## Box Plot Comparison: MSE and Hybrid Loss for BAST-NSP and BAST-SP ### Overview The image presents four box plots comparing the Mean Square Error (MSE) loss and Hybrid loss for two models, BAST-NSP and BAST-SP, across three different operations: Concatenation (Concat.), Addition (Add.), and Subtraction (Sub.). The box plots show the distribution of the error for "left" and "right" data. ### Components/Axes * **Titles:** * Top-Left: "MSE loss" * Top-Right: "Hybrid loss" * Left-Side (Top and Bottom): "BAST-NSP" and "BAST-SP" respectively. * **Y-Axis (Vertical):** "Mean square error" * Top Plots (BAST-NSP): Scale from 0.000 to 0.010, incrementing by 0.002. * Bottom Plots (BAST-SP): Scale from 0.00 to 0.07, incrementing by 0.01. * **X-Axis (Horizontal):** "Concat.", "Add.", "Sub." representing different operations. * **Legend:** Located at the top-center of the image. * Blue: "left" * Orange: "right" * **Statistical Significance:** Asterisks (*) indicate statistically significant differences between groups. ### Detailed Analysis **1. MSE Loss (BAST-NSP - Top-Left)** * **Concat.:** The "left" data (blue) has a median around 0.0025, with the box extending from approximately 0.0015 to 0.004. The "right" data (orange) has a median around 0.002, with the box extending from approximately 0.001 to 0.003. * **Add.:** The "left" data (blue) has a median around 0.0015, with the box extending from approximately 0.001 to 0.003. The "right" data (orange) has a median around 0.002, with the box extending from approximately 0.001 to 0.004. There is an outlier at approximately 0.005. * **Sub.:** The "left" data (blue) has a median around 0.0015, with the box extending from approximately 0.001 to 0.0025. The "right" data (orange) has a median around 0.002, with the box extending from approximately 0.001 to 0.003. There is an outlier at approximately 0.005. * **Statistical Significance:** There is a statistically significant difference between "left" and "right" for both "Concat." and "Add." operations. **2. Hybrid Loss (BAST-NSP - Top-Right)** * **Concat.:** The "left" data (blue) has a median around 0.003, with the box extending from approximately 0.002 to 0.004. The "right" data (orange) has a median around 0.0045, with the box extending from approximately 0.003 to 0.006. * **Add.:** The "left" data (blue) has a median around 0.0015, with the box extending from approximately 0.001 to 0.0025. The "right" data (orange) has a median around 0.0015, with the box extending from approximately 0.001 to 0.003. There are outliers for the "right" data at approximately 0.002 and 0.003. * **Sub.:** Both "left" (blue) and "right" (orange) data have medians around 0.001, with boxes extending from approximately 0.0005 to 0.0015. There are outliers for the "right" data at approximately 0.002 and 0.003. **3. MSE Loss (BAST-SP - Bottom-Left)** * **Concat.:** Both "left" (blue) and "right" (orange) data have medians close to 0.00, with boxes extending from approximately 0.00 to 0.001. * **Add.:** The "left" data (blue) has a median around 0.015, with the box extending from approximately 0.01 to 0.025. The "right" data (orange) has a median around 0.015, with the box extending from approximately 0.01 to 0.02. There is an outlier for the "left" data at approximately 0.055. * **Sub.:** Both "left" (blue) and "right" (orange) data have medians close to 0.00, with boxes extending from approximately 0.00 to 0.001. **4. Hybrid Loss (BAST-SP - Bottom-Right)** * **Concat.:** Both "left" (blue) and "right" (orange) data have medians close to 0.00, with boxes extending from approximately 0.00 to 0.001. There is an outlier for the "left" data at approximately 0.015. * **Add.:** The "left" data (blue) has a median around 0.02, with the box extending from approximately 0.01 to 0.03. The "right" data (orange) has a median around 0.03, with the box extending from approximately 0.02 to 0.04. The "right" data has a long tail extending to approximately 0.07. * **Sub.:** Both "left" (blue) and "right" (orange) data have medians close to 0.00, with boxes extending from approximately 0.00 to 0.002. ### Key Observations * For BAST-NSP, the MSE loss shows statistically significant differences between "left" and "right" data for "Concat." and "Add." operations. * For BAST-SP, the MSE loss is significantly higher for the "Add." operation compared to "Concat." and "Sub." * For BAST-SP, the Hybrid loss is also higher for the "Add." operation compared to "Concat." and "Sub.", with a long tail for the "right" data. * BAST-SP generally has higher error values than BAST-NSP, especially for the "Add." operation. ### Interpretation The box plots provide a comparative analysis of the performance of BAST-NSP and BAST-SP models under different loss functions (MSE and Hybrid) and operations (Concat., Add., Sub.). The data suggests that: * The choice of operation significantly impacts the error, particularly for BAST-SP, where "Add." results in much higher error values. * The Hybrid loss function seems to mitigate the error for BAST-SP in the "Add." operation compared to the MSE loss. * The statistical significance observed in BAST-NSP's MSE loss for "Concat." and "Add." indicates a consistent difference in performance between "left" and "right" data for these operations. * BAST-NSP generally performs better than BAST-SP, as indicated by the lower error values across most operations and loss functions.

