Abstract

**Package**: PathwaySpace 0.99.4

- Produces landscape images with geodesic paths.
- Applies a convolutional algorithm to project signals onto a 2D space.
- Projects signals using decay functions to model signal attenuation.
- Uses k-nearest neighbors to define contributing vertices for signal projection.

For a given *igraph* object containing vertices, edges, and a
signal associated with the vertices, *PathwaySpace* performs a
convolution operation, which involves a weighted combination of
neighboring node signals based on the graph structure. **Figure
1** illustrates the convolution operation problem. Each vertexâ€™s
signal is placed at a specific position in the 2D space. The
`x`

and `y`

coordinates of this space correspond
either to vertex-signal positions (*e.g.* red, green, and blue
lollipops in **Fig.1A**) or null-signal positions for which
no signal information is available (question marks in
**Fig.1A**). Our model considers the vertex-signal
positions as source points (or transmitters) and the null-signal
positions as end points (or receivers). The signal values from
vertex-signal positions are then projected to the null-signal positions
according to a decay function, which will control how the signal values
attenuate as they propagate across the 2D space. Available decay
functions include linear, exponential, and Weibull functions
(**Fig.1B**). For a given null-signal position, a k-nearest
neighbors (kNN) algorithm is used to define the contributing vertices
for signal convolution. The convolution operation combines the signals
from these contributing vertices, considering their distances and signal
strengths, and applies the decay function to model the attenuation of
the signal. Users can adjust both the decay functionâ€™s parameters and
the value of k in the kNN algorithm. These parameters control how the
signal decays, allowing users to explore different scenarios and observe
how varying parameters influence the landscape image. The resulting
image forms geodesic paths in which the signal has been projected from
vertex- to null-signal positions, using a density metric to measure the
signal intensity along these paths.