## 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). Seven different algorithms are compared: 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 0, 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend:** Located on the right 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, pentagon marker) * Biscotti (gray, star marker) * FoolsGold (brown, inverted triangle marker) * Ours (red, circle marker) ### Detailed Analysis * **FedAvg (blue, square marker):** The accuracy starts at approximately 74% at 0% attack ratio and decreases to approximately 47% at 30% attack ratio, then further decreases to approximately 10% at 50% attack ratio. * **ShieldFL (orange, diamond marker):** The accuracy starts at approximately 78% at 0% attack ratio and decreases to approximately 46% at 30% attack ratio, then further decreases to approximately 7% at 50% attack ratio. * **PBFL (green, triangle marker):** The accuracy starts at approximately 79% at 0% attack ratio and decreases to approximately 56% at 30% attack ratio, then further decreases to approximately 6% at 50% attack ratio. * **Median (purple, pentagon marker):** The accuracy starts at approximately 67% at 0% attack ratio and decreases to approximately 47% at 30% attack ratio, then further decreases to approximately 5% at 50% attack ratio. * **Biscotti (gray, star marker):** The accuracy starts at approximately 62% at 0% attack ratio and decreases to approximately 42% at 30% attack ratio, then further decreases to approximately 21% at 50% attack ratio. * **FoolsGold (brown, inverted triangle marker):** The accuracy starts at approximately 79% at 0% attack ratio and decreases to approximately 32% at 30% attack ratio, then further decreases to approximately 4% at 50% attack ratio. * **Ours (red, circle marker):** The accuracy starts at approximately 75% at 0% attack ratio, decreases to approximately 65% at 30% attack ratio, then decreases to approximately 31% at 50% attack ratio. ### Key Observations * All algorithms experience a decrease in accuracy as the attack ratio increases. * The "Ours" algorithm (red line) consistently maintains a higher accuracy compared to the other algorithms, especially at higher attack ratios. * FoolsGold, ShieldFL, and Median algorithms show the most significant drop in accuracy as the attack ratio increases. ### Interpretation The chart demonstrates the impact of increasing attack ratios on the accuracy of various federated learning algorithms. The "Ours" algorithm appears to be more robust to attacks compared to the other algorithms tested, as it maintains a higher accuracy even at higher attack ratios. This suggests that the "Ours" algorithm may incorporate some form of defense mechanism against adversarial attacks. The other algorithms are more susceptible to attacks, as their accuracy drops significantly with increasing attack ratios. The data highlights the importance of developing robust federated learning algorithms that can withstand adversarial attacks to ensure reliable performance in real-world scenarios.

## Chart Type: Line Chart - Accuracy vs. Attack Ratio ### Overview This image displays a 2D line chart comparing the "Accuracy (%)" of seven different methods against varying "Attack ratio (%)". Each method is represented by a distinct colored line with a unique marker, and their performance is tracked across six discrete attack ratio percentages. The chart illustrates how the accuracy of these methods degrades as the attack ratio increases. ### Components/Axes The chart consists of a main plotting area, a Y-axis on the left, an X-axis at the bottom, and a legend in the bottom-left corner. * **X-axis:** * **Title:** "Attack ratio (%)" * **Range:** From 0 to 50. * **Major Ticks:** Labeled at 0, 10, 20, 30, 40, and 50. * **Y-axis:** * **Title:** "Accuracy (%)" * **Range:** From 0 to 80. * **Major Ticks:** Labeled at 0, 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend (located in the bottom-left of the plotting area):** * **FedAvg**: Blue line with a square marker. * **ShieldFL**: Orange line with a diamond marker. * **PBFL**: Green line with an upward-pointing triangle marker. * **Median**: Purple line with a square-cross marker. * **Biscotti**: Gray line with a star marker. * **FoolsGold**: Brown line with a downward-pointing triangle marker. * **Ours**: Red line with a circle marker. ### Detailed Analysis The chart plots the accuracy of each method at attack ratios of 0%, 10%, 20%, 30%, 40%, and 50%. 