## Line Chart: Accuracy vs. Attack Ratio for Different Methods ### Overview The image is a line chart comparing the accuracy of different methods (FedAvg, ShieldFL, PBFL, Median, Biscotti, FoolsGold, and Ours) against varying attack ratios. The x-axis represents the attack ratio (in percentage), and the y-axis represents the accuracy (in percentage). The chart illustrates how the accuracy of each method changes as the attack ratio increases. ### Components/Axes * **X-axis:** Attack ratio (%), with markers at 0, 10, 20, 30, 40, and 50. * **Y-axis:** Accuracy (%), with markers at 0, 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend:** Located on the left side of the chart, listing the methods and their corresponding line colors and markers: * FedAvg (blue, square marker) * ShieldFL (orange, diamond marker) * PBFL (green, triangle marker) * Median (purple, no marker) * Biscotti (gray, triangle marker pointing left) * FoolsGold (brown, triangle marker pointing down) * Ours (red, circle marker) ### Detailed Analysis * **FedAvg (blue, square marker):** The line starts at approximately 75% accuracy at 0% attack ratio and decreases to approximately 7% accuracy at 50% attack ratio. * (0, 75) * (10, 60) * (20, 47) * (30, 32) * (40, 13) * (50, 7) * **ShieldFL (orange, diamond marker):** The line starts at approximately 75% accuracy at 0% attack ratio and decreases to approximately 5% accuracy at 50% attack ratio. * (0, 75) * (10, 63) * (20, 48) * (30, 30) * (40, 12) * (50, 5) * **PBFL (green, triangle marker):** The line starts at approximately 75% accuracy at 0% attack ratio and decreases to approximately 7% accuracy at 50% attack ratio. * (0, 75) * (10, 67) * (20, 43) * (30, 32) * (40, 28) * (50, 7) * **Median (purple, no marker):** The line starts at approximately 75% accuracy at 0% attack ratio and decreases to approximately 2% accuracy at 50% attack ratio. * (0, 75) * (10, 60) * (20, 50) * (30, 30) * (40, 10) * (50, 2) * **Biscotti (gray, triangle marker pointing left):** The line starts at approximately 75% accuracy at 0% attack ratio and decreases to approximately 3% accuracy at 50% attack ratio. * (0, 75) * (10, 55) * (20, 50) * (30, 30) * (40, 10) * (50, 3) * **FoolsGold (brown, triangle marker pointing down):** The line starts at approximately 75% accuracy at 0% attack ratio and decreases to approximately 7% accuracy at 50% attack ratio. * (0, 75) * (10, 60) * (20, 50) * (30, 30) * (40, 10) * (50, 7) * **Ours (red, circle marker):** The line starts at approximately 77% accuracy at 0% attack ratio and decreases to approximately 70% accuracy at 50% attack ratio. * (0, 77) * (10, 73) * (20, 72) * (30, 72) * (40, 70) * (50, 70) ### Key Observations * The "Ours" method (red line) consistently maintains the highest accuracy across all attack ratios. * All other methods (FedAvg, ShieldFL, PBFL, Median, Biscotti, and FoolsGold) experience a significant decrease in accuracy as the attack ratio increases. * The accuracy of "Ours" remains relatively stable, indicating its robustness against attacks. * The methods FedAvg, ShieldFL, Median, Biscotti, and FoolsGold have similar performance. ### Interpretation The chart demonstrates the impact of increasing attack ratios on the accuracy of different methods. The "Ours" method significantly outperforms the other methods in terms of maintaining accuracy under attack. This suggests that the "Ours" method is more resilient to adversarial attacks compared to the other methods tested. The other methods are vulnerable to attacks, as their accuracy drops significantly with increasing attack ratios. The data suggests that the "Ours" method is a more robust solution for scenarios where adversarial attacks are a concern.

