Data Visualization

Decision framework for translating data into effective visual form. Synthesizes Bertin, Cleveland, Tufte, Cairo, Wilke, and Knaflic — optimized for scientific work with cosmology-specific conventions.

The Intake Protocol

Before plotting, establish two dimensions:

1. Data Structure Analysis

Identify what you're visualizing:

2. Communication Mode

Determine the venue—this switches the entire rule set:

Mode A: Analytical/Paper

• Audience: Expert peers, reviewers
• Optimize for: Precision, black/white printing, convention
• Philosophy: Tufte/Cleveland/Wilke—density is permitted, accuracy is paramount
• Color: Restrained, colorblind-safe, grayscale-compatible
• Default: This mode unless otherwise specified

Mode B: Presentation/Outreach

• Audience: Mixed expertise, attention-competitive
• Optimize for: Impact, engagement, narrative clarity
• Philosophy: Cairo/McCandless/Knaflic—preattentive pop, visual hierarchy
• Color: Bold accent colors, clear entry points
• Use when: Talks, posters, press releases, social media

The Decision Framework

Route from data to visualization form:

Step 1: Analyze Variables (Bertin)

For each variable, classify:

• Quantitative: Continuous numeric (position, intensity, redshift)
• Ordered: Categorical with sequence (low/med/high, redshift bins)
• Categorical: Nominal groups (experiments, instruments, sky regions)

Check for uncertainty: Is there error on mean (discrete bars) or intrinsic spread (continuous band)?

Step 2: Select Encoding (Cleveland)

Match importance to perceptual accuracy:

Rule: If precise comparison is needed, use position. If gestalt impression is needed, use color/area.

Step 3: Select Form (Wilke)

Consult viz-catalog.md for the specific form. Key mappings:

Step 4: Apply Mode-Specific Rules

If Mode A (Paper):

• Enforce strict linear/log scaling
• No bubble charts for precise quantities
• No dual y-axes
• Redundant encoding (shape + color) for colorblind safety
• Direct labeling over legends when <=4 series
• Light grid lines, subordinate to data

If Mode B (Outreach):

• Establish visual hierarchy—most important data most salient
• One clear entry point (where does eye go first?)
• Bolder colors, but maintain accuracy
• Annotations that guide reading
• Title states the takeaway, not the topic

Cosmology-Specific Overrides

These conventions override general principles for domain consistency:

Power Spectra

• Flatten steeply falling spectra: Multiply by x-axis factor to reveal percent-level features
  • Angular: Plot ell^n C_ell (commonly D_ell = ell(ell+1)C_ell/2pi, but factor varies)
  • Matter: Plot k^3 P(k) or Delta^2(k) to flatten
  • Correlation functions: Plot theta xi(theta) or similar
• Log-linear preferred: Log scale on x (multipole/k), linear on y after flattening
  • Reveals small differences hidden by log-log compression
  • Reserve log-log only when dynamic range is the message
• Label x-axis with actual values (10, 100, 1000), not exponents
• Residual panel: Show (data - model)/sigma or data/model below main panel
• Uncertainty: Confidence bands if dense sampling, error bars if sparse

Covariance Matrices

• Diverging colormap required (RdBu, coolwarm)
• White/neutral at zero (or at 1 for correlation matrices)
• Explicit colorbar with position-based lookup for precise values
• Consider: Showing only upper/lower triangle for symmetry

Triangle/Corner Plots

• Standard layout: 1D posteriors on diagonal, 2D contours off-diagonal
• Contour levels: 68%, 95% (1sigma, 2sigma)
• Consistent axis ranges across all panels showing same parameter
• Direct parameter labels on axes, not legend

Sky Maps (Healpix/Mollweide)

• Projection matters: Mollweide for full-sky, orthographic for regions
• Graticule: RA/Dec grid, labeled at edges
• Sequential colormap for intensity, diverging for residuals

Error Representation

• Asymmetric errors: Make asymmetry visually obvious
• Bands vs bars: Use bands for continuous functions, bars for discrete points
• Multiple sigma levels: Gradient opacity (dark = 1sigma, light = 2sigma)

Encoding Principles

Brief rules from perceptual science:

Preattentive Attributes (Cairo)

These "pop out" in <250ms—use for key distinctions:

• Color (hue)
• Size
• Position
• Orientation

If your main finding should be visible at a glance, encode it preattentively.

Working Memory Limits

Humans hold ~4 chunks in working memory:

• Legends with >4 items require constant back-and-forth
• Direct labeling dramatically reduces cognitive load
• Group by meaningful categories to chunk (8 items -> 2 groups of 4)

Redundant Encoding (Wilke)

Never rely on color alone:

• Shape + color for categories
• Position + color for emphasis
• Ensures colorblind safety and bad projector survival

The Refinement Loop

After generating the plot, inspect against:

The Squint Test (Knaflic)

Squint at the figure. What stands out? If it's not your main finding, you have:

• Clutter competing with signal
• Wrong visual hierarchy
• Preattentive attributes on wrong elements

Data-Ink Ratio (Tufte)

For each element, ask: "Does this earn its ink?"

• Remove chart frames if not essential
• Lighten or remove gridlines
• Replace legends with direct labels
• Remove redundant axis lines

The 1+1=3 Principle (Tufte)

Two elements create emergent visual artifacts (the space between). Check:

• Dense grids creating moire
• Grouped bars creating unintended rhythms
• Close parallel lines creating "third" shapes

Colorblind Check

Verify with simulation (viridis is designed for CVD safety). Test: Would the message survive grayscale printing?

Reference Files

Consult as needed:

• viz-catalog.md — Form directory organized by visualization function
• color-palettes.md — Colormaps, categorical palettes, Porch Morning theme
• design-system.md — Typography, decluttering checklist, styling

Library preference: Use seaborn over raw matplotlib when possible. Seaborn provides cleaner defaults and better statistical visualization primitives.

Quick Reference: Common Mistakes