figure Generation
          → Vectorized PDF figures

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H2C Gene Panel

The H2C Gene Panel consists of 37 genes that are completely non-significant under conventional Euclidean statistical testing (p > 0.05) but are identified as highly influential through topological analysis.

Representative genes:

Gene	TDA Rank	Euclidean p-value	Biological Function
EFCAB3	8	0.791	Calcium-binding domain protein
PGC	11	0.908	Pepsinogen C
RPRM	13	0.206	p53 target involved in G2 checkpoint regulation
RPRML	14	0.333	Reprimo-like protein
HSPB9	18	0.924	Small heat shock protein

Complete gene list: phase3_gene_traceback/results/tda_only_genes.csv

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Software Environment

Component	Version
Python	3.12.13 (conda: tda)
PyTorch	2.11.0+cu126
ripser	0.6.14
persim	0.3.8
gudhi	3.12.0
scikit-learn	1.8.0
gseapy	1.1.13

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Related Repositories

Repository	Description
Data-preprocessing	Data preprocessing and Topological Autoencoder training
FindVar	TDA analysis and H2C biomarker discovery