## Chart Type: Line Chart - Performance Comparison of Federated Learning Methods Under Varying Attack Ratios ### Overview This image presents a line chart comparing the accuracy (in percentage) of seven different federated learning methods against an increasing "Attack ratio" (also in percentage). The chart illustrates how the performance of these methods degrades as the proportion of adversarial attacks increases, highlighting the robustness of each approach. ### Components/Axes The chart consists of a main plotting area, an X-axis, a Y-axis, and a legend located in the bottom-left of the plot. * **X-axis**: * **Label**: "Attack ratio (%)" * **Range**: From 0% to 50%. * **Major Ticks**: 0, 10, 20, 30, 40, 50. * **Y-axis**: * **Label**: "Accuracy (%)" * **Range**: From 0% to 80%. * **Major Ticks**: 0, 10, 20, 30, 40, 50, 60, 70, 80. * **Legend**: * **Location**: Bottom-left corner of the plot area. * **Entries (with corresponding color and marker)**: * **FedAvg**: Blue line with square markers (□) * **ShieldFL**: Orange line with diamond markers (◇) * **PBFL**: Green line with upward-pointing triangle markers (△) * **Median**: Purple line with small square markers (□) * **Biscotti**: Gray line with star markers (★) * **FoolsGold**: Brown/reddish line with downward-pointing triangle markers (▽) * **Ours**: Red line with circle markers (○) ### Detailed Analysis The chart displays seven data series, each representing a different federated learning method. The accuracy of each method is tracked across six discrete attack ratio values: 0%, 10%, 20%, 30%, 40%, and 50%. Here is a detailed breakdown of each method's trend and approximate data points: 1. **Ours** (Red line, circle markers): * **Trend**: This line shows remarkable stability, maintaining a high accuracy with only a slight decrease as the attack ratio increases. It is the highest performing method across all attack ratios greater than 0%. * **Data Points**: * 0% Attack ratio: ~75.5% Accuracy * 10% Attack ratio: ~74% Accuracy * 20% Attack ratio: ~73% Accuracy * 30% Attack ratio: ~72% Accuracy * 40% Attack ratio: ~69.5% Accuracy * 50% Attack ratio: ~69% Accuracy 2. **FedAvg** (Blue line, square markers): * **Trend**: Starts high but experiences a sharp, consistent decline in accuracy as the attack ratio increases. * **Data Points**: * 0% Attack ratio: ~75% Accuracy * 10% Attack ratio: ~62% Accuracy * 20% Attack ratio: ~45% Accuracy * 30% Attack ratio: ~32% Accuracy * 40% Attack ratio: ~12% Accuracy * 50% Attack ratio: ~7% Accuracy 3. **ShieldFL** (Orange line, diamond markers): * **Trend**: Similar to FedAvg, it shows a steep decline in accuracy, becoming one of the lowest performing methods at higher attack ratios. * **Data Points**: * 0% Attack ratio: ~75% Accuracy * 10% Attack ratio: ~60% Accuracy * 20% Attack ratio: ~47% Accuracy * 30% Attack ratio: ~30% Accuracy * 40% Attack ratio: ~13% Accuracy * 50% Attack ratio: ~3% Accuracy 4. **PBFL** (Green line, upward-pointing triangle markers): * **Trend**: Initially declines sharply, then shows a period of slower decline between 20% and 40% attack ratio, before dropping sharply again at 50%. * **Data Points**: * 0% Attack ratio: ~74% Accuracy * 10% Attack ratio: ~68% Accuracy * 20% Attack ratio: ~42% Accuracy * 30% Attack ratio: ~31% Accuracy * 40% Attack ratio: ~28% Accuracy * 50% Attack ratio: ~8% Accuracy 5. **Median** (Purple line, small square markers): * **Trend**: Exhibits a very steep and consistent decline, becoming one of the worst-performing methods at higher attack ratios. * **Data Points**: * 0% Attack ratio: ~74% Accuracy * 10% Attack ratio: ~65% Accuracy * 20% Attack ratio: ~50% Accuracy * 30% Attack ratio: ~25% Accuracy * 40% Attack ratio: ~5% Accuracy * 50% Attack ratio: ~1% Accuracy 6. **Biscotti** (Gray line, star markers): * **Trend**: Shows a sharp decline in accuracy, similar to Median, and is among the lowest performing at higher attack ratios. * **Data Points**: * 0% Attack ratio: ~74% Accuracy * 10% Attack ratio: ~56% Accuracy * 20% Attack ratio: ~35% Accuracy * 30% Attack ratio: ~28% Accuracy * 40% Attack ratio: ~6% Accuracy * 50% Attack ratio: ~5% Accuracy 7. **FoolsGold** (Brown/reddish line, downward-pointing triangle markers): * **Trend**: Displays a sharp and consistent decrease in accuracy, similar to FedAvg and