1. **FedAvg** (Blue line with square marker): * **Trend:** Generally decreasing, with a sharp drop between 10% and 20%, and another significant drop between 30% and 40%. * **Data Points:** * 0% Attack: ~78% Accuracy * 10% Attack: ~74% Accuracy * 20% Attack: ~51% Accuracy * 30% Attack: ~47% Accuracy * 40% Attack: ~17% Accuracy * 50% Attack: ~7% Accuracy 2. **ShieldFL** (Orange line with diamond marker): * **Trend:** Similar to FedAvg, showing a general decrease with sharp drops in the same intervals. * **Data Points:** * 0% Attack: ~76% Accuracy * 10% Attack: ~69% Accuracy * 20% Attack: ~49% Accuracy * 30% Attack: ~45% Accuracy * 40% Attack: ~14% Accuracy * 50% Attack: ~6% Accuracy 3. **PBFL** (Green line with upward-pointing triangle marker): * **Trend:** Relatively stable from 0% to 10%, then a sharp drop, followed by a slight recovery between 20% and 30%, and then a continuous decrease. * **Data Points:** * 0% Attack: ~75% Accuracy * 10% Attack: ~75% Accuracy * 20% Attack: ~52% Accuracy * 30% Attack: ~56% Accuracy * 40% Attack: ~31% Accuracy * 50% Attack: ~15% Accuracy 4. **Median** (Purple line with square-cross marker): * **Trend:** Consistently decreasing across all attack ratios, with a particularly sharp decline after 30%. * **Data Points:** * 0% Attack: ~67% Accuracy * 10% Attack: ~64% Accuracy * 20% Attack: ~49% Accuracy * 30% Attack: ~36% Accuracy * 40% Attack: ~10% Accuracy * 50% Attack: ~0% Accuracy (or very close to 0%) 5. **Biscotti** (Gray line with star marker): * **Trend:** Shows a more gradual and steady decrease in accuracy compared to most other methods, especially at higher attack ratios. * **Data Points:** * 0% Attack: ~62% Accuracy * 10% Attack: ~59% Accuracy * 20% Attack: ~50% Accuracy * 30% Attack: ~44% Accuracy * 40% Attack: ~36% Accuracy * 50% Attack: ~21% Accuracy 6. **FoolsGold** (Brown line with downward-pointing triangle marker): * **Trend:** Starts with high accuracy, then experiences a very sharp drop between 10% and 20%, and another significant drop between 30% and 40%. * **Data Points:** * 0% Attack: ~79% Accuracy * 10% Attack: ~74% Accuracy * 20% Attack: ~37% Accuracy * 30% Attack: ~32% Accuracy * 40% Attack: ~7% Accuracy * 50% Attack: ~5% Accuracy 7. **Ours** (Red line with circle marker): * **Trend:** Relatively stable or slightly increasing from 0% to 30% attack ratio, then shows a significant but less steep decline compared to other methods at higher attack ratios. This method demonstrates the highest resilience. * **Data Points:** * 0% Attack: ~74% Accuracy * 10% Attack: ~74% Accuracy * 20% Attack: ~63% Accuracy * 30% Attack: ~65% Accuracy * 40% Attack: ~43% Accuracy * 50% Attack: ~30% Accuracy ### Key Observations * At 0% attack ratio, "FoolsGold" shows the highest accuracy (~79%), closely followed by "FedAvg" (~78%), "ShieldFL" (~76%), and "PBFL" (~75%). "Ours" is also competitive at ~74%. "Biscotti" and "Median" start at lower accuracies (~62% and ~67% respectively). * As the attack ratio increases, most methods experience a significant drop in accuracy. "FoolsGold", "FedAvg", and "ShieldFL" show particularly sharp declines between 10% and 20% attack ratio. * The "Ours" method (red circle) consistently maintains the highest accuracy at higher attack ratios (30%, 40%, and 50%). At 50% attack ratio, "Ours" has an accuracy of approximately 30%, which is substantially higher than all other methods. * "Median" (purple square-cross) performs the worst at high attack ratios, dropping to near 0% accuracy at 50% attack ratio. * "Biscotti" (gray star) shows a more gradual decline than most other methods, indicating some inherent stability, but its absolute accuracy is lower than "Ours" at higher attack ratios. * The "PBFL" method (green triangle) shows a unique behavior with a slight increase in accuracy between 20% and 30% attack ratio before continuing its decline. ### Interpretation This chart effectively demonstrates the robustness of different methods against adversarial attacks, measured by their accuracy as the "Attack ratio (%)" increases. The general expectation is that accuracy will decrease with higher attack ratios, and this trend is largely observed across all methods. The most significant finding is the superior performance of the method labeled "Ours". While its initial accuracy at 0% attack ratio is comparable to several other top-performing methods, its ability to maintain a much higher accuracy under increasing attack pressure sets it apart. At 50% attack ratio, "Ours" retains approximately 30% accuracy, whereas all other methods have dropped significantly, with most falling below 10%. This suggests that "Ours" possesses a strong defense mechanism or inherent resilience against the type of attacks being simulated. Conversely, methods like "Median" and "FoolsGold" show poor resilience, with their accuracy plummeting to near zero at higher attack ratios. "FedAvg" and "ShieldFL" also exhibit substantial vulnerability, experiencing sharp drops in performance. "Biscotti" shows a more graceful degradation, implying a degree of stability, but its overall accuracy is not as high as "Ours" when attacks are severe. In conclusion, the data strongly indicates that the "Ours" method is the most robust and effective solution among those evaluated for maintaining performance in the presence of increasing adversarial attack ratios. This makes it a highly promising candidate for applications requiring high reliability under adversarial conditions.

