## Line Chart: Accuracy vs. Attack Ratio for Different Federated Learning Algorithms ### Overview The image is a line chart comparing the accuracy of different federated learning algorithms as the attack ratio increases. The x-axis represents the attack ratio (percentage), and the y-axis represents the accuracy (percentage). Several algorithms are compared, including FedAvg, ShieldFL, PBFL, Median, Biscotti, FoolsGold, and "Ours". ### Components/Axes * **X-axis:** Attack ratio (%), with markers at 0, 10, 20, 30, 40, and 50. * **Y-axis:** Accuracy (%), with markers at 84, 86, 88, 90, 92, 94, and 96. * **Legend:** Located on the left side of the chart, listing the algorithms and their corresponding line colors and markers: * FedAvg (blue, square marker) * ShieldFL (orange, diamond marker) * PBFL (green, triangle marker) * Median (purple, circle marker) * Biscotti (gray, star marker) * FoolsGold (brown, inverted triangle marker) * Ours (red, circle marker) ### Detailed Analysis * **FedAvg (blue, square marker):** Starts at approximately 96.2% accuracy at 0% attack ratio. It remains relatively stable until an attack ratio of 40%, where it begins to drop sharply, reaching approximately 87% at 50% attack ratio. * (0, 96.2) * (10, 96.2) * (20, 96.2) * (30, 95.8) * (40, 95.2) * (50, 87) * **ShieldFL (orange, diamond marker):** Starts at approximately 96.3% accuracy at 0% attack ratio. It remains relatively stable until an attack ratio of 40%, where it begins to drop sharply, reaching approximately 87% at 50% attack ratio. * (0, 96.3) * (10, 96.2) * (20, 96.2) * (30, 96.1) * (40, 95.1) * (50, 87) * **PBFL (green, triangle marker):** Starts at approximately 96.4% accuracy at 0% attack ratio. It remains relatively stable until an attack ratio of 40%, where it begins to drop sharply, reaching approximately 87% at 50% attack ratio. * (0, 96.4) * (10, 96.3) * (20, 96.2) * (30, 95.7) * (40, 95.3) * (50, 87.2) * **Median (purple, circle marker):** Starts at approximately 96.1% accuracy at 0% attack ratio. It remains relatively stable until an attack ratio of 40%, where it begins to drop sharply, reaching approximately 87% at 50% attack ratio. * (0, 96.1) * (10, 96.1) * (20, 96.1) * (30, 96) * (40, 95.9) * (50, 87.3) * **Biscotti (gray, star marker):** Starts at approximately 96.1% accuracy at 0% attack ratio. It decreases linearly as the attack ratio increases, reaching approximately 83% at 50% attack ratio. * (0, 96.1) * (10, 95.5) * (20, 91) * (30, 87.5) * (40, 83.5) * (50, 83) * **FoolsGold (brown, inverted triangle marker):** Starts at approximately 96.3% accuracy at 0% attack ratio. It remains relatively stable until an attack ratio of 40%, where it begins to drop sharply, reaching approximately 85.5% at 50% attack ratio. * (0, 96.3) * (10, 96.2) * (20, 96.1) * (30, 95.9) * (40, 94.8) * (50, 85.5) * **Ours (red, circle marker):** Starts at approximately 96.5% accuracy at 0% attack ratio. It remains relatively stable until an attack ratio of 40%, where it begins to drop sharply, reaching approximately 87.5% at 50% attack ratio. * (0, 96.5) * (10, 96.4) * (20, 96.3) * (30, 96.2) * (40, 96) * (50, 87.5) ### Key Observations * The Biscotti algorithm (gray line) is the most sensitive to increasing attack ratios, showing a steady decline in accuracy. * The other algorithms (FedAvg, ShieldFL, PBFL, Median, FoolsGold, and "Ours") maintain relatively high accuracy until the attack ratio reaches 40%, after which their accuracy drops sharply. * The "Ours" algorithm (red line) appears to have the highest accuracy at 0% attack ratio and maintains a slightly higher accuracy than the other algorithms until the 40% attack ratio mark. * At 50% attack ratio, the algorithms FedAvg, ShieldFL, PBFL, Median, and "Ours" converge to a similar accuracy level. ### Interpretation The chart demonstrates the impact of increasing attack ratios on the accuracy of different federated learning algorithms. The Biscotti algorithm is significantly more vulnerable to attacks compared to the other algorithms tested. The algorithms FedAvg, ShieldFL, PBFL, Median, FoolsGold, and "Ours" exhibit similar resilience to attacks up to a certain threshold (40% attack ratio), beyond which their performance degrades rapidly. The "Ours" algorithm shows a slight advantage in maintaining higher accuracy at lower attack ratios. The data suggests that the choice of federated learning algorithm is crucial in environments where adversarial attacks are a concern, and that some algorithms are better equipped to handle such attacks than others.