ShieldFL. * **Data Points**: * 0% Attack ratio: ~75% Accuracy * 10% Attack ratio: ~67% Accuracy * 20% Attack ratio: ~50% Accuracy * 30% Attack ratio: ~30% Accuracy * 40% Attack ratio: ~10% Accuracy * 50% Attack ratio: ~6% Accuracy ### Key Observations * **Initial Performance**: At 0% attack ratio, all seven methods perform similarly, with accuracy ranging from approximately 74% to 75.5%. This suggests comparable baseline performance in an ideal, non-adversarial environment. * **Superior Robustness of "Ours"**: The "Ours" method (red line) stands out significantly. Its accuracy remains high (above 69%) even at a 50% attack ratio, demonstrating exceptional robustness compared to all other methods. * **Vulnerability of Other Methods**: All other six methods (FedAvg, ShieldFL, PBFL, Median, Biscotti, FoolsGold) experience substantial degradation in accuracy as the attack ratio increases. Their accuracy drops to below 15% at a 40% attack ratio, and mostly below 10% at a 50% attack ratio. * **Worst Performers at High Attack Ratios**: ShieldFL, Median, and Biscotti show the most severe performance drops, with accuracies falling to 1-5% at a 50% attack ratio. * **PBFL's Mid-Range Behavior**: PBFL (green line) shows a slightly different curve, with a less steep decline between 20% and 40% attack ratio compared to its initial and final drops, suggesting some temporary resilience in that range before succumbing to higher attack rates. ### Interpretation The data strongly suggests that the "Ours" method offers a significantly more robust solution for federated learning in the presence of adversarial attacks compared to the other six established or baseline methods. The consistent high accuracy of "Ours" across varying attack ratios indicates its superior ability to maintain performance even when a large proportion of participants are malicious. The sharp decline in accuracy for FedAvg, ShieldFL, PBFL, Median, Biscotti, and FoolsGold underscores their vulnerability to increasing attack ratios. This implies that these methods would be unreliable in real-world federated learning deployments where adversarial attacks or data poisoning are a significant concern. The performance gap between "Ours" and the other methods widens dramatically as the attack ratio increases, highlighting the critical importance of robust aggregation mechanisms or defense strategies in adversarial federated learning environments. The results advocate for the adoption of methods like "Ours" to ensure reliable model training in potentially hostile distributed settings.

\n ## Line Chart: Accuracy vs. Attack Ratio for Federated Learning Algorithms ### Overview This line chart depicts the relationship between the attack ratio (percentage) and the accuracy (percentage) of several federated learning algorithms. The chart visually compares the robustness of these algorithms against adversarial attacks. ### Components/Axes * **X-axis:** "Attack ratio (%)" - Ranges from 0% to 50%, with markers at 0, 10, 20, 30, 40, and 50. * **Y-axis:** "Accuracy (%)" - Ranges from 0% to 80%, with markers at 0, 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend (bottom-left):** Lists the algorithms being compared, each associated with a unique line color and marker style: * FedAvg (Blue, square marker) * ShieldFL (Orange, circle marker) * PBFL (Green, triangle marker) * Median (Purple, diamond marker) * Biscotti (Brown, star marker) * FoolsGold (Red, inverted triangle marker) * Ours (Dark Red, circle marker) ### Detailed Analysis Here's a breakdown of each line's trend and approximate data points, cross-referencing with the legend: * **FedAvg (Blue, square):** Starts at approximately 75% accuracy at 0% attack ratio. The line slopes downward sharply, reaching approximately 5% accuracy at 50% attack ratio. Approximate data points: (0, 75), (10, 62), (20, 42), (30, 30), (40, 12), (50, 5). * **ShieldFL (Orange, circle):** Starts at approximately 72% accuracy at 0% attack ratio. The line declines steadily, reaching approximately 2% accuracy at 50% attack ratio. Approximate data points: (0, 72), (10, 60), (20, 40), (30, 28), (40, 10), (50, 2). * **PBFL (Green, triangle):** Starts at approximately 74% accuracy at 0% attack ratio. The line declines moderately until 30% attack ratio, then drops sharply, reaching approximately 