## Line Chart: NDCG@10% Performance Across Dimensions
### Overview
The chart compares the normalized discounted cumulative gain (NDCG@10%) performance of four methods (PCA, Search-Adaptor, MRL-Adaptor, SMEC) across increasing data dimensions (128 to 768). All methods show upward trends, with SMEC consistently outperforming others.
### Components/Axes
- **X-axis (Dimensions)**: Logarithmic scale with values 128, 256, 384, 512, 768.
- **Y-axis (NDCG@10%)**: Linear scale from 14% to 24%.
- **Legend**: Located in the bottom-right corner, mapping:
- Blue circles: PCA
- Orange crosses: Search-Adaptor
- Green triangles: MRL-Adaptor
- Yellow squares: SMEC
### Detailed Analysis
1. **PCA (Blue Circles)**:
- 128D: ~13.7%
- 256D: ~16.3%
- 384D: ~17.9%
- 512D: ~18.4%
- 768D: ~18.8%
- *Trend*: Gradual, sublinear growth. Slope decreases with higher dimensions.
2. **Search-Adaptor (Orange Crosses)**:
- 128D: ~19.3%
- 256D: ~20.5%
- 384D: ~21.9%
- 512D: ~22.6%
- 768D: ~23.1%
- *Trend*: Steady linear increase (~0.5% per dimension step).
3. **MRL-Adaptor (Green Triangles)**:
- 128D: ~22.0%
- 256D: ~22.8%
- 384D: ~23.5%
- 512D: ~23.9%
- 768D: ~24.1%
- *Trend*: Near-linear growth (~0.3–0.4% per step).
4. **SMEC (Yellow Squares)**:
- 128D: ~22.6%
- 256D: ~23.4%
- 384D: ~23.8%
- 512D: ~24.1%
- 768D: ~24.4%
- *Trend*: Consistent linear rise (~0.4% per step).
### Key Observations
- **Performance Gaps**:
- PCA starts ~9% below SMEC at 128D but narrows to ~5.6% at 768D.
- Search-Adaptor and MRL-Adaptor maintain ~1.5% separation throughout.
- **Diminishing Returns**: PCA’s growth rate slows significantly after 256D.
- **SMEC Dominance**: SMEC outperforms all methods by ~1.8% at 768D.
### Interpretation
The data demonstrates that higher dimensions generally improve NDCG@10% for all methods, but with varying efficiency:
- **PCA**: Less effective at leveraging high-dimensional data, showing sublinear gains. Likely due to its linear projection limitations.
- **Search-Adaptor/MRL-Adaptor**: Similar scalability, suggesting comparable architectural strengths in handling dimensionality.
- **SMEC**: Most efficient at utilizing increased dimensions, possibly due to advanced feature integration or regularization mechanisms.
The convergence of MRL-Adaptor and SMEC performance implies that both methods are robust to dimensionality, while PCA’s plateau highlights its inherent constraints in high-dimensional spaces. These trends are critical for selecting methods in applications requiring scalable information retrieval.