## Box Plot: BASt Performance Comparison ### Overview The image presents a 2x2 grid of box plots comparing the performance of different methods ("Concat.", "Add.", "Sub.") under two loss functions ("MSE loss", "Hybrid loss") and two BASt metrics ("BASt-NSP", "BASt-SP"). Each box plot shows the distribution of mean square error for "left" and "right" conditions. Statistical significance is indicated by asterisks above the box plots. ### Components/Axes * **X-axis:** Method - "Concat." (Concatenation), "Add." (Addition), "Sub." (Subtraction) * **Y-axis:** Mean square error (ranging from 0 to 0.10 for BASt-NSP and 0 to 0.07 for BASt-SP) * **Grouping:** Two groups are represented by color: "left" (orange) and "right" (blue). * **Loss Function:** Two columns represent different loss functions: "MSE loss" and "Hybrid loss". * **BASt Metric:** Two rows represent different BASt metrics: "BASt-NSP" and "BASt-SP". * **Legend:** Located in the top-left corner of the first plot, indicating "left" (orange) and "right" (blue). * **Significance Markers:** Asterisks (*) above the box plots indicate statistical significance. ### Detailed Analysis or Content Details **Top-Left: MSE loss, BASt-NSP** * **Concat:** "left" ~0.005, "right" ~0.002. The "left" boxplot is significantly higher than the "right". * **Add:** "left" ~0.003, "right" ~0.002. The "left" boxplot is slightly higher than the "right". * **Sub:** "left" ~0.003, "right" ~0.002. The "left" boxplot is slightly higher than the "right". * Statistical significance is indicated between "Concat" and "Add", and between "Concat" and "Sub". **Top-Right: Hybrid loss, BASt-NSP** * **Concat:** "left" ~0.006, "right" ~0.003. The "left" boxplot is significantly higher than the "right". * **Add:** "left" ~0.004, "right" ~0.002. The "left" boxplot is higher than the "right". * **Sub:** "left" ~0.002, "right" ~0.001. The "left" boxplot is slightly higher than the "right". **Bottom-Left: MSE loss, BASt-SP** * **Concat:** "left" ~0.001, "right" ~0.001. The "left" and "right" boxplots are very similar. * **Add:** "left" ~0.025, "right" ~0.015. The "left" boxplot is significantly higher than the "right". * **Sub:** "left" ~0.005, "right" ~0.001. The "left" boxplot is higher than the "right". **Bottom-Right: Hybrid loss, BASt-SP** * **Concat:** "left" ~0.001, "right" ~0.001. The "left" and "right" boxplots are very similar. * **Add:** "left" ~0.03, "right" ~0.01. The "left" boxplot is significantly higher than the "right". * **Sub:** "left" ~0.005, "right" ~0.001. The "left" boxplot is higher than the "right". ### Key Observations * For BASt-NSP, "Concat" consistently shows the highest error for the "left" condition, and is statistically significant. * For BASt-SP, "Add" consistently shows the highest error for the "left" condition, and is statistically significant. * The "left" condition generally exhibits higher error than the "right" condition, particularly for "Concat" and "Add" methods. * The scale of the y-axis differs between BASt-NSP and BASt-SP, indicating different magnitudes of error. ### Interpretation The data suggests that the choice of method ("Concat", "Add", "Sub") and loss function ("MSE loss", "Hybrid loss") significantly impacts performance, as measured by BASt-NSP and BASt-SP. The consistent higher error for the "left" condition across most methods and metrics suggests a potential asymmetry in the data or model's ability to process information from the "left" versus the "right". The statistical significance markers highlight that the differences observed are not likely due to random chance. The different scales on the y-axis for BASt-NSP and BASt-SP indicate that these metrics capture different aspects of performance, and the optimal method may vary depending on the specific metric of interest. The "Concat" method appears to be particularly sensitive to the "left" condition when using the BASt-NSP metric, while the "Add" method shows similar sensitivity when using the BASt-SP metric. This suggests that the concatenation method may be more prone to errors when dealing with the "left" input, and the addition method may be more prone to errors when dealing with the "left" input.