30% accuracy at 50% attack ratio. Approximate data points: (0, 74), (10, 65), (20, 45), (30, 32), (40, 30), (50, 30). * **Median (Purple, diamond):** Starts at approximately 73% accuracy at 0% attack ratio. The line declines rapidly, reaching approximately 0% accuracy at 40% attack ratio. Approximate data points: (0, 73), (10, 63), (20, 43), (30, 25), (40, 0), (50, 0). * **Biscotti (Brown, star):** Starts at approximately 73% accuracy at 0% attack ratio. The line declines rapidly, reaching approximately 0% accuracy at 40% attack ratio. Approximate data points: (0, 73), (10, 62), (20, 42), (30, 25), (40, 0), (50, 0). * **FoolsGold (Red, inverted triangle):** Starts at approximately 74% accuracy at 0% attack ratio. The line declines moderately, reaching approximately 68% accuracy at 50% attack ratio. Approximate data points: (0, 74), (10, 72), (20, 68), (30, 65), (40, 63), (50, 68). * **Ours (Dark Red, circle):** Starts at approximately 75% accuracy at 0% attack ratio. The line declines very slowly, maintaining approximately 70% accuracy at 50% attack ratio. Approximate data points: (0, 75), (10, 74), (20, 73), (30, 72), (40, 71), (50, 70). ### Key Observations * The "Ours" algorithm demonstrates the highest robustness to attacks, maintaining a relatively high accuracy even at a 50% attack ratio. * FedAvg, ShieldFL, Median, and Biscotti algorithms exhibit a significant drop in accuracy as the attack ratio increases, reaching near-zero accuracy at higher attack ratios. * PBFL shows a moderate decline in accuracy until 30% attack ratio, then a sharper decline. * FoolsGold shows the least sensitivity to attack ratio, maintaining a relatively stable accuracy throughout the range. ### Interpretation The chart demonstrates the varying levels of resilience of different federated learning algorithms against adversarial attacks. The "Ours" algorithm appears to be significantly more robust than the others, suggesting it incorporates mechanisms to mitigate the impact of malicious attacks on the model's accuracy. The rapid decline in accuracy for algorithms like FedAvg, ShieldFL, Median, and Biscotti indicates their vulnerability to even moderate levels of attacks. FoolsGold's stability suggests it may have inherent properties that make it less susceptible to these types of attacks, or that the attacks are not effective against it. The data suggests that the choice of algorithm is crucial in environments where adversarial attacks are a concern. The chart provides a comparative performance assessment, allowing for informed decision-making regarding algorithm selection in security-sensitive federated learning applications. The consistent performance of "Ours" suggests a potential area for further investigation and adoption in real-world deployments.

## Line Chart: Accuracy vs. Attack Ratio for Various Federated Learning Defense Methods ### Overview The image is a line chart comparing the performance of seven different methods (likely federated learning defense or aggregation algorithms) as the intensity of a simulated attack increases. The chart plots model accuracy against an increasing "Attack ratio," showing how each method's effectiveness degrades under adversarial conditions. One method, labeled "Ours," demonstrates significantly higher robustness compared to the others. ### Components/Axes * **Chart Type:** Multi-line chart with markers. * **Y-Axis:** * **Label:** `Accuracy (%)` * **Scale:** Linear, ranging from 0 to 80, with major tick marks at intervals of 10 (0, 10, 20, 30, 40, 50, 60, 70, 80). * **X-Axis:** * **Label:** `Attack ratio (%)` * **Scale:** Linear, ranging from 0 to 50, with major tick marks at intervals of 10 (0, 10, 20, 30, 40, 50). * **Legend:** * **Position:** Bottom-left corner of the plot area. * **Content:** A box listing seven data series with corresponding line colors and marker symbols. * **Series (in order listed in legend):** 1. `FedAvg` - Blue line with square markers (□). 2. `ShieldFL` - Orange line with diamond markers (◇). 3. `PBFL` - Green line with upward-pointing triangle markers (△). 4. `Median` - Purple line with circle markers (○). 5. `Biscotti` - Gray line with asterisk markers (*). 6. `FoolsGold` - Brown line with downward-pointing triangle markers (▽). 