## Heatmap: Performance vs. Percentage and Width ### Overview The image is a heatmap visualizing performance (represented by color intensity) as a function of two parameters: "percentage p" (y-axis) and "width of near-zero range c" (x-axis). The heatmap displays numerical values within each cell, indicating the performance score for the corresponding parameter combination. The color gradient ranges from light yellow (lower performance) to dark blue (higher performance), as indicated by the colorbar on the right. ### Components/Axes * **X-axis:** "width of near-zero range c" with values 0.05, 0.1, 0.15, 0.2, 0.25, and 0.3. * **Y-axis:** "percentage p" with values 85.0, 90.0, 92.5, 95.0, 97.0, and 99.5. * **Colorbar:** Ranges from approximately 64.0 (light yellow) to 67.0 (dark blue), representing the performance score. ### Detailed Analysis The heatmap displays the following performance values for each combination of "percentage p" and "width of near-zero range c": | percentage p | 0.05 | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 | | :----------- | :--- | :--- | :--- | :--- | :--- | :--- | | 99.5 | 65.2 | 64.6 | 66.4 | 66.0 | 64.4 | 65.2 | | 97.0 | 65.4 | 65.4 | 65.2 | 65.6 | 65.2 | 65.2 | | 95.0 | 64.8 | 64.4 | 64.4 | 65.6 | 64.6 | 64.2 | | 92.5 | 65.0 | 64.2 | 64.8 | 64.8 | 65.2 | 65.0 | | 90.0 | 64.6 | 64.6 | 64.6 | 64.4 | 65.6 | 65.2 | | 85.0 | 64.0 | 64.4 | 64.8 | 64.6 | 67.0 | 66.2 | **Trends:** * For "percentage p = 85.0", the performance is relatively low for "width of near-zero range c" values from 0.05 to 0.2, then spikes to the highest value (67.0) at c = 0.25, and decreases slightly to 66.2 at c = 0.3. * For "percentage p = 99.5", the performance is highest at c = 0.15 (66.4) and 0.2 (66.0). * The highest performance value (67.0) is observed at "percentage p = 85.0" and "width of near-zero range c = 0.25". * The lowest performance value (64.0) is observed at "percentage p = 85.0" and "width of near-zero range c = 0.05". ### Key Observations * The performance varies significantly depending on the combination of "percentage p" and "width of near-zero range c". * A "width of near-zero range c" of 0.25 appears to yield high performance when "percentage p" is low (85.0). * Higher "percentage p" values (97.0 and 99.5) show relatively consistent performance across different "width of near-zero range c" values. ### Interpretation The heatmap suggests that the optimal configuration of "percentage p" and "width of near-zero range c" depends on the specific application or context. A lower "percentage p" may benefit from a "width of near-zero range c" of 0.25, while higher "percentage p" values are less sensitive to changes in "width of near-zero range c". The data indicates that the relationship between these parameters is not linear, and careful tuning is required to achieve the best performance. The "width of near-zero range c" parameter seems to have a more significant impact on performance when the "percentage p" is at its lowest value.

