## Heatmap: Accuracy Difference between BO and GCN ### Overview The image is a heatmap visualizing the difference in test accuracy (Acc_test) between Bayesian Optimization (BO) and Graph Convolutional Networks (GCN) across different values of parameters lambda (λ) and mu (μ). The color intensity represents the magnitude of the accuracy difference, with yellow indicating higher accuracy for BO compared to GCN, and dark purple indicating lower accuracy. ### Components/Axes * **X-axis (Horizontal):** λ (lambda), ranging from 0.25 to 2.00 in increments of 0.25. * **Y-axis (Vertical):** μ (mu), ranging from 0.25 to 2.00 in increments of 0.25. * **Colorbar (Right):** Represents Acc_test (BO - GCN), ranging from approximately 0.00 (dark purple) to 0.12 (yellow). ### Detailed Analysis The heatmap consists of a grid of colored cells, where each cell represents a combination of λ and μ values. The color of each cell indicates the difference in test accuracy between BO and GCN for that specific parameter combination. Here's a breakdown of the data based on visual inspection: * **Trend:** The top-left region of the heatmap (low λ, high μ) shows the highest accuracy difference (yellow), indicating that BO performs significantly better than GCN in this parameter range. As we move towards the bottom-right (high λ, low μ), the color shifts towards dark purple, indicating that the accuracy difference decreases, and GCN may perform comparably or better than BO. * **Specific Values (Approximate):** * λ = 0.25, μ = 2.00: Acc_test (BO - GCN) ≈ 0.12 (Yellow) * λ = 0.25, μ = 1.75: Acc_test (BO - GCN) ≈ 0.11 (Yellow-Green) * λ = 0.50, μ = 2.00: Acc_test (BO - GCN) ≈ 0.10 (Yellow-Green) * λ = 0.25, μ = 1.50: Acc_test (BO - GCN) ≈ 0.09 (Green) * λ = 2.00, μ = 0.25: Acc_test (BO - GCN) ≈ 0.00 (Dark Purple) * λ = 1.75, μ = 0.25: Acc_test (BO - GCN) ≈ 0.01 (Dark Purple) ### Key Observations * The largest positive difference in accuracy (BO > GCN) occurs when λ is low (0.25-0.50) and μ is high (1.75-2.00). * The accuracy difference decreases as λ increases and μ decreases. * The smallest difference in accuracy (BO ≈ GCN or BO < GCN) occurs when λ is high (1.75-2.00) and μ is low (0.25-0.50). ### Interpretation The heatmap suggests that the relative performance of Bayesian Optimization (BO) compared to Graph Convolutional Networks (GCN) is highly dependent on the values of parameters λ and μ. Specifically, BO tends to outperform GCN when λ is small and μ is large. This could indicate that BO is better suited for certain types of optimization problems or network architectures characterized by these parameter ranges. Conversely, GCN may be more effective when λ is large and μ is small. The choice between BO and GCN should therefore consider the specific characteristics of the problem and the desired parameter settings.

