Data Visualization

Warm-Up Activity

1. What is the visualization trying to show?
2. What are its methods?
3. What are the strengths / weaknesses?

http://old.vijayp.ca/blog/2012/06/colours-in-movie-posters-since-1914/

Today's Topics

• Transformations
• Colors
• Color mapping
• Data Characteristics
• Choosing Visualizations

Transformations

Affine transformations satisfy:

$ \vec{y} = A\vec{x} + \vec{b} $

Transformations

Affine transformations satisfy:

$ \vec{y} = A\vec{x} + \vec{b} $

We can use these to accomplish:

• Shifts

Transformations

Affine transformations satisfy:

$ \vec{y} = A\vec{x} + \vec{b} $

We can use these to accomplish:

• Shifts
• Rotations

Transformations

Affine transformations satisfy:

$ \vec{y} = A\vec{x} + \vec{b} $

We can use these to accomplish:

• Shifts
• Rotations
• Scaling

Choosing a Visualization

When we are examining data, what can we look for?

• Does this data describe a geometric object?
• Are the data points connected to each other?
• Can we describe data points with a fixed set of categories?
• Is there a quantity associated with the data?
• Are the datapoints continuous along one or more dimensions?

Categories and Continuity

Today we'll talk about representing things based on categories and based on continuities.

How Do Colors Work?

Rods (low-light) and cones (color) mediate vision. Humans have about 20 times as many rods (120 million) as cones (6 million).

https://upload.wikimedia.org/wikipedia/commons/e/e8/1414_Rods_and_Cones.jpg By OpenStax College CC BY 3.0, via Wikimedia Commons

Let's Try It

http://enchroma.com/test/instructions/

Color Matching Function

Responsivity Function

"Naming" Colors

• RGB triplets, often expressed in hexadecimel ("#00FFAA", etc)
• Color spaces
  • HSV (Hue, saturation, value)
  • CIELAB
  • sRGB, Adobe sRGB
• List of colors by name
  • Web
  • matplotlib

Color Palettes

• Colorbrewer Categories
  • Sequential
  • Diverging
  • Qualitative
• Resources:
  • colorbrewer.org
  • palettable (package)

Sequential Colormaps

Diverging Colormaps

Qualitative Colormaps

(See? Works better as discrete!)

It's full of colors

https://commons.wikimedia.org/wiki/File:16777216colors.png

HSV Wheel

https://commons.wikimedia.org/wiki/File:HSV_color_solid_cylinder.png

By HSV_color_solid_cylinder.png: SharkD derivative work: SharkD Talk [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons

Palette Mapping

Assign each value to a specific color or element.

Color Mapping

$f(v) \rightarrow (R, G, B)$

We can also re-map:

$f(v') \rightarrow (R, G, B)$

$v' = f(v)$

For instance, with logs or squares.

Color Mapping: Linear Mapping

We map from a range of values to (0, 1):

$ v' = (v - v_0)/(v_1 - v_0) $

Colormaps: Loading Data

Today we will explore images and colors, and how our choice of colormaps affects our perception of them.

You will need to load data into your notebook, which you can do using these commands:

import numpy as np
import h5py

fn1 = "/home/shared/sp18-is590dv/data/michigan_lld/michigan_lld.flt"
michigan = np.fromfile(fn1, dtype='f4').reshape((5365, 4201))

fn2 = "/home/shared/sp18-is590dv/data/single_dicom.h5"
with h5py.File(fn2) as f:
    scan = f["/scan"][:]

Colormaps: Prep Work

We will now utilize the plt.imshow command to show these images, and discuss how to modify the transformation of the data beforehand.

Colormaps

With the Michigan data and the scan data, evaluate:

• How to choose a colormap
• What are some good "bounds" for that colormap
• How do we set our transform?