# Technical Data Extraction: Control Effect Analysis (Layer 1) This document provides a comprehensive extraction of data from a technical visualization consisting of eight line charts and one summary heatmap. The data explores the "Control effect (d)" across various "Target axes" and "Affected axes" (LR and Principal Components PC1 through PC512) as a function of the number of examples. --- ## 1. Summary Heatmap: Control effect (d): layer 1 **Location:** Right side of the image. **Description:** A square matrix showing the final control effect value for different Target/Affected axis pairs. **Legend:** A vertical color bar on the right ranging from -1 (Blue) to 0 (White) to 1 (Red). ### Data Table (Heatmap Values) The Y-axis represents the **Target axis**, and the X-axis represents the **Affected axis**. Values in bold boxes indicate the diagonal (Target axis = Affected axis). | Target \ Affected | LR | PC1 | PC2 | PC4 | PC8 | PC32 | PC128 | PC512 | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | **PC512** | 0.13 | -0.09 | 0.20 | -0.12 | 0.06 | -0.15 | 0.10 | **0.10** | | **PC128** | -0.32 | 0.14 | 0.02 | 0.06 | 0.10 | -0.14 | **0.03** | - | | **PC32** | 0.39 | -0.05 | -0.43 | 0.03 | -0.04 | **-0.21** | -0.09 | - | | **PC8** | -0.07 | 0.34 | -0.04 | 0.33 | **-0.00** | -0.11 | -0.17 | - | | **PC4** | -0.27 | 0.05 | 0.77 | **0.03** | 0.20 | 0.05 | 0.01 | - | | **PC2** | -1.18 | 1.51 | **-0.22** | 0.20 | 0.02 | -0.49 | -0.12 | - | | **PC1** | 1.33 | **-0.97** | -0.32 | 0.02 | -0.23 | 0.20 | 0.02 | - | | **LR** | **2.12** | -1.41 | 1.12 | -0.19 | -0.07 | -0.49 | -0.45 | -0.01 | --- ## 2. Line Charts: Temporal Trends by Target Axis Each chart shares the following axes: * **X-axis:** # Examples (Scale: 0 to 250) * **Y-axis:** Control effect (d) * **Legend (Affected axis):** * **LR:** Solid Red line * **PC1:** Yellow dotted line * **PC2:** Light Green solid line * **PC4:** Green dotted line * **PC8:** Teal solid line * **PC32:** Blue dotted line * **PC128:** Dark Blue solid line * **PC512:** Purple dotted line ### Chart 1: Target axis: LR * **Trend:** The LR (Red) line shows a sharp upward slope, stabilizing around d=2.0. PC1 (Yellow) and PC2 (Green) show significant negative and positive deviations respectively, while higher PCs cluster near zero. * **Key Final Values:** LR ≈ 2.1, PC1 ≈ -1.4, PC2 ≈ 1.1. ### Chart 2: Target axis: PC1 * **Trend:** PC1 (Yellow) shows a sharp initial increase, stabilizing above 1.0. The LR (Red) line or other components show a mirror negative trend. * **Key Final Values:** PC1 ≈ 1.3, LR (implied) ≈ -1.0. ### Chart 3: Target axis: PC2 * **Trend:** PC2 (Light Green) slopes upward and stabilizes near 1.5. Most other axes remain near or slightly below zero. * **Key Final Values:** PC2 ≈ 1.5, PC1 ≈ -0.5. ### Chart 4: Target axis: PC4 * **Trend:** PC4 (Green dotted) shows a moderate upward trend, peaking and stabilizing near 0.75. * **Key Final Values:** PC4 ≈ 0.8. ### Chart 5: Target axis: PC8 * **Trend:** High variance initially. PC8 (Teal solid) stabilizes slightly above 0. PC4 (Green dotted) shows a higher positive trend in this specific target context. * **Key Final Values:** PC4 ≈ 0.4, PC8 ≈ 0.3. ### Chart 6: Target axis: PC32 * **Trend:** Most lines cluster around zero. PC1 (Yellow) shows a slight upward trend toward 0.4. * **Key Final Values:** PC1 ≈ 0.4, PC32 ≈ -0.2. ### Chart 7: Target axis: PC128 * **Trend:** Significant noise/variance (shaded areas). Most values converge between -0.2 and 0.2. * **Key Final Values:** PC1 ≈ 0.2, PC128 ≈ 0.0. ### Chart 8: Target axis: PC512 * **Trend:** Highly compressed scale. All lines stay within the -0.2 to 0.2 range. * **Key Final Values:** PC2 ≈ 0.2, PC512 ≈ 0.1. --- ## 3. Component Observations * **Diagonal Dominance:** In the heatmap, the highest absolute values are often found when the Target axis matches the Affected axis (e.g., LR/LR at 2.12), though PC1 and PC2 show strong cross-interference. * **Convergence:** In all line charts, the "Control effect" typically stabilizes after approximately 100 examples. * **Variance:** Shaded regions around lines indicate confidence intervals or variance, which appears larger for higher-order PCs (PC128, PC512).

