## Line Chart: NDCG@10/% vs Dimensions ### Overview The chart illustrates the performance of four different methods (PCA, Search-Adaptor, MRL-Adaptor, SMEC) in terms of NDCG@10/% across varying dimensions (128, 256, 512, 768, 1024). Each method is represented by a distinct line with unique markers and colors, showing how their performance evolves as the number of dimensions increases. ### Components/Axes - **X-axis (Dimensions)**: Labeled "Dimensions" with discrete values: 128, 256, 512, 768, 1024. - **Y-axis (NDCG@10/%**: Labeled "NDCG@10/%" with a range from 40 to 52. - **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)**: - Starts at **40%** at 128 dimensions. - Increases steadily to **46%** at 256, **47.5%** at 512, **48%** at 768, and **48.5%** at 1024. - **Trend**: Gradual upward slope with minimal acceleration. 2. **Search-Adaptor (Orange Crosses)**: - Begins at **46.5%** at 128 dimensions. - Rises sharply to **49.5%** at 256, **51.5%** at 512, **52%** at 768, and **52.5%** at 1024. - **Trend**: Steep initial increase, then plateaus slightly. 3. **MRL-Adaptor (Green Triangles)**: - Starts at **49%** at 128 dimensions. - Increases to **50.5%** at 256, **51.8%** at 512, **52.2%** at 768, and **52.5%** at 1024. - **Trend**: Consistent upward trajectory with moderate growth. 4. **SMEC (Yellow Squares)**: - Begins at **50%** at 128 dimensions. - Rises to **51%** at 256, **52%** at 512, **52.5%** at 768, and **53%** at 1024. - **Trend**: Steady linear increase with minimal fluctuation. ### Key Observations - **PCA** consistently underperforms compared to other methods, showing the slowest growth. - **Search-Adaptor** and **MRL-Adaptor** exhibit similar performance, with Search-Adaptor slightly outperforming at higher dimensions. - **SMEC** maintains the highest performance across all dimensions, with a slight edge over MRL-Adaptor at 1024. - All methods show improvement as dimensions increase, but the rate of improvement varies. ### Interpretation The data suggests that increasing the number of dimensions generally enhances NDCG@10/% performance for all methods. However, **SMEC** and **MRL-Adaptor** demonstrate superior scalability, achieving higher scores even at lower dimensions. **PCA** lags behind, indicating it may not be as effective for this task. The sharp rise of **Search-Adaptor** at lower dimensions suggests it is particularly sensitive to dimensionality changes, potentially making it a strong candidate for scenarios where dimensionality is constrained. The plateau in Search-Adaptor’s growth at higher dimensions implies diminishing returns beyond a certain point. This chart highlights the trade-offs between computational complexity (dimensions) and performance gains, guiding method selection based on specific use cases.