data-visualization

# 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: | Data Type | Description | Likely Forms | |-----------|-------------|--------------| | **Amounts** | Values across categories | Bar, dot plot, heatmap | | **Distributions** | Spread/shape of values | Histogram, KDE, violin, ridgeline | | **X-Y Relationships** | Continuous variables | Scatter, line, confidence bands | | **Uncertainty** | Error on measurements | Error bars, bands, gradient ribbons | | **Proportions** | Parts of whole | Stacked bar, pie (rarely) | | **Spatial/Maps** | Geographic or sky data | Mollweide, healpix, choropleth | | **Correlations** | Variable relationships | Covariance matrix, triangle plot | ### 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: | Rank | Encoding | Use For | |------|----------|---------| | 1 | Position on common scale | Primary comparisons, precise values | | 2 | Position on non-aligned scales | Secondary comparisons | | 3 | Length | Bar charts (amounts only) | | 4 | Angle/Slope | Avoid for precise reading | | 5 | Area | Gestalt impressions, bubble charts | | 6 | Color saturation | Tertiary encoding, density | **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](references/viz-catalog.md) for the specific form. Key mappings: | You Have | Consider | |----------|----------| | Spectrum (continuous x, continuous y, uncertainty) | Line + confidence band, residual subplot | | Correlation/covariance matrix | Heatmap, diverging colormap, white at zero | | Parameter posteriors | Triangle plot, ridgeline, violin | | Comparison across groups | Small multiples > overlay when groups > 4 | | Time series | Line, banking to 45 degrees | | Amounts across categories | Dot plot (Cleveland) > bar chart | ### 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](references/viz-catalog.md) — Form directory organized by visualization function - [color-palettes.md](references/color-palettes.md) — Colormaps, categorical palettes, Porch Morning theme - [design-system.md](references/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 | Mistake | Fix | |---------|-----| | Jet/rainbow colormap | Use `forestdawn` (diverging) or `mako`/`rocket` (sequential) | | >5 colors in legend | Small multiples or direct labeling | | Dual y-axes | Two separate plots or faceting | | 3D effects | Never. Use 2D with color/facets | | Pie charts for comparison | Dot plot or bar chart | | Bar chart not starting at zero | Start at zero (length encoding) or use dot plot | | Truncated axis exaggerating effect | Show full range or use log scale | | Heavy matplotlib defaults | Apply decluttering checklist |