\n ## Heatmap: BO - GCN Accuracy ### Overview The image presents a heatmap visualizing the relationship between two parameters, λ (lambda) and μ (mu), and their impact on the test accuracy (Acc_test) of a Bayesian Optimization - Graph Convolutional Network (BO-GCN) model. The heatmap displays a color gradient representing the accuracy values, ranging from approximately 0.02 (dark purple) to 0.12 (bright yellow). ### Components/Axes * **X-axis:** λ (lambda) - ranges from 0.25 to 2.00, with increments of approximately 0.25. * **Y-axis:** μ (mu) - ranges from 0.25 to 2.00, with increments of approximately 0.25. * **Color Scale (Legend):** Located on the right side of the heatmap, the color scale represents the Acc_test (BO - GCN) values. * Yellow: ~0.12 * Light Green: ~0.10 * Green: ~0.08 * Light Blue: ~0.06 * Blue: ~0.04 * Dark Purple: ~0.02 ### Detailed Analysis The heatmap is a 9x9 grid, representing combinations of λ and μ values. The color intensity at each grid point corresponds to the Acc_test value for that specific combination. Here's a breakdown of approximate Acc_test values based on the color gradient: * **λ = 0.25:** * μ = 0.25: ~0.02 * μ = 0.50: ~0.04 * μ = 0.75: ~0.06 * μ = 1.00: ~0.08 * μ = 1.25: ~0.08 * μ = 1.50: ~0.06 * μ = 1.75: ~0.04 * μ = 2.00: ~0.02 * **λ = 0.50:** * μ = 0.25: ~0.04 * μ = 0.50: ~0.06 * μ = 0.75: ~0.08 * μ = 1.00: ~0.10 * μ = 1.25: ~0.10 * μ = 1.50: ~0.08 * μ = 1.75: ~0.06 * μ = 2.00: ~0.04 * **λ = 0.75:** * μ = 0.25: ~0.06 * μ = 0.50: ~0.08 * μ = 0.75: ~0.10 * μ = 1.00: ~0.12 * μ = 1.25: ~0.10 * μ = 1.50: ~0.08 * μ = 1.75: ~0.06 * μ = 2.00: ~0.04 * **λ = 1.00:** * μ = 0.25: ~0.08 * μ = 0.50: ~0.10 * μ = 0.75: ~0.12 * μ = 1.00: ~0.12 * μ = 1.25: ~0.10 * μ = 1.50: ~0.08 * μ = 1.75: ~0.06 * μ = 2.00: ~0.04 * **λ = 1.25:** * μ = 0.25: ~0.08 * μ = 0.50: ~0.10 * μ = 0.75: ~0.10 * μ = 1.00: ~0.08 * μ = 1.25: ~0.06 * μ = 1.50: ~0.04 * μ = 1.75: ~0.02 * μ = 2.00: ~0.02 * **λ = 1.50:** * μ = 0.25: ~0.06 * μ = 0.50: ~0.08 * μ = 0.75: ~0.10 * μ = 1.00: ~0.08 * μ = 1.25: ~0.06 * μ = 1.50: ~0.04 * μ = 1.75: ~0.02 * μ = 2.00: ~0.02 * **λ = 1.75:** * μ = 0.25: ~0.04 * μ = 0.50: ~0.06 * μ = 0.75: ~0.08 * μ = 1.00: ~0.06 * μ = 1.25: ~0.04 * μ = 1.50: ~0.02 * μ = 1.75: ~0.02 * μ = 2.00: ~0.02 * **λ = 2.00:** * μ = 0.25: ~0.02 * μ = 0.50: ~0.04 * μ = 0.75: ~0.06 * μ = 1.00: ~0.04 * μ = 1.25: ~0.02 * μ = 1.50: ~0.02 * μ = 1.75: ~0.02 * μ = 2.00: ~0.02 ### Key Observations * The highest accuracy values (around 0.12) are concentrated in the region where both λ and μ are around 0.75 to 1.00. * Accuracy generally decreases as λ and μ move away from this optimal region, towards lower or higher values. * There's a noticeable diagonal pattern, suggesting a correlation between λ and μ in influencing the accuracy. * The bottom-left and top-right corners of the heatmap consistently show the lowest accuracy values (around 0.02). ### Interpretation The heatmap demonstrates the impact of the hyperparameters λ and μ on the performance of the BO-GCN model. The optimal combination of these parameters appears to be around λ = 0.75-1.00 and μ = 0.75-1.00, where the model achieves the highest test accuracy. The decrease in accuracy as these parameters deviate from the optimal range suggests that these values are crucial for the model's ability to effectively learn and generalize. The diagonal pattern indicates that the interplay between λ and μ is important; increasing one parameter may require adjusting the other to maintain optimal performance. The heatmap provides valuable insights for hyperparameter tuning, guiding the selection of λ and μ values to maximize the model's accuracy. The data suggests a non-linear relationship between the parameters and the accuracy, as the highest accuracy is not achieved at the maximum values of either parameter.