## Heatmap: Percentage p vs. Width of Near-Zero Range c ### Overview This image presents a heatmap visualizing the relationship between two variables: "percentage p" and "width of near-zero range c". The heatmap uses a color gradient to represent the values associated with each combination of these variables. The color scale ranges from approximately 64.0 to 67.0. ### Components/Axes * **X-axis:** "width of near-zero range c" with values: 0.05, 0.1, 0.15, 0.2, 0.25, 0.3. * **Y-axis:** "percentage p" with values: 85, 90, 92.5, 95, 97, 99.5. * **Color Scale:** Ranges from approximately 64.0 (dark blue) to 67.0 (light yellow). The scale is positioned on the right side of the heatmap. * **Data Points:** Each cell in the heatmap represents a specific combination of "percentage p" and "width of near-zero range c", with the cell's color indicating the corresponding value. ### Detailed Analysis The heatmap contains 36 data points, arranged in a 6x6 grid. Here's a breakdown of the values, row by row: * **p = 85:** * c = 0.05: 64.0 * c = 0.1: 64.4 * c = 0.15: 64.8 * c = 0.2: 64.6 * c = 0.25: 67.0 * c = 0.3: 66.2 * **p = 90:** * c = 0.05: 64.6 * c = 0.1: 64.6 * c = 0.15: 64.6 * c = 0.2: 64.4 * c = 0.25: 65.6 * c = 0.3: 65.2 * **p = 92.5:** * c = 0.05: 65.0 * c = 0.1: 64.2 * c = 0.15: 64.8 * c = 0.2: 64.8 * c = 0.25: 65.2 * c = 0.3: 65.0 * **p = 95:** * c = 0.05: 64.8 * c = 0.1: 64.4 * c = 0.15: 64.4 * c = 0.2: 65.6 * c = 0.25: 64.6 * c = 0.3: 64.2 * **p = 97:** * c = 0.05: 65.4 * c = 0.1: 65.4 * c = 0.15: 65.2 * c = 0.2: 65.6 * c = 0.25: 65.2 * c = 0.3: 65.2 * **p = 99.5:** * c = 0.05: 65.2 * c = 0.1: 64.6 * c = 0.15: 66.4 * c = 0.2: 66.0 * c = 0.25: 64.4 * c = 0.3: 65.2 ### Key Observations * The values generally fall between 64.0 and 67.0. * The highest value (67.0) occurs at p = 85 and c = 0.25. * The lowest value (64.0) occurs at p = 85 and c = 0.05. * There isn't a strong, clear trend across the heatmap. Values appear relatively consistent, with some localized variations. * For p = 90, the values are very similar across all values of c. ### Interpretation The heatmap suggests a complex relationship between "percentage p" and "width of near-zero range c". The relatively small range of values (64.0-67.0) indicates that the variable being measured is not highly sensitive to changes in either "percentage p" or "width of near-zero range c" within the tested ranges. The peak at p=85 and c=0.25 might indicate an optimal condition for whatever process these variables represent, but further investigation would be needed to confirm this. The consistency of values for p=90 suggests that the measured variable is largely independent of the "width of near-zero range c" at that percentage level. Without knowing the context of these variables, it's difficult to draw more specific conclusions. The data could represent the efficiency of an algorithm, the accuracy of a measurement, or any other quantifiable process.

\n ## Heatmap: Performance vs. Near-Zero Range Width and Percentage Threshold ### Overview The image is a heatmap chart visualizing a numerical metric (likely a performance score or accuracy percentage) as a function of two parameters: the "width of near-zero range c" (x-axis) and a "percentage p" (y-axis). The chart uses a color gradient from light yellow (lower values) to dark blue (higher values) to represent the metric's magnitude. All text is in English. ### Components/Axes * **Chart Type:** 2D Heatmap / Grid Plot. * **X-Axis (Horizontal):** * **Label:** `width of near-zero range c` * **Scale/Markers:** Categorical with values: `0.05`, `0.1`, `0.15`, `0.2`, `0.25`, `0.3`. * **Y-Axis (Vertical):** * **Label:** `percentage p` * **Scale/Markers:** Categorical with values: `85.0`, `90.0`, `92.5`, `95.0`, `97.0`, `99.5`. * **Legend / Color Bar:** * **Placement:** Vertically aligned on the right side of the chart. * **Scale:** Continuous gradient from light yellow to dark blue. * **Labeled Ticks:** `64.0` (bottom, light yellow), `64.5`, `65.0`, `65.5`, `66.0`, `66.5`, `67.0` (top, dark blue). * **Data Grid:** A 6x6 grid of cells, each containing a numerical value and colored according to the legend. ### Detailed Analysis The following table reconstructs the data from the heatmap. Values are read