Projection-class {RPointCloud}

Projection Objects For Visualizing 3D Topological Data Analysis Results in 2D

Description

The Projection class is a tool for understanding and visualizing voids (topological spheres) and the features that can be used to define and interpret them. The core idea is to first project all data points in dimension (at least) 3 radially onto the surface of the sphere. We then use spherical coordinates on the sphere (the latitude, psi from 0 to 180 degrees and the longitude, phi, from -180 to 180 degrees) to locate the points. The plot method shows these points in two dimensions, colored based on the expression of the chosen Feature. The image method uses a loess fit to smooth the observed data points across the entire surface of the sphere and displays the resulting image. Using latitude and longitude in this way is similar to a Mercator projection of the surface of the Earth onto a two-dimensional plot.

It is worth noting that, for purposes of computing the smoothed version, we actually take two "trips" around the "equator" to fit the model, but only display the middle section of that fit. The point of this approach is to avoid edge effects in smoothing the data.

Usage

Projection(cycle, view, feature, span = 0.3, resn = 25)
## S4 method for signature 'Projection,missing'
plot(x, y, pch = 16, ...)
## S4 method for signature 'Projection'
image(x, ...)

Arguments

cycle

A Cycle object representing a void, or 2-cycle.

view

A (layout) matrix with coordinates showing where to plot each point in the feature. Must be at least three-dimensional.

feature

A Feature object, representing the expression levels of one of the features in the underlying data set.

span

Parameter used for a loess fit.

resn

The number of steps used to create the vectors psi and half-phi.

x

A Projection object.

y

ignored.

pch

A number; the graphical plotting character parameter pch.

...

The usual set of additional graphical parameters.

Value

The Projection function constructs and returns an object of the Projection class

The plot and image methods return (invisibly) the Projection object that was their first argument.

Slots

phi:

A numeric vector

psi:

A numeric vector

displayphi:

A numeric vector

displaypsi:

A numeric vector

value:

A matrix.

feature:

A Feature object.

Methods

plot(x, y, lwd = 2, ...):

Produce a 2-dimensional scatter plot of a Projection object.

image(x, ...)

Produce a 2D heatmap image of a Projection object.

Author(s)

Kevin R. Coombes <[e-mail]>

Examples

data(CLL)
cyc <- Cycle(ripdiag, 2, NULL, "black")
V <- cmdscale(daisydist, 3)
feat <- Feature(clinical[,"stat13"], "Deletion 13q",
               c("green", "magenta"), c("Abnormal", "Normal"))
ob <- Projection(cyc, V, feat, span = 0.2)
plot(ob)
image(ob, col = colorRampPalette(c("green", "gray", "magenta"))(64))