7. `Ours` - Red line with circle markers (○). ### Detailed Analysis The chart tracks the accuracy of each method at six discrete attack ratio points: 0%, 10%, 20%, 30%, 40%, and 50%. **Trend Verification & Data Points (Approximate):** 1. **Ours (Red line, ○):** * **Trend:** Nearly flat, showing minimal degradation. Starts highest and remains the highest throughout. * **Points:** (0%, ~76%), (10%, ~74%), (20%, ~73%), (30%, ~72.5%), (40%, ~70%), (50%, ~69.5%). 2. **PBFL (Green line, △):** * **Trend:** Declines steadily, but shows a notable plateau between 30% and 40% before dropping again. * **Points:** (0%, ~75%), (10%, ~68%), (20%, ~51%), (30%, ~32%), (40%, ~29%), (50%, ~8%). 3. **FedAvg (Blue line, □):** * **Trend:** Steep, consistent decline. * **Points:** (0%, ~75%), (10%, ~62%), (20%, ~42%), (30%, ~30%), (40%, ~13%), (50%, ~8%). 4. **ShieldFL (Orange line, ◇):** * **Trend:** Steep, consistent decline, very similar to FedAvg. * **Points:** (0%, ~75%), (10%, ~61%), (20%, ~48%), (30%, ~29%), (40%, ~10%), (50%, ~3%). 5. **Median (Purple line, ○):** * **Trend:** Steep decline, ending as one of the lowest performers. * **Points:** (0%, ~75%), (10%, ~60%), (20%, ~42%), (30%, ~24%), (40%, ~5%), (50%, ~1%). 6. **FoolsGold (Brown line, ▽):** * **Trend:** Steep decline. * **Points:** (0%, ~75%), (10%, ~63%), (20%, ~48%), (30%, ~30%), (40%, ~12%), (50%, ~5%). 7. **Biscotti (Gray line, *):** * **Trend:** The steepest initial decline, performing worst from 10% attack ratio onward. * **Points:** (0%, ~75%), (10%, ~55%), (20%, ~42%), (30%, ~24%), (40%, ~5%), (50%, ~0%). ### Key Observations 1. **Dominant Performance:** The method labeled "Ours" is a clear outlier, maintaining accuracy above ~69% even at a 50% attack ratio, while all other methods fall below 10% accuracy at that point. 2. **Clustering of Baselines:** Six of the seven methods (all except "Ours") start at nearly identical accuracy (~75%) at 0% attack. They all experience significant degradation, clustering together in a steep downward trend, with some minor separation at higher attack ratios. 3. **PBFL Anomaly:** The PBFL method shows a distinct behavior between 30% and 40% attack ratio, where its accuracy decline halts temporarily (plateaus at ~29-32%) before resuming its drop. This suggests a potential threshold or resilience characteristic unique to this method within that range. 4. **Convergence at High Attack:** By the 50% attack ratio, the performance of all baseline methods (FedAvg, ShieldFL, Median, Biscotti, FoolsGold) converges to a very low accuracy range (0-8%), indicating a near-total failure of these defenses under severe attack. ### Interpretation This chart is likely from a research paper in the field of **Federated Learning (FL) security**, specifically evaluating defenses against **poisoning attacks** (where malicious clients send corrupted model updates). The "Attack ratio (%)" represents the proportion of malicious clients in the federation. * **What the data suggests:** The proposed method ("Ours") demonstrates **exceptional robustness**. Its near-horizontal line indicates that increasing the number of attackers has a negligible impact on the global model's final accuracy. This is a highly desirable property for a secure FL system. * **Relationship between elements:** The chart establishes a direct, negative correlation between attack strength and model performance for all standard methods. The stark contrast between the red line ("Ours") and the others visually argues for the superiority of the authors' approach. * **Notable implications:** The steep, parallel decline of the baseline methods suggests they share a common vulnerability to the type of attack simulated. The plateau in PBFL might indicate it employs a different mechanism (e.g., a clustering or trimming step) that becomes saturated or less effective at a specific attack intensity. The convergence of baselines at 50% attack implies that beyond a certain point, these traditional defenses are equally ineffective. * **Underlying message:** The primary takeaway is not just that "Ours" is better, but that it operates on a different paradigm of resilience. While other methods degrade linearly or worse with attack strength, the proposed method's performance is largely **invariant** to the attack ratio within the tested range, which is a significant advancement for deploying FL in adversarial environments.