directly from the cells. The color description is based on visual matching to the legend. | percentage p \ width c | 0.05 | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | **99.5** | 65.2 (Light Green-Blue) | 64.6 (Light Yellow-Green) | **66.4 (Dark Blue)** | **66.0 (Medium Blue)** | 64.4 (Light Yellow) | 65.2 (Light Green-Blue) | | **97.0** | 65.4 (Light Green-Blue) | 65.4 (Light Green-Blue) | 65.2 (Light Green-Blue) | 65.6 (Medium Green-Blue) | 65.2 (Light Green-Blue) | 65.2 (Light Green-Blue) | | **95.0** | 64.8 (Light Yellow-Green) | 64.4 (Light Yellow) | 64.4 (Light Yellow) | 65.6 (Medium Green-Blue) | 64.6 (Light Yellow-Green) | 64.2 (Light Yellow) | | **92.5** | 65.0 (Light Green-Blue) | 64.2 (Light Yellow) | 64.8 (Light Yellow-Green) | 64.8 (Light Yellow-Green) | 65.2 (Light Green-Blue) | 65.0 (Light Green-Blue) | | **90.0** | 64.6 (Light Yellow-Green) | 64.6 (Light Yellow-Green) | 64.6 (Light Yellow-Green) | 64.4 (Light Yellow) | 65.6 (Medium Green-Blue) | 65.2 (Light Green-Blue) | | **85.0** | 64.0 (Light Yellow) | 64.4 (Light Yellow) | 64.8 (Light Yellow-Green) | 64.6 (Light Yellow-Green) | **67.0 (Darkest Blue)** | **66.2 (Dark Blue)** | **Trend Verification:** * **Horizontal Trend (Fixed p):** There is no single consistent trend across all rows. For example, at `p=99.5`, the value peaks sharply at `c=0.15` and `c=0.2` before dropping. At `p=85.0`, the value increases dramatically at the highest `c` values (`0.25`, `0.3`). * **Vertical Trend (Fixed c):** Similarly, trends vary by column. At `c=0.25`, the value is relatively stable (~65.2) for higher `p` but jumps to 67.0 at `p=85.0`. At `c=0.15`, the value is highest at the top (`p=99.5`). ### Key Observations 1. **Global Maximum:** The highest value in the grid is **67.0**, located at the intersection of `p=85.0` and `c=0.25` (bottom row, second column from the right). This cell is colored the darkest blue. 2. **Global Minimum:** The lowest value is **64.0**, located at `p=85.0` and `c=0.05` (bottom-left corner). This cell is the lightest yellow. 3. **High-Value Clusters:** * A cluster of high values (66.4, 66.0) appears in the top row (`p=99.5`) for mid-range `c` values (0.15, 0.2). * Another high-value cluster (67.0, 66.2) appears in the bottom row (`p=85.0`) for high `c` values (0.25, 0.3). 4. **Low-Value Region:** The lower-left quadrant of the chart (lower `p` and lower `c`) generally contains the lowest values, ranging from 64.0 to 64.8. 5. **Stability:** The row for `p=97.0` shows remarkably stable values, all between 65.2 and 65.6, indicating the metric is least sensitive to changes in `c` at this percentage threshold. ### Interpretation This heatmap likely illustrates the performance of a system or algorithm where two hyperparameters are being tuned: a percentage threshold (`p`) and the width of a "near-zero range" (`c`). The metric being measured (values ~64-67) could be accuracy, F1-score, or a similar performance indicator. The data suggests a complex, non-linear interaction between the parameters: * **Optimal Performance is Context-Dependent:** There is no single "best" setting. Peak performance (67.0) is achieved with a low percentage threshold (`p=85.0`) and a relatively high near-zero range width (`c=0.25`). However, a nearly as high score (66.4) is achieved with a very high threshold (`p=99.5`) and a moderate width (`c=0.15`). This implies the optimal configuration depends on other constraints or priorities in the system. * **Sensitivity Varies:** The system's performance is highly sensitive to parameter changes in some regions (e.g., the bottom-right corner shows a steep increase) but very stable in others (e.g., the entire `p=97.0` row). * **Potential Trade-off:** The two high-performance clusters (top-center and bottom-right) might represent two different operating regimes or strategies that yield similar results. Choosing between them could involve trade-offs not visible in this chart, such as computational cost or robustness. **Uncertainty Note:** The values are transcribed from the image with high confidence, but minor reading errors (±0.1) are possible due to color perception and cell alignment. The exact meaning of the parameters `p` and `c` and the measured metric is not provided in the image.