\n ## Heatmap: Acc_BO-GCN vs. μ and λ ### Overview The image is a 2D heatmap visualizing the relationship between two parameters, μ (mu) and λ (lambda), and a performance metric labeled "Acc_BO-GCN" (likely Accuracy of a Bayesian Optimization - Graph Convolutional Network model). The color intensity represents the accuracy value, with a gradient from dark purple (low accuracy) to bright yellow (high accuracy). ### Components/Axes * **X-Axis (Horizontal):** * **Label:** λ (lambda) * **Scale:** Linear, ranging from approximately 0.25 to 2.00. * **Markers:** Major ticks are present at 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00. * **Y-Axis (Vertical):** * **Label:** μ (mu) * **Scale:** Linear, ranging from approximately 0.25 to 2.00. * **Markers:** Major ticks are present at 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00. * **Color Bar (Legend):** * **Placement:** Right side of the heatmap, vertically oriented. * **Label:** Acc_BO-GCN * **Scale:** Linear, ranging from approximately 0.02 to 0.12. * **Gradient:** The color scale transitions from dark purple at the bottom (≈0.02) through teal and green to bright yellow at the top (≈0.12). The bar has pointed ends, indicating the scale extends slightly beyond the labeled ticks. ### Detailed Analysis The heatmap is a grid of colored cells, where each cell's color corresponds to the Acc_BO-GCN value for a specific (λ, μ) pair. The grid appears to have a resolution of approximately 8x8 major cells, with smooth color interpolation between them. **Trend Verification:** The overall visual trend shows a diagonal gradient. Accuracy is highest in the top-left region and decreases towards the bottom-right. * **High Accuracy Region (Top-Left):** The brightest yellow cells are concentrated where λ is low (≈0.25-0.50) and μ is high (≈1.75-2.00). The peak accuracy (≈0.12) appears to be at the very top-left corner (λ≈0.25, μ≈2.00). * **Medium Accuracy Region (Diagonal Band):** A band of green and teal colors runs diagonally from the top-right (high λ, high μ) to the bottom-left (low λ, low μ). For example, at (λ≈1.00, μ≈1.00), the color is a medium teal, corresponding to an accuracy of approximately 0.06-0.07. * **Low Accuracy Region (Bottom-Right):** The darkest purple cells are in the bottom-right corner, where both λ and μ are high (λ≈1.75-2.00, μ≈0.25-0.50). The lowest accuracy (≈0.02) is found in this region. **Spatial Grounding & Approximate Values:** * At (λ=0.25, μ=2.00): Bright yellow, Acc_BO-GCN ≈ 0.12. * At (λ=0.50, μ=1.50): Light green, Acc_BO-GCN ≈ 0.09. * At (λ=1.00, μ=1.00): Teal, Acc_BO-GCN ≈ 0.065. * At (λ=1.50, μ=0.75): Dark blue/purple, Acc_BO-GCN ≈ 0.03. * At (λ=2.00, μ=0.25): Darkest purple, Acc_BO-GCN ≈ 0.02. ### Key Observations 1. **Strong Diagonal Gradient:** The most prominent pattern is the smooth, diagonal transition from high accuracy (top-left) to low accuracy (bottom-right). This indicates a strong interaction effect between λ and μ on the model's accuracy. 2. **Optimal Parameter Region:** The model performance is maximized for **low λ combined with high μ**. This suggests that for this specific BO-GCN configuration, a smaller λ parameter and a larger μ parameter are beneficial. 3. **Performance Degradation:** Accuracy degrades most rapidly as one moves from the top-left towards the bottom-right corner. Moving purely horizontally (increasing λ while holding μ constant) or purely vertically (decreasing μ while holding λ constant) also decreases accuracy, but the combined effect is strongest along the diagonal. 4. **No Extreme Outliers:** The color gradient is smooth without isolated cells of contrasting color, suggesting the model's performance changes predictably and consistently across this parameter space. ### Interpretation This heatmap provides a clear visual guide for hyperparameter tuning of the BO-GCN model. The data demonstrates that the parameters λ and μ are not independent; their joint values critically determine model accuracy. * **What it Suggests:** The model is sensitive to the balance between λ and μ. The optimal configuration lies in a specific region of the parameter space (low λ, high μ). This could imply that λ controls a regularization or complexity term that should be kept small, while μ might control a feature or influence term that should be emphasized. * **Relationship Between Elements:** The axes (λ, μ) are the independent control variables, and the color (Acc_BO-GCN) is the dependent performance metric. The color bar is the essential key that translates the visual pattern into quantitative insight. * **Notable Implications:** The smooth gradient indicates that the performance surface is well-behaved in this region, which is favorable for optimization algorithms like Bayesian Optimization. A practitioner would use this map to narrow their search for the best parameters to the top-left quadrant, potentially saving significant computational resources. The absence of performance "cliffs" or plateaus suggests that fine-tuning within the high-accuracy region should yield reliable improvements.