## Chart: Accuracy vs. Attack Ratio for Different Methods ### Overview This image displays a 2D line chart illustrating the performance, measured in accuracy, of seven different methods against varying attack ratios. The chart plots "Accuracy (%)" on the Y-axis against "Attack ratio (%)" on the X-axis. Each line represents a distinct method, identified by a unique color and marker, with a legend provided in the bottom-left corner. The primary purpose of the chart is to compare the robustness of these methods to increasing attack ratios. ### Components/Axes The chart consists of a main plotting area, an X-axis, a Y-axis, and a legend. * **X-axis**: * **Title**: "Attack ratio (%)" * **Range**: From 0% to 50% * **Major Ticks**: 0, 10, 20, 30, 40, 50 * **Y-axis**: * **Title**: "Accuracy (%)" * **Range**: From 84% to 96% * **Major Ticks**: 84, 86, 88, 90, 92, 94, 96 * **Legend (Bottom-left of the plot area)**: * **FedAvg**: Blue line with an empty square marker. * **ShieldFL**: Orange line with an empty diamond marker. * **PBFL**: Green line with an upward-pointing triangle marker. * **Median**: Purple line with a square marker containing a cross. * **Biscotti**: Gray line with a star marker. * **FoolsGold**: Brown line with a downward-pointing triangle marker. * **Ours**: Red line with an empty circle marker. ### Detailed Analysis The chart presents the accuracy of seven methods as the attack ratio increases from 0% to 50%. 1. **Ours (Red line, empty circle marker)**: * **Trend**: This line demonstrates exceptional stability, maintaining high accuracy across all attack ratios. It is the most robust method shown. * **Data Points**: * 0% Attack ratio: Approximately 96.3% Accuracy * 10% Attack ratio: Approximately 96.3% Accuracy * 20% Attack ratio: Approximately 96.2% Accuracy * 30% Attack ratio: Approximately 96.1% Accuracy * 40% Attack ratio: Approximately 96.0% Accuracy * 50% Attack ratio: Approximately 95.8% Accuracy 2. **FedAvg (Blue line, empty square marker)**: * **Trend**: This method maintains high accuracy up to 30% attack ratio, then experiences a moderate drop at 40%, followed by a sharp decline at 50%. * **Data Points**: * 0% Attack ratio: Approximately 96.2% Accuracy * 10% Attack ratio: Approximately 96.2% Accuracy * 20% Attack ratio: Approximately 96.0% Accuracy * 30% Attack ratio: Approximately 95.9% Accuracy * 40% Attack ratio: Approximately 94.8% Accuracy * 50% Attack ratio: Approximately 86.5% Accuracy 3. **ShieldFL (Orange line, empty diamond marker)**: * **Trend**: Similar to FedAvg, it shows good stability initially, then a noticeable drop at 30-40%, and a sharp decline at 50%. * **Data Points**: * 0% Attack ratio: Approximately 96.3% Accuracy * 10% Attack ratio: Approximately 96.2% Accuracy * 20% Attack ratio: Approximately 96.1% Accuracy * 30% Attack ratio: Approximately 95.5% Accuracy * 40% Attack ratio: Approximately 94.5% Accuracy * 50% Attack ratio: Approximately 85.3% Accuracy 4. **PBFL (Green line, upward-pointing triangle marker)**: * **Trend**: This method is highly stable up to 30% attack ratio, then shows a moderate drop at 40%, followed by a sharp decline at 50%. * **Data Points**: * 0% Attack ratio: Approximately 96.4% Accuracy * 10% Attack ratio: Approximately 96.2% Accuracy * 20% Attack ratio: Approximately 96.0% Accuracy * 30% Attack ratio: Approximately 95.5% Accuracy * 40% Attack ratio: Approximately 95.0% Accuracy * 50% Attack ratio: Approximately 86.8% Accuracy 5. **Median (Purple line, square with cross marker)**: * **Trend**: This method exhibits strong stability up to 30% attack ratio, then a moderate drop at 40%, and a sharp decline at 50%. * **Data Points**: * 