\n ## Line Chart: Accuracy vs. Attack Ratio for Federated Learning Defenses ### Overview This line chart depicts the accuracy of several Federated Learning (FL) defense mechanisms as a function of the attack ratio. The x-axis represents the attack ratio (in percentage), and the y-axis represents the accuracy (in percentage). The chart compares the performance of "FedAvg", "ShieldFL", "PBFL", "Median", "Biscotti", "FoolsGold", and "Ours" under increasing attack conditions. ### Components/Axes * **X-axis:** "Attack ratio (%)" - Scale ranges from 0% to 50%, with markers at 0, 10, 20, 30, 40, and 50. * **Y-axis:** "Accuracy (%)" - Scale ranges from 0% to 80%, with markers at 0, 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend:** Located in the bottom-left corner. The legend maps colors to the following defense mechanisms: * Blue Square: FedAvg * Orange Triangle: ShieldFL * Green Triangle: PBFL * Purple Diamond: Median * Gray Hexagon: Biscotti * Red Hexagon: FoolsGold * Red Circle: Ours ### Detailed Analysis The chart displays seven lines, each representing a different defense mechanism. * **FedAvg (Blue Square):** Starts at approximately 74% accuracy at 0% attack ratio. The line slopes downward, reaching approximately 16% accuracy at 50% attack ratio. Data points (approximate): (0, 74), (10, 65), (20, 48), (30, 46), (40, 20), (50, 16). * **ShieldFL (Orange Triangle):** Starts at approximately 77% accuracy at 0% attack ratio. The line initially decreases slightly, then drops more rapidly, reaching approximately 32% accuracy at 50% attack ratio. Data points (approximate): (0, 77), (10, 73), (20, 41), (30, 45), (40, 34), (50, 32). * **PBFL (Green Triangle):** Starts at approximately 75% accuracy at 0% attack ratio. The line decreases steadily, reaching approximately 14% accuracy at 50% attack ratio. Data points (approximate): (0, 75), (10, 68), (20, 52), (30, 52), (40, 35), (50, 14). * **Median (Purple Diamond):** Starts at approximately 63% accuracy at 0% attack ratio. The line decreases rapidly, reaching approximately 6% accuracy at 50% attack ratio. Data points (approximate): (0, 63), (10, 58), (20, 38), (30, 28), (40, 12), (50, 6). * **Biscotti (Gray Hexagon):** Starts at approximately 66% accuracy at 0% attack ratio. The line decreases steadily, reaching approximately 8% accuracy at 50% attack ratio. Data points (approximate): (0, 66), (10, 61), (20, 42), (30, 32), (40, 16), (50, 8). * **FoolsGold (Red Hexagon):** Starts at approximately 75% accuracy at 0% attack ratio. The line initially increases to a peak around 30% attack ratio, then decreases, reaching approximately 30% accuracy at 50% attack ratio. Data points (approximate): (0, 75), (10, 73), (20, 66), (30, 67), (40, 42), (50, 30). * **Ours (Red Circle):** Starts at approximately 73% accuracy at 0% attack ratio. The line decreases steadily, reaching approximately 32% accuracy at 50% attack ratio. Data points (approximate): (0, 73), (10, 70), (20, 49), (30, 44), (40, 34), (50, 32). ### Key Observations * All defense mechanisms experience a decrease in accuracy as the attack ratio increases. * "FoolsGold" exhibits a unique behavior, with accuracy initially increasing before decreasing. * "Median" and "Biscotti" show the most significant decline in accuracy with increasing attack ratio. * "ShieldFL", "Ours", and "PBFL" maintain relatively higher accuracy compared to others at higher attack ratios (40-50%). * "FedAvg" shows a consistent, linear decline in accuracy. ### Interpretation The chart demonstrates the vulnerability of Federated Learning systems to attacks and the effectiveness of different defense mechanisms in mitigating these attacks. The attack ratio represents the proportion of malicious participants in the federated learning process. The accuracy represents the performance of the model trained under these conditions. The varying slopes of the lines indicate different levels of robustness. A steeper slope suggests a more significant performance degradation under attack. The "FoolsGold" mechanism's initial increase in accuracy could be due to a specific attack pattern that it handles well at lower attack ratios, but it eventually becomes overwhelmed as the attack intensifies. The relatively stable performance of "ShieldFL", "Ours", and "PBFL" suggests that these mechanisms are more resilient to attacks, potentially due to their design principles. The rapid decline of "Median" and "Biscotti" indicates that these methods are easily compromised by malicious participants. The chart highlights the importance of choosing appropriate defense mechanisms based on the expected attack environment. Further investigation into the specific vulnerabilities exploited by the attacks and the underlying mechanisms of each defense strategy would be valuable. The data suggests that no single defense is universally effective, and a combination of strategies might be necessary to achieve robust security in Federated Learning systems.

