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Scatterplot Matrix

The Scatterplot Matrix page displays pairwise scatter plots of variables and objectives, making it easy to identify correlations and relationships in your optimization data.

Overview

A scatterplot matrix (SPLOM) shows: - All pairwise combinations of selected variables - Scatter plots in a grid layout - Correlations and relationships at a glance - Separate matrices for variables and objectives

Features

Result Selection

Select Result: Choose which optimization result to visualize - Currently supports single result selection - Both matrices update when you change the selection

Variable Selection

Select Variables: Choose which design variables to include - Default: First 3 variables are selected - Recommendation: Select 2-6 variables for best readability - Purpose: Understand relationships between input parameters

Objective Selection

Select Objectives: Choose which objectives to include - Default: First 3 objectives are selected - Recommendation: Select 2-6 objectives for clarity - Purpose: Explore trade-offs between optimization goals

Understanding the Plots

Matrix Layout

Each matrix is organized as a grid: - Rows: Represent one variable/objective - Columns: Represent another variable/objective - Cell: Scatter plot of row variable vs column variable

Reading a Cell

  • X-axis: Column variable
  • Y-axis: Row variable
  • Points: Individual solutions
  • Color: Result name (when comparing multiple results)

Diagonal

The diagonal cells (where row = column) are hidden since they would show a variable plotted against itself.

Interpretation

Correlation Patterns

Positive Correlation: - Points form an upward-sloping line - As one variable increases, the other increases - Example: Larger size → higher cost

Negative Correlation: - Points form a downward-sloping line - As one variable increases, the other decreases - Example: Higher efficiency → lower emissions

No Correlation: - Points are scattered randomly - Variables are independent - No clear relationship

Non-Linear Relationships: - Points form curves or clusters - Complex dependencies - May indicate constraints or physical limits

Pareto Front in Objectives

For multi-objective optimization: - Look for the "edge" of the point cloud - This represents the Pareto front - Shows trade-offs between objectives

Usage Workflows

Workflow 1: Variable Relationships

  1. Select design variables of interest
  2. Examine the variables matrix
  3. Identify correlated parameters
  4. Look for constraints or boundaries
  5. Understand design space structure

Workflow 2: Objective Trade-offs

  1. Select all objectives
  2. Examine the objectives matrix
  3. Identify conflicting objectives (negative correlation)
  4. Find synergistic objectives (positive correlation)
  5. Understand multi-objective landscape
  1. Select key variables and objectives
  2. Look at cross-plots (variables vs objectives)
  3. Identify which variables most affect each objective
  4. Find sensitive parameters
  5. Guide design decisions

Workflow 4: Constraint Identification

  1. Include constraint values as "observables"
  2. Plot constraints against variables
  3. Identify constraint boundaries
  4. Understand feasible region shape

Best Practices

Selection Strategy

Start Small: - Begin with 2-3 variables/objectives - Add more as needed - Too many creates visual clutter

Choose Wisely: - Select most important or interesting variables - Include conflicting objectives - Add variables you suspect are related

Balance: - 3-5 variables: Ideal for detailed analysis - 6-8 variables: Still readable but dense - >8 variables: Consider splitting into multiple views

Analysis Approach

Systematic Scan: 1. Scan each row left to right 2. Look for patterns in each column 3. Note strong correlations 4. Identify outliers

Targeted Investigation: 1. Focus on specific variable pairs 2. Zoom in on interesting regions 3. Compare with domain knowledge 4. Validate hypotheses

Color Usage

When comparing multiple results: - Different colors distinguish results - Look for separation or overlap - Identify result-specific patterns

Common Patterns

Design Variables

Clustered Points: - Limited exploration of design space - Optimizer converged to specific region - May indicate local optimum

Uniform Distribution: - Good design space coverage - Effective exploration - Diverse solutions

Linear Relationships: - Variables are coupled - May indicate redundancy - Consider reducing dimensionality

Objectives

Pareto Front: - Points along an edge or curve - Clear trade-off boundary - Well-defined optimization problem

Dominated Region: - Points away from the front - Suboptimal solutions - May indicate infeasible solutions

Knee Points: - Sharp bends in the front - Best compromise solutions - High value for decision making

Tips and Tricks

Visualization

Zoom and Pan: - Use Plotly's built-in zoom tools - Focus on interesting regions - Reset view with double-click

Hover Information: - Hover over points for exact values - Identify specific solutions - Note solution indices

Export: - Download plots for reports - Save as PNG or SVG - Include in presentations

Analysis

Compare Matrices: - Look for similar patterns in both matrices - Identify variable-objective relationships - Understand system behavior

Outlier Investigation: - Identify points far from clusters - Check if they're feasible - Investigate why they're different

Symmetry: - Matrix is symmetric (upper-right mirrors lower-left) - Only need to examine one triangle - Diagonal is omitted

Advanced Usage

Combining with Sets

  1. Create sets in Sets Manager (e.g., Pareto, feasible)
  2. View different sets separately
  3. Compare patterns across sets
  4. Identify set-specific characteristics

Multi-Result Comparison

  1. Load multiple results
  2. Select all for comparison
  3. Look for differences in patterns
  4. Validate optimization consistency

Sensitivity Analysis

  1. Plot variables against objectives
  2. Identify steep slopes (high sensitivity)
  3. Find flat regions (low sensitivity)
  4. Prioritize important variables

Troubleshooting

Too Many Points

  • Use sets to filter solutions
  • Select fewer variables/objectives
  • Focus on Pareto front or feasible solutions

Can't See Patterns

  • Adjust number of selected variables
  • Try different variable combinations
  • Check axis scales

Plots Not Updating

  • Ensure a result is selected
  • Check that variables/objectives are selected
  • Refresh the page if needed
  • Path: /scatterplot-matrix
  • Category: Visualization
  • Icon: Scatter plot icon
  • Requires Data: Yes