0% Attack ratio: Approximately 96.0% Accuracy * 10% Attack ratio: Approximately 96.0% Accuracy * 20% Attack ratio: Approximately 95.9% Accuracy * 30% Attack ratio: Approximately 95.9% Accuracy * 40% Attack ratio: Approximately 94.9% Accuracy * 50% Attack ratio: Approximately 86.0% Accuracy 6. **FoolsGold (Brown line, downward-pointing triangle marker)**: * **Trend**: This method is very stable up to 30% attack ratio, then experiences a moderate drop at 40%, followed by a sharp decline at 50%. * **Data Points**: * 0% Attack ratio: Approximately 96.1% Accuracy * 10% Attack ratio: Approximately 96.1% Accuracy * 20% Attack ratio: Approximately 96.1% Accuracy * 30% Attack ratio: Approximately 96.0% Accuracy * 40% Attack ratio: Approximately 94.5% Accuracy * 50% Attack ratio: Approximately 85.2% Accuracy 7. **Biscotti (Gray line, star marker)**: * **Trend**: This method shows a continuous and significant decrease in accuracy starting from 0% attack ratio, making it the least robust method. The decline is steep until 40%, after which it stabilizes at a low accuracy. * **Data Points**: * 0% Attack ratio: Approximately 96.0% Accuracy * 10% Attack ratio: Approximately 95.5% Accuracy * 20% Attack ratio: Approximately 91.0% Accuracy * 30% Attack ratio: Approximately 86.5% Accuracy * 40% Attack ratio: Approximately 83.5% Accuracy * 50% Attack ratio: Approximately 83.2% Accuracy ### Key Observations * **Superior Robustness of "Ours"**: The "Ours" method (red line) stands out significantly, maintaining an accuracy above 95.8% even at a 50% attack ratio, demonstrating remarkable resilience to attacks. * **Clustered Performance of Most Methods**: FedAvg, ShieldFL, PBFL, Median, and FoolsGold exhibit similar performance profiles. They maintain high accuracy (above 95%) up to an attack ratio of 30%, then experience a noticeable drop at 40%, and a sharp decline to accuracies between 85% and 87% at 50% attack ratio. * **Vulnerability of Biscotti**: The "Biscotti" method (gray line) is the most vulnerable, with its accuracy steadily decreasing from the start and falling below 90% at 20% attack ratio, and below 84% at 40% attack ratio. It reaches the lowest accuracy among all methods at 50% attack ratio (around 83.2%). * **Threshold Effect**: For most methods (excluding "Ours" and "Biscotti"), there appears to be a threshold between 30% and 40% attack ratio where their performance begins to degrade significantly. ### Interpretation The data strongly suggests that the "Ours" method offers a substantial improvement in robustness against adversarial attacks compared to the other evaluated methods. While FedAvg, ShieldFL, PBFL, Median, and FoolsGold show some resilience up to moderate attack ratios (around 30%), their performance degrades sharply as the attack ratio increases further, indicating a vulnerability to higher levels of adversarial interference. The "Biscotti" method is clearly ineffective in adversarial environments, showing a rapid and continuous decline in accuracy even at low attack ratios. This chart highlights the critical importance of developing robust methods for scenarios where systems are exposed to adversarial attacks. The "Ours" method's ability to maintain high accuracy despite increasing attack ratios implies a significant advantage in real-world applications requiring high reliability and security in potentially hostile environments. The sharp drop-off observed in most other methods at higher attack ratios suggests that these methods may not be suitable for applications where the risk of high attack ratios is present, or they would require additional defense mechanisms to maintain acceptable performance.