## Line Chart: Federated Learning Method Accuracy vs. Attack Ratio ### Overview This image is a line chart comparing the performance of seven different federated learning methods or aggregation strategies. The chart plots the model accuracy (in percentage) against an increasing "Attack ratio" (in percentage), which likely represents the proportion of malicious or adversarial participants in the federated learning system. The chart demonstrates how each method's accuracy degrades as the system comes under a stronger attack. ### Components/Axes * **Chart Type:** Multi-line chart with markers. * **X-Axis:** Labeled **"Attack ratio (%)"**. The axis has major tick marks at 0, 10, 20, 30, 40, and 50. * **Y-Axis:** Labeled **"Accuracy (%)"**. The axis has major tick marks at 0, 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend:** Located in the **center-left** portion of the chart area. It lists seven data series with corresponding 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 asterisk markers (*). 6. **FoolsGold** - Brown line with downward-pointing triangle markers (▽). 7. **Ours** - Red line with pentagram markers (☆). ### Detailed Analysis The following table reconstructs the approximate data points for each method at the given attack ratios. Values are estimated from the chart's grid lines and marker positions. **Uncertainty is ±2-3% for most points due to visual estimation.** | Attack Ratio (%) | FedAvg (Blue, □) | ShieldFL (Orange, ◇) | PBFL (Green, △) | Median (Purple, ○) | Biscotti (Gray, *) | FoolsGold (Brown, ▽) | Ours (Red, ☆) | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | **0** | ~75% | ~74% | ~79% | ~67% | ~62% | ~75% | ~74% | | **10** | ~69% | ~68% | ~75% | ~63% | ~58% | ~63% | ~75% | | **20** | ~51% | ~49% | ~51% | ~50% | ~50% | ~37% | ~63% | | **30** | ~46% | ~45% | ~56% | ~36% | ~32% | ~32% | ~65% | | **40** | ~16% | ~14% | ~31% | ~15% | ~36% | ~7% | ~43% | | **50** | ~6% | ~5% | ~13% | ~0% | ~21% | ~4% | ~31% | **Trend Verification per Data Series:** * **FedAvg (Blue):** Starts high (~75%), declines steadily and sharply after 20% attack ratio, ending very low (~6%). * **ShieldFL (Orange):** Follows a nearly identical trend to FedAvg, starting slightly lower and ending at a similar low point (~5%). * **PBFL (Green):** Starts the highest (~79%), maintains a lead until 30%, then declines but remains more resilient than FedAvg/ShieldFL, ending at ~13%. * **Median (Purple):** Starts moderately (~67%), declines consistently, and suffers a catastrophic drop to near 0% at 50% attack ratio. * **Biscotti (Gray):** Starts the lowest (~62%), shows a unique trend by dipping at 30% but then *increasing* at 40% before falling again. It is the second-best performer at 50% (~21%). * **FoolsGold (Brown):** Starts high (~75%), experiences the most severe and early drop, plummeting to ~37% at 20% attack ratio and ending among the worst (~4%). * **Ours (Red):** Starts high (~74%), maintains or even slightly increases accuracy up to 30% attack ratio (~65%), then declines but remains the top performer at all points from 20% onward, finishing at ~31%. ### Key Observations 1. **Universal Degradation:** All methods show a decrease in accuracy as the attack ratio increases from 0% to 50%. 2. **Performance Tiers at High Attack (50%):** * **Top Tier:** "Ours" (~31%) is the clear leader. * **Middle Tier:** Biscotti (~21%) and PBFL (~13%) show moderate resilience. * **Low Tier:** FedAvg, ShieldFL, Median, and FoolsGold all collapse to ≤6% accuracy. 3. **Critical Threshold:** A significant performance drop for most methods occurs between the 20% and 40% attack ratio marks. 4. **Anomaly - Biscotti's Mid-Attack Resilience:** The Biscotti method is the only one that does not follow a strictly monotonic decrease; its accuracy at 40% attack (~36%) is higher than at 30% (~32%). 