## Heatmap: Relationship Between Percentage p and Width of Near-Zero Range c ### Overview The image is a heatmap visualizing the relationship between two variables: "percentage p" (y-axis) and "width of near-zero range c" (x-axis). Each cell contains a numerical value representing a metric (likely a percentage or score) that varies based on the combination of p and c. The color gradient transitions from light yellow (low values) to dark blue (high values), with a legend on the right indicating the scale. --- ### Components/Axes - **X-axis (width of near-zero range c)**: - Labels: 0.05, 0.1, 0.15, 0.2, 0.25, 0.3 - Scale: Linear increments of 0.05 - **Y-axis (percentage p)**: - Labels: 85.0, 90.0, 92.5, 95.0, 97.0, 99.5 - Scale: Linear increments of 2.5 (except 85.0 to 90.0, which is 5.0) - **Legend**: - Position: Right side of the heatmap - Color gradient: Light yellow (64.0) to dark blue (67.0) - Label: Implied to represent the metric values in the cells --- ### Detailed Analysis #### Data Table Structure The heatmap is organized as a 6x6 grid, with rows corresponding to percentage p values and columns to width c values. Each cell contains a numerical value and a color intensity matching the legend. Below is the reconstructed table: | **p (%)** | **c = 0.05** | **c = 0.1** | **c = 0.15** | **c = 0.2** | **c = 0.25** | **c = 0.3** | |-----------|--------------|-------------|--------------|-------------|--------------|-------------| | 99.5 | 65.2 | 64.6 | 66.4 | 66.0 | 64.4 | 65.2 | | 97.0 | 65.4 | 65.4 | 65.2 | 65.6 | 65.2 | 65.2 | | 95.0 | 64.8 | 64.4 | 64.4 | 65.6 | 64.6 | 64.2 | | 92.5 | 65.0 | 64.2 | 64.8 | 64.8 | 65.2 | 65.0 | | 90.0 | 64.6 | 64.6 | 64.6 | 64.4 | 65.6 | 65.2 | | 85.0 | 64.0 | 64.4 | 64.8 | 64.6 | 67.0 | 66.2 | #### Color-Space Verification - **Darkest blue (67.0)**: Located at (85.0%, 0.3) - **Lightest yellow (64.0)**: Located at (99.5%, 0.05) - All other values align with the legend’s gradient (e.g., 65.2 corresponds to a medium-blue shade). --- ### Key Observations 1. **Highest Value**: 67.0 at (85.0%, 0.3) — the lowest p and widest c. 2. **Lowest Value**: 64.0 at (99.5%, 0.05) — the highest p and narrowest c. 3. **Trend**: - Values generally increase as c increases (e.g., 64.0 → 66.2 for p=85.0%). - For fixed c, values fluctuate slightly with p but show no clear monotonic trend. 4. **Anomalies**: - At p=95.0%, the value drops to 64.2 at c=0.3, breaking the upward trend observed in other rows. - At p=90.0%, the value at c=0.2 is 64.4, lower than adjacent cells. --- ### Interpretation The heatmap suggests a **trade-off relationship** between p and c: - **Lower p (85.0%)** and **wider c (0.3)** yield the highest values (67.0), indicating optimal performance under these conditions. - **Higher p (99.5%)** and **narrow c (0.05)** result in the lowest values (64.0), suggesting suboptimal performance. - The anomaly at p=95.0% and c=0.3 (64.2) may indicate a non-linear interaction or an outlier in the dataset. The color gradient reinforces that the metric being measured (e.g., efficiency, accuracy) improves as the width of the near-zero range increases, particularly when the percentage p is lower. This could imply that broader near-zero ranges are more effective in scenarios with lower p values, though further context is needed to confirm causality. --- ### Spatial Grounding - **Legend**: Right-aligned, vertically oriented, with a clear gradient from yellow to blue. - **Axes**: Labeled with precise numerical increments; grid lines divide the heatmap into discrete cells. - **Cell Values**: Centered in each cell, ensuring readability. This structured layout ensures the data is both visually accessible and quantitatively precise.