## 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 compares the performance of FedAvg, ShieldFL, PBFL, Median, Biscotti, FoolsGold, and a method labeled "Ours" under increasing attack conditions. ### Components/Axes * **X-axis:** "Attack ratio (%)" ranging from 0 to 50, with markers at 0, 10, 20, 30, 40, and 50. * **Y-axis:** "Accuracy (%)" ranging from approximately 84 to 97, with markers at 84, 86, 88, 90, 92, 94, 96. * **Legend:** Located in the bottom-left corner, listing the following algorithms with corresponding line colors: * FedAvg (Blue) * ShieldFL (Orange) * PBFL (Green) * Median (Purple) * Biscotti (Grey) * FoolsGold (Red) * Ours (Brown/Maroon) ### Detailed Analysis Here's a breakdown of each line's trend and approximate data points, verified against the legend colors: * **FedAvg (Blue):** The line starts at approximately 96.2% accuracy at 0% attack ratio and sharply declines to approximately 84.5% at 50% attack ratio. It is a nearly linear downward slope. * (0%, 96.2%) * (10%, 95.8%) * (20%, 94.8%) * (30%, 93.5%) * (40%, 88.5%) * (50%, 84.5%) * **ShieldFL (Orange):** The line begins at approximately 96.1% accuracy at 0% attack ratio and gradually decreases to approximately 94.5% at 50% attack ratio. * (0%, 96.1%) * (10%, 95.9%) * (20%, 95.5%) * (30%, 95.2%) * (40%, 94.8%) * (50%, 94.5%) * **PBFL (Green):** The line starts at approximately 95.8% accuracy at 0% attack ratio and declines to approximately 86.5% at 50% attack ratio. * (0%, 95.8%) * (10%, 95.6%) * (20%, 94.8%) * (30%, 94.2%) * (40%, 90.5%) * (50%, 86.5%) * **Median (Purple):** The line begins at approximately 96.1% accuracy at 0% attack ratio and declines to approximately 88.5% at 50% attack ratio. * (0%, 96.1%) * (10%, 95.9%) * (20%, 95.3%) * (30%, 94.8%) * (40%, 92.5%) * (50%, 88.5%) * **Biscotti (Grey):** The line starts at approximately 96.2% accuracy at 0% attack ratio and declines to approximately 94.5% at 50% attack ratio. * (0%, 96.2%) * (10%, 96.0%) * (20%, 95.6%) * (30%, 95.3%) * (40%, 95.0%) * (50%, 94.5%) * **FoolsGold (Red):** The line begins at approximately 96.1% accuracy at 0% attack ratio and declines to approximately 95.0% at 50% attack ratio. * (0%, 96.1%) * (10%, 95.9%) * (20%, 95.5%) * (30%, 95.3%) * (40%, 95.2%) * (50%, 95.0%) * **Ours (Brown/Maroon):** The line starts at approximately 96.2% accuracy at 0% attack ratio and remains relatively stable, declining slightly to approximately 95.8% at 50% attack ratio. * (0%, 96.2%) * (10%, 96.1%) * (20%, 96.0%) * (30%, 95.9%) * (40%, 95.8%) * (50%, 95.8%) ### Key Observations * FedAvg exhibits the most significant drop in accuracy as the attack ratio increases, indicating high vulnerability. * "Ours" demonstrates the highest resilience to attacks, maintaining a relatively stable accuracy level across all attack ratios. * ShieldFL, Biscotti, and FoolsGold show relatively minor declines in accuracy, suggesting good robustness. * PBFL and Median show moderate declines in accuracy. ### Interpretation The chart demonstrates the varying levels of robustness of different federated learning algorithms against adversarial attacks. The "attack ratio" likely represents the proportion of malicious participants in the federated learning process. The results suggest that FedAvg is highly susceptible to attacks, while the proposed method ("Ours") offers significantly improved resilience. This could be due to the implementation of specific defense mechanisms within "Ours" that mitigate the impact of malicious contributions. The relatively stable performance of "Ours" indicates a potential advantage in real-world deployments where the presence of adversarial actors is a concern. The differences in performance between the algorithms highlight the importance of considering security and robustness when selecting a federated learning approach. The chart provides empirical evidence supporting the claim that "Ours" is a more secure and reliable federated learning algorithm compared to the others tested.