# Technical Document Extraction: Control Effect Analysis ## Overview The image contains **eight line graphs** and a **heatmap** analyzing control effects across different principal components (PCs). Each graph visualizes the relationship between the number of examples and control effect magnitude, with color-coded lines representing specific PCs. The heatmap quantifies pairwise control effects between target and affected axes. --- ## Line Graphs Analysis ### General Structure - **X-axis**: Number of examples (0–200) - **Y-axis**: Control effect (d) ranging from -1 to 2.0 - **Legend**: Located on the right side of each graph, mapping line styles/colors to PCs (PC1–PC512) and LR (Logistic Regression). ### Graph-by-Graph Breakdown #### 1. Target Axis: LR (Logistic Regression) - **Affected Axes**: PC1–PC512 - **Legend**: - Red solid line: LR - Dotted lines: PC1–PC512 (colors vary) - **Trend**: - LR line slopes upward from 0 to ~2.0. - PC lines show mixed trends (e.g., PC1 increases, PC2 decreases). - **Data Points**: - LR: Starts at 0, peaks at 2.0. - PC1: Starts at 0, peaks at ~1.5. #### 2. Target Axis: PC1 - **Affected Axes**: PC1–PC512 - **Legend**: - Orange solid line: PC1 - Dotted lines: Other PCs - **Trend**: - PC1 line remains flat near 0. - PC2 shows a slight upward trend. - **Data Points**: - PC1: ~0.0 throughout. - PC2: ~0.5 at 200 examples. #### 3. Target Axis: PC2 - **Affected Axes**: PC1–PC512 - **Legend**: - Green solid line: PC2 - Dotted lines: Other PCs - **Trend**: - PC2 line slopes upward to ~1.5. - PC1 shows a downward trend. - **Data Points**: - PC2: ~1.5 at 200 examples. - PC1: ~-0.5 at 200 examples. #### 4. Target Axis: PC4 - **Affected Axes**: PC1–PC512 - **Legend**: - Teal solid line: PC4 - Dotted lines: Other PCs - **Trend**: - PC4 line fluctuates but stabilizes near 0.5. - PC8 shows a downward trend. - **Data Points**: - PC4: ~0.5 at 200 examples. - PC8: ~-0.2 at 200 examples. #### 5. Target Axis: PC8 - **Affected Axes**: PC1–PC512 - **Legend**: - Dark blue solid line: PC8 - Dotted lines: Other PCs - **Trend**: - PC8 line slopes downward to ~-0.5. - PC128 shows minimal change. - **Data Points**: - PC8: ~-0.5 at 200 examples. - PC128: ~0.0 at 200 examples. #### 6. Target Axis: PC32 - **Affected Axes**: PC1–PC512 - **Legend**: - Purple solid line: PC32 - Dotted lines: Other PCs - **Trend**: - PC32 line fluctuates but trends upward to ~0.5. - PC128 shows a slight downward trend. - **Data Points**: - PC32: ~0.5 at 200 examples. - PC128: ~-0.1 at 200 examples. #### 7. Target Axis: PC128 - **Affected Axes**: PC1–PC512 - **Legend**: - Dark purple solid line: PC128 - Dotted lines: Other PCs - **Trend**: - PC128 line remains near 0. - PC512 shows a slight upward trend. - **Data Points**: - PC128: ~0.0 at 200 examples. - PC512: ~0.1 at 200 examples. #### 8. Target Axis: PC512 - **Affected Axes**: PC1–PC512 - **Legend**: - Black solid line: PC512 - Dotted lines: Other PCs - **Trend**: - PC512 line slopes upward to ~0.5. - PC1 shows a downward trend. - **Data Points**: - PC512: ~0.5 at 200 examples. - PC1: ~-0.2 at 200 examples. --- ## Heatmap Analysis ### Structure - **Rows**: Target axes (LR, PC1, PC2, PC4, PC8, PC32, PC128, PC512) - **Columns**: Affected axes (PC1, PC2, PC4, PC8, PC32, PC128, PC512) - **Color Scale**: - Red: Positive control effect (closer to 1) - Blue: Negative control effect (closer to -1) - White: Neutral (near 0) ### Key Values | Target Axis | PC1 | PC2 | PC4 | PC8 | PC32 | PC128 | PC512 | |-------------|-------|-------|-------|-------|-------|-------|-------| | **LR** | 0.13 | -0.09 | 0.20 | -0.12 | 0.06 | -0.15 | 0.10 | | **PC1** | -0.32 | 0.14 | 0.02 | 0.06 | 0.10 | -0.14 | 0.03 | | **PC2** | 0.39 | -0.05 | -0.43 | 0.03 | -0.04 | -0.21 | -0.09 | | **PC4** | -0.07 | 0.34 | -0.04 | 0.33 | -0.00 | -0.11 | -0.17 | | **PC8** | -0.27 | 0.05 | 0.77 | 0.03 | 0.20 | 0.05 | 0.01 | | **PC32** | -1.18 | 1.51 | -0.22 | 0.20 | -0.49 | -0.12 | -0.18 | | **PC128** | 1.33 | -0.97 | -0.32 | 0.02 | -0.23 | 0.20 | 0.02 | | **PC512** | -2.12 | 1.41 | 1.12 | -0.19 | -0.07 | -0.49 | -0.45 | ### Observations - **Strongest Positive Effect**: PC32 → PC2 (1.51) - **Strongest Negative Effect**: LR → PC512 (-2.12) - **Neutral Effects**: Diagonal entries (e.g., PC1 → PC1: 0.13) show minimal impact. --- ## Spatial Grounding & Validation 1. **Legend Placement**: All legends are positioned on the right side of their respective graphs. 2. **Color Consistency**: - PC1 (orange) matches all orange lines across graphs. - PC512 (black) matches black lines in PC512-target graphs. 3. **Trend Verification**: - LR line in the first graph slopes upward, aligning with its data points (0 → 2.0). - PC32 line in its graph trends upward, matching its data points (~0.5 at 200 examples). --- ## Conclusion The analysis reveals significant control effects between specific PCs (e.g., PC32 → PC2) and notable negative effects from LR to PC512. The heatmap provides a quantitative summary of these relationships, with color gradients highlighting magnitude and direction.