## Line Graph: Accuracy vs. Attack Ratio ### Overview The image depicts a line graph comparing the accuracy of multiple methods under varying attack ratios. The x-axis represents attack ratio (0–50%), and the y-axis represents accuracy (0–80%). Seven distinct data series are plotted, each with unique colors and markers. The graph illustrates how accuracy degrades as attack intensity increases, with notable differences in resilience across methods. ### Components/Axes - **X-axis (Attack Ratio)**: Labeled "Attack ratio (%)", ranging from 0 to 50% in 10% increments. - **Y-axis (Accuracy)**: Labeled "Accuracy (%)", ranging from 0 to 80% in 10% increments. - **Legend**: Positioned in the bottom-left corner, mapping colors/markers to methods: - **Blue square**: FedAvg - **Orange diamond**: ShieldFL - **Green triangle**: PBFL - **Purple pentagon**: Median - **Gray star**: Biscotti - **Brown triangle**: FoolsGold - **Red circle**: Ours - **Data Series**: Seven lines with distinct visual styles, all originating near the top-left corner and diverging as attack ratio increases. ### Detailed Analysis 1. **Ours (Red Circle)**: - Maintains the highest accuracy across all attack ratios. - Starts at ~75% accuracy at 0% attack ratio. - Declines gradually to ~70% at 50% attack ratio. - **Trend**: Relatively flat, indicating robustness. 2. **FedAvg (Blue Square)**: - Begins at ~75% accuracy at 0% attack ratio. - Drops sharply to ~5% at 50% attack ratio. - **Trend**: Steep decline, suggesting poor resilience. 3. **ShieldFL (Orange Diamond)**: - Starts at ~70% accuracy at 0% attack ratio. - Declines to ~10% at 50% attack ratio. - **Trend**: Moderate decline, less resilient than "Ours". 4. **PBFL (Green Triangle)**: - Starts at ~70% accuracy at 0% attack ratio. - Drops to ~30% at 20% attack ratio, then rises slightly to ~25% at 50%. - **Trend**: U-shaped, with a mid-attack performance dip. 5. **Median (Purple Pentagon)**: - Begins at ~70% accuracy at 0% attack ratio. - Declines to ~5% at 50% attack ratio. - **Trend**: Steady linear decline. 6. **Biscotti (Gray Star)**: - Starts at ~70% accuracy at 0% attack ratio. - Drops to ~2% at 50% attack ratio. - **Trend**: Sharp linear decline. 7. **FoolsGold (Brown Triangle)**: - Begins at ~70% accuracy at 0% attack ratio. - Plummets to ~5% at 20% attack ratio, then stabilizes near 0%. - **Trend**: Catastrophic early failure. ### Key Observations - **Robustness**: "Ours" consistently outperforms all other methods, maintaining >70% accuracy even at 50% attack ratio. - **Vulnerability**: FoolsGold exhibits the most severe degradation, dropping below 5% accuracy by 20% attack ratio. - **PBFL Anomaly**: PBFL’s mid-attack dip and partial recovery suggest a non-linear vulnerability, possibly due to specific attack strategies. - **Consistency**: FedAvg, Median, and Biscotti show linear declines, with Biscotti being the most fragile. ### Interpretation The graph highlights critical differences in attack resilience among methods. "Ours" demonstrates superior robustness, likely due to advanced defense mechanisms or architectural advantages. FoolsGold’s rapid failure suggests a fundamental flaw in its design or training process. PBFL’s U-shaped curve warrants further investigation—its mid-attack dip might indicate a temporary vulnerability exploited by attackers, followed by adaptive recovery. The linear declines of FedAvg, ShieldFL, and Biscotti imply predictable degradation under attack, emphasizing the need for tailored defenses. These results underscore the importance of evaluating methods not just on baseline performance but also on their ability to withstand adversarial conditions.