\n ## Line Chart: Accuracy vs. Attack Ratio for Federated Learning Methods ### Overview The image is a line chart comparing the performance (accuracy) of seven different federated learning methods or defense mechanisms as the ratio of adversarial attacks increases. The chart demonstrates how each method's accuracy degrades under increasing attack pressure. ### Components/Axes * **X-Axis:** Labeled "Attack ratio (%)". It represents the percentage of malicious participants or attacks in the system. The axis has major tick marks at 0, 10, 20, 30, 40, and 50. * **Y-Axis:** Labeled "Accuracy (%)". It represents the model's accuracy. The axis has major tick marks at 84, 86, 88, 90, 92, 94, and 96. * **Legend:** Located in the bottom-left quadrant of the chart area. It lists seven data series with corresponding line colors and marker symbols: 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 star/asterisk markers (☆). 6. **FoolsGold:** Brown line with downward-pointing triangle markers (▽). 7. **Ours:** Red line with circle markers (○). ### Detailed Analysis The chart plots Accuracy (%) against Attack ratio (%). All methods start at a high accuracy (approximately 96%) when the attack ratio is 0%. As the attack ratio increases, the accuracy of most methods declines, but at dramatically different rates. **Data Series Trends & Approximate Values:** 1. **Ours (Red line, ○):** * **Trend:** Shows the most robust performance. The line remains nearly flat, exhibiting only a very slight downward slope. * **Data Points:** ~96.2% (0%), ~96.1% (10%), ~96.1% (20%), ~96.0% (30%), ~95.9% (40%), ~95.8% (50%). 2. **Median (Purple line, ○):** * **Trend:** Very stable, similar to "Ours" but with a marginally steeper decline at the highest attack ratio. * **Data Points:** ~96.0% (0%), ~95.9% (10%), ~95.8% (20%), ~95.7% (30%), ~95.6% (40%), ~95.0% (50%). 3. **FedAvg (Blue line, □), ShieldFL (Orange line, ◇), PBFL (Green line, △), FoolsGold (Brown line, ▽):** * **Trend:** These four methods follow a very similar pattern. They maintain high accuracy (~96%) until an attack ratio of 30-40%, after which they experience a sharp, precipitous drop. * **Data Points (Approximate for the group):** ~96.0% (0%), ~96.0% (10%), ~95.8% (20%), ~95.5% (30%). At 40%, they begin to diverge slightly: FedAvg/PBFL ~95.0%, ShieldFL ~94.8%, FoolsGold ~94.5%. At 50%, they all drop significantly: FedAvg ~86.5%, PBFL ~87.0%, ShieldFL ~87.0%, FoolsGold ~85.2%. 4. **Biscotti (Gray line, ☆):** * **Trend:** Exhibits the worst performance and earliest degradation. The line shows a steady, steep downward slope from the beginning. * **Data Points:** ~96.0% (0%), ~95.5% (10%), ~91.0% (20%), ~86.5% (30%), ~83.5% (40%), ~83.2% (50%). ### Key Observations 1. **Clear Performance Tiers:** The methods cluster into three distinct performance tiers under attack: * **Tier 1 (Highly Robust):** "Ours" and "Median" maintain accuracy above ~95% even at a 50% attack ratio. * **Tier 2 (Moderately Robust, then Collapse):** FedAvg, ShieldFL, PBFL, and FoolsGold are resilient up to a ~30-40% attack ratio but fail catastrophically beyond that point. * **Tier 3 (Vulnerable):** Biscotti's accuracy degrades linearly and significantly with any increase in attack ratio. 2. **Critical Threshold:** For four of the seven methods, an attack ratio between 30% and 40% appears to be a critical failure threshold. 3. **"Ours" is the Top Performer:** The method labeled "Ours" demonstrates the highest and most consistent accuracy across the entire range of attack ratios tested. ### Interpretation This chart is a robustness evaluation of federated learning aggregation or defense strategies. The "Attack ratio" simulates an increasingly hostile environment where a larger portion of participating devices are malicious (e.g., sending poisoned model updates). * **What the data suggests:** The proposed method ("Ours") and the "Median" aggregation are significantly more resilient to Byzantine (malicious) attacks than the other compared methods. Their design likely incorporates robust statistics or other mechanisms that are not easily fooled by a high volume of adversarial inputs. * **How elements relate:** The sharp drop-off for FedAvg, ShieldFL, PBFL, and FoolsGold indicates they have a breaking point. Their defense mechanisms may work well when malicious actors are a minority but become overwhelmed and fail completely when malicious participants approach or exceed 40-50% of the total. Biscotti's linear decline suggests its defense is fundamentally less effective, offering little resistance as attacks increase. * **Notable Anomaly:** The near-identical performance of FedAvg, ShieldFL, PBFL, and FoolsGold until the 30% mark is striking. It suggests that under moderate attack conditions, these different methods offer similar levels of protection, and their key differentiator is their failure mode under extreme conditions. * **Practical Implication:** For a real-world federated learning system where security is a concern, choosing an aggregation method from Tier 1 ("Ours" or "Median") would provide a much larger safety margin. Methods from Tier 2 might be acceptable only if the system can guarantee the attack ratio will never approach the 30-40% threshold.