5. **Anomaly - "Ours" at 30%:** The proposed method ("Ours") shows a slight accuracy *increase* from 20% (~63%) to 30% (~65%), suggesting potential robustness or a specific response to that level of adversarial presence. ### Interpretation This chart is a robustness evaluation of federated learning aggregation algorithms under poisoning or Byzantine attacks. The "Attack ratio" represents the fraction of malicious clients sending corrupted model updates. * **The data suggests** that the proposed method ("Ours") is significantly more robust to adversarial attacks than the six baseline methods compared. Its performance advantage becomes pronounced once the attack ratio exceeds 10-20%. * **The elements relate** to show a clear hierarchy of resilience. Traditional methods like FedAvg and its variant ShieldFL are highly vulnerable. Median and FoolsGold, often used for robustness, also fail catastrophically at high attack ratios. PBFL and Biscotti offer intermediate levels of protection. * **Notable trends** include the early collapse of FoolsGold and the non-linear, somewhat resilient response of Biscotti. The most important anomaly is the sustained high performance of "Ours" up to a 30% attack ratio, which is a critical threshold where most other systems fail. This indicates the proposed method likely employs a more sophisticated mechanism for identifying and neutralizing malicious updates without discarding useful information from benign clients. The chart's primary message is the superior security-utility trade-off achieved by the authors' approach.

## Line Graph: Accuracy vs. Attack Ratio ### Overview The graph compares the accuracy (%) of seven different methods (FedAvg, ShieldFL, PBFL, Median, Biscotti, FoolsGold, Ours) as the attack ratio (%) increases from 0 to 50. All methods start with high accuracy at 0% attack ratio but degrade as the attack ratio increases, with varying rates of decline. ### Components/Axes - **Y-axis**: Accuracy (%) ranging from 0 to 80. - **X-axis**: Attack ratio (%) ranging from 0 to 50. - **Legend**: Located on the left, associating colors and markers with methods: - **FedAvg**: Blue squares (■) - **ShieldFL**: Orange diamonds (◇) - **PBFL**: Green triangles (△) - **Median**: Purple pentagons (⬤) - **Biscotti**: Gray stars (★) - **FoolsGold**: Brown inverted triangles (▼) - **Ours**: Red circles (●) ### Detailed Analysis 1. **Ours (Red circles)**: Starts near 75% accuracy at 0% attack ratio, declines gradually to ~30% at 50% attack ratio. Maintains the highest accuracy across most attack ratios. 2. **ShieldFL (Orange diamonds)**: Begins at ~70% accuracy, drops sharply to ~10% by 50% attack ratio. Steepest decline among all methods. 3. **PBFL (Green triangles)**: Starts at ~75%, declines moderately to ~15% at 50% attack ratio. Slightly outperforms Biscotti at higher attack ratios. 4. **Median (Purple pentagons)**: Begins at ~65%, plummets to near 0% by 50% attack ratio. Most drastic drop. 5. **Biscotti (Gray stars)**: Starts at ~60%, declines steadily to ~20% at 50% attack ratio. Linear degradation. 6. **FoolsGold (Brown inverted triangles)**: Starts at ~70%, drops rapidly to ~5% by 50% attack ratio. Second-steepest decline after ShieldFL. 7. **FedAvg (Blue squares)**: Begins at ~70%, declines moderately to ~10% at 50% attack ratio. Similar trend to PBFL but slightly worse at higher attack ratios. ### Key Observations - **Crossing Lines**: Lines intersect at multiple points (e.g., FedAvg and PBFL cross near 20% attack ratio), indicating no single method dominates across all attack ratios. - **Outliers**: "Median" and "FoolsGold" exhibit the most severe degradation, while "Ours" and "PBFL" retain higher accuracy longer. - **Gradual vs. Sharp Declines**: Methods like "Ours" and "Biscotti" show gradual declines, whereas "ShieldFL" and "FoolsGold" drop sharply. ### Interpretation The data suggests that **Ours** is the most robust method against adversarial attacks, maintaining higher accuracy even at 50% attack ratio. In contrast, **Median** and **FoolsGold** are highly vulnerable, with accuracy collapsing under moderate attack ratios. The graph highlights a trade-off between initial accuracy and robustness: methods with higher starting accuracy (e.g., PBFL, Ours) degrade more slowly, while others (e.g., ShieldFL, Median) sacrifice accuracy rapidly. The crossing lines imply that the optimal method depends on the expected attack ratio, emphasizing the need for context-aware system design.