## Box Plot: Comparison of Mean Square Error (MSE) and Hybrid Loss for BAST-NSP and BAST-SP Models ### Overview The image contains four box plots comparing the **mean square error (MSE)** and **hybrid loss** for two models: **BAST-NSP** and **BAST-SP**. Each plot evaluates three methods: **Concat**, **Add**, and **Sub**. The y-axis represents the mean square error, while the x-axis categorizes the methods. Legends indicate "left" (blue) and "right" (orange) data splits, with asterisks (*) denoting statistical significance. --- ### Components/Axes - **X-axis**: Methods (Concat, Add, Sub) - **Y-axis**: Mean square error (ranging from 0.00 to 0.07) - **Legends**: - Blue: "left" - Orange: "right" - **Titles**: - Top-left: "MSE loss" - Top-right: "Hybrid loss" - Bottom-left: "BAST-NSP" - Bottom-right: "BAST-SP" --- ### Detailed Analysis #### BAST-NSP (MSE loss) - **Concat**: Median ~0.02, range 0.01–0.04 - **Add**: Median ~0.03, range 0.02–0.05 - **Sub**: Median ~0.01, range 0.005–0.02 - **Hybrid loss**: - **Concat**: Median ~0.04, range 0.03–0.06 - **Add**: Median ~0.03, range 0.02–0.05 - **Sub**: Median ~0.02, range 0.01–0.03 #### BAST-SP (MSE loss) - **Concat**: Median ~0.01, range 0.005–0.02 - **Add**: Median ~0.02, range 0.01–0.03 - **Sub**: Median ~0.005, range 0.002–0.01 - **Hybrid loss**: - **Concat**: Median ~0.005, range 0.003–0.01 - **Add**: Median ~0.01, range 0.005–0.02 - **Sub**: Median ~0.003, range 0.001–0.005 **Asterisks (*)**: Indicate statistical significance (e.g., *p < 0.05*) for differences between methods. --- ### Key Observations 1. **BAST-SP outperforms BAST-NSP** in both MSE and hybrid loss across all methods, with lower median values. 2. **Add method** consistently shows higher error rates than **Concat** and **Sub** in both models. 3. **Hybrid loss** generally has higher error values than **MSE loss** for both models. 4. **Statistical significance** is marked for the **Add method** in BAST-NSP (MSE loss) and **Concat** in BAST-SP (hybrid loss). --- ### Interpretation - The **BAST-SP model** demonstrates superior performance, likely due to architectural or training improvements. - The **Add method** introduces higher error, suggesting potential instability or overfitting in this configuration. - **Hybrid loss** may reflect a trade-off between model complexity and generalization, as it shows higher variability. - The **asterisks** highlight critical differences, emphasizing the importance of method selection in model design. This analysis underscores the need to optimize both model architecture (e.g., BAST-SP vs. BAST-NSP) and method selection (e.g., avoiding the Add method) to minimize error.