## Line Chart: Accuracy vs. Attack Ratio ### Overview The chart compares the accuracy retention of various machine learning defense mechanisms against adversarial attacks, measured as attack ratio percentage. Accuracy is plotted on the y-axis (84-96%) and attack ratio on the x-axis (0-50%). Seven defense strategies are compared through distinct colored lines with unique markers. ### Components/Axes - **Y-axis**: Accuracy (%) [84-96], labeled "Accuracy (%)" - **X-axis**: Attack ratio (%) [0-50], labeled "Attack ratio (%)" - **Legend**: Located in bottom-left corner, mapping: - Blue squares: FedAvg - Orange diamonds: ShieldFL - Green triangles: PBFL - Purple diamonds: Median - Gray stars: Biscotti - Brown triangles: FoolsGold - Red circles: Ours ### Detailed Analysis 1. **FedAvg** (blue squares): Starts at ~96.5% accuracy at 0% attack ratio, shows gradual decline to ~95.5% at 50% attack ratio. 2. **ShieldFL** (orange diamonds): Begins at ~96.2%, maintains near-horizontal trajectory until 40% attack ratio, then drops sharply to ~87%. 3. **PBFL** (green triangles): Starts at ~96.3%, shows moderate decline to ~94.5% at 50% attack ratio. 4. **Median** (purple diamonds): Remains relatively flat at ~95.8% across all attack ratios. 5. **Biscotti** (gray stars): Starts at ~96%, shows steep linear decline to ~83.5% at 50% attack ratio. 6. **FoolsGold** (brown triangles): Begins at ~96.1%, maintains stability until 40% attack ratio, then plummets to ~85%. 7. **Ours** (red circles): Maintains highest accuracy throughout, starting at ~96.4% and ending at ~95.8% with minimal decline. ### Key Observations - **Robustness**: "Ours" demonstrates superior resilience, maintaining >95% accuracy across all attack ratios. - **Vulnerability**: "Biscotti" and "FoolsGold" exhibit the most severe degradation, dropping >12% accuracy at maximum attack ratio. - **Stability**: "Median" and "PBFL" show moderate stability, with <2% accuracy loss across the attack spectrum. - **Threshold Behavior**: "ShieldFL" and "FoolsGold" exhibit threshold-like behavior, maintaining high accuracy until a critical attack ratio (~40%) before rapid decline. ### Interpretation The data reveals fundamental differences in attack resilience among defense mechanisms. The "Ours" method's consistent performance suggests architectural advantages in adversarial robustness. The sharp declines in "Biscotti" and "FoolsGold" indicate potential single points of failure in their designs. Notably, the "Median" method's stability implies that simple averaging techniques may provide baseline protection against certain attack types. The threshold behavior observed in "ShieldFL" and "FoolsGold" suggests these methods might employ confidence-based filtering mechanisms that become ineffective beyond certain attack intensities. These findings highlight the importance of defense mechanism design in maintaining model utility under adversarial conditions, with "Ours" establishing a new benchmark for attack resilience in this evaluation.