# Barnacle Tensor Decomposition Convergence Analysis

## Executive Summary

**None of the 94 parameter combinations tested achieved convergence** for the Barnacle SparseCP tensor decomposition on the multiomics dataset. This indicates a fundamental challenge with the current dataset and/or algorithm configuration that prevents convergence within reasonable computational limits.

## Testing Methodology

### Parameters Tested

1. **Maximum Iterations**: 1000, 2000, 5000, 10000
2. **Convergence Tolerances**: 1e-5, 1e-4, 1e-3
3. **Lambda Regularization Values**:
   - Gene regularization: 0.01, 0.05, 0.1, 0.2, 0.5, 1.0
   - Sample regularization: 0.1, 0.2, 0.5
   - Time regularization: 0.05, 0.1, 0.2

### Test Coverage

- **Total Combinations**: 94 unique parameter sets
- **Successful Runs**: 94/94 (100% success rate)
- **Converged Runs**: 0/94 (0% convergence rate)
- **Final Loss Range**: 840,915 - 1,006,770
- **Tensor Dimensions**: 10,223 genes × 30 samples × 4 timepoints

## Detailed Results

### Convergence Failure Patterns

1. **All parameter combinations failed to converge**
2. **Increasing iterations did not help** (tested up to 10,000 iterations)
3. **Relaxing tolerance did not achieve convergence** (tested down to 1e-3)
4. **No clear pattern of improvement** with different regularization values

### Loss Values by Parameter Category

| Parameter Category | Loss Range | Best Performance |
|-------------------|------------|------------------|
| Baseline (max_iter=1000, tol=1e-5) | 840,915 - 886,452 | 840,915 (λ_gene=0.01) |
| Increased iterations (2000) | 840,915 - 911,497 | 840,915 (λ_gene=0.01) |
| Relaxed tolerance (1e-4) | 864,254 - 911,497 | 864,254 (λ_gene=0.01) |
| High iterations (5000) | 840,915 - 911,497 | 840,915 (λ_gene=0.01) |
| Very relaxed tolerance (1e-3) | 882,064 - 1,006,770 | 882,064 (λ_gene=0.01) |

## Analysis of Results

### Key Findings

1. **Lowest loss consistently achieved** with λ_gene=0.01 across all parameter combinations
2. **No convergence achieved** even with extreme parameters (10,000 iterations, 1e-3 tolerance)
3. **Algorithm stalls** at similar loss values regardless of parameter settings
4. **No evidence** that further parameter tuning will achieve convergence

### Potential Issues

1. **Dataset characteristics** may be incompatible with SparseCP assumptions
2. **Rank 5** may be inappropriate for this 3D tensor (10,223 × 30 × 4)
3. **Data preprocessing** may need revision
4. **Algorithm limitations** with this specific data structure

## Next Steps & Recommendations

### Immediate Actions

1. **Document current state** - Accept that convergence cannot be achieved with current approach
2. **Preserve results** - All 94 test outputs are available for future analysis
3. **Consider alternative approaches** - Evaluate different tensor decomposition methods

### Alternative Approaches to Consider

#### 1. Different Tensor Decomposition Methods
```python
# Consider trying:
# - Tucker decomposition (lower rank core tensor)
# - PARAFAC without sparsity constraints
# - Non-negative matrix factorization on unfolded tensor
# - Canonical correlation analysis approaches
```

#### 2. Data Preprocessing Modifications
- **Normalization strategies**: Try different normalization methods
- **Feature selection**: Reduce gene set size (e.g., top 1000-5000 genes)
- **Rank exploration**: Test ranks 2, 3, 4, 6, 8 instead of rank 5
- **Data transformation**: Consider log-transformation or standardization

#### 3. Algorithm Parameter Reconsideration
- **Different optimization algorithms** within Barnacle
- **Multiple random initializations** (increase n_initializations)
- **Orthogonal constraints** instead of non-negativity
- **Different sparsity patterns**

#### 4. Validation with Simpler Datasets
- **Test on synthetic data** with known structure
- **Compare with smaller real datasets** that should converge
- **Validate algorithm installation** and version compatibility

### Computational Considerations

- **Current approach**: 94 tests × ~5-30 minutes each = ~8-40 hours total
- **Future testing**: Consider parallel processing for parameter sweeps
- **Hardware**: May benefit from GPU acceleration if available

## Conclusion

The systematic convergence testing revealed that **Barnacle SparseCP cannot achieve convergence** on this multiomics dataset with any of the tested parameter combinations. This suggests either:

1. **Fundamental incompatibility** between the algorithm and dataset characteristics
2. **Need for substantial preprocessing changes** or alternative approaches
3. **Algorithm limitations** for this specific data structure

**Recommendation**: Shift focus to alternative tensor decomposition methods or data preprocessing strategies rather than continued parameter optimization.

## Files and Outputs

- **Test outputs**: `M-multi-species/output/14.1-barnacle-convergence-tests/test_001/` through `test_094/`
- **Intermediate results**: Available in `intermediate_results_*.csv` and `intermediate_results_*.json`
- **Parameter combinations**: Defined in `convergence_test.py`
- **Individual run logs**: Available in each test directory

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*Analysis completed: $(date)*
*Total tests: 94*
*Converged: 0*
*Success rate: 100%*
*Convergence rate: 0%*