## Heatmap: Accuracy Difference (Acc_test(BO - GCN)) vs. μ and λ ### Overview The image is a heatmap visualizing the difference in test accuracy (Acc_test) between Bayesian Optimization (BO) and Graph Convolutional Networks (GCN) across varying hyperparameters μ (y-axis) and λ (x-axis). The color gradient ranges from purple (low values) to yellow (high values), with a legend on the right indicating numerical values from 0.02 to 0.12. ### Components/Axes - **X-axis (λ)**: Labeled "λ", with values ranging from 0.25 to 2.00 in increments of 0.25. - **Y-axis (μ)**: Labeled "μ", with values ranging from 0.25 to 2.00 in increments of 0.25. - **Color Scale**: Vertical legend on the right, labeled "Acc_test(BO - GCN)", with a gradient from purple (0.02) to yellow (0.12). - **Grid**: White grid lines separate cells corresponding to discrete μ and λ values. ### Detailed Analysis - **Top-Left Region (High μ, Low λ)**: - Cells are yellow (≈0.12), indicating the highest accuracy differences. - Example: At μ=2.00 and λ=0.25, the value is ≈0.12. - **Middle Rows (Moderate μ, Moderate λ)**: - Colors transition from green (≈0.08–0.10) to blue (≈0.04–0.06). - Example: At μ=1.50 and λ=1.00, the value is ≈0.06. - **Bottom-Right Region (Low μ, High λ)**: - Cells are dark purple (≈0.02), indicating the lowest accuracy differences. - Example: At μ=0.25 and λ=2.00, the value is ≈0.02. - **Gradient Trends**: - Accuracy decreases monotonically as λ increases (left to right). - Accuracy decreases monotonically as μ decreases (top to bottom). ### Key Observations 1. **Optimal Region**: The highest accuracy differences (≈0.12) occur at high μ (2.00) and low λ (0.25). 2. **Worst Region**: The lowest accuracy differences (≈0.02) occur at low μ (0.25) and high λ (2.00). 3. **Trade-off**: Increasing λ or decreasing μ reduces accuracy, suggesting a trade-off between these parameters. 4. **Consistency**: The gradient is smooth, with no abrupt color changes, indicating a predictable relationship between μ, λ, and accuracy. ### Interpretation The heatmap demonstrates that **higher μ and lower λ values** maximize the accuracy difference between BO and GCN. This implies that BO outperforms GCN most significantly under these parameter settings. Conversely, GCN performs relatively better (smaller accuracy gap) when μ is low and λ is high. The monotonic trends suggest that μ and λ have opposing effects on model performance, with μ likely controlling exploration/exploitation in BO and λ regulating regularization or graph structure in GCN. The absence of outliers indicates a stable, predictable relationship between these hyperparameters and accuracy.