In maszdev/dist2location: Find Location For Points Described By Distance Matrix

General idea

As an input for algorithm distance matrix is provided (see vignette("dist2location")). As output point locations are expected - data.frame (n rows for n points and m columns for m-dimensions)).

After every iteration "better" point position is found and current error is calculated. Algorithm stops when error is smaller than threshold or number of iterations exceeds limit.

How error is calculated?

Distance matrix for all current point position is calculated (let's call it "current DM"). It's compared to distance matrix which is used as an input. For every element (i,j) in both distance matrices (so for element which is related with distance between points with indexes i and j) error is calculated. One can create error matrix for input distance matrix (input_dm) and current distance matrix (current_dm).

error_matrix[i,j] = |input_dm[i,j] - current_dm[i,j]|/input_dm[i,j] # for i<>j
error_matrix[i,j] = 0 # for i = j

Error is needed to calculate if new distance matrix (for new point positions) is better than previous. One can calculate it by taking average (or max) from elements of error_matrix which are not on diagonal (it corresponds to error for distances between points and themselves which is always 0).

Ideas above are base for all algorithms.

Algorithm 1

Set initial step and initial point positions
Prepare distance matrix for initial position
set error_threshold and iteration_limit( to keep condition to stop calculations)

i  = 1
For iteration i:
  For every point:
    For every dimension:
      Move point in one direction through the dimension and calculate new distance matrix. 
      If error is smaller than for previous distance matrix keep this new position and new 
      related distance matrix. If error is not minimized, try to move in second direction 
      and check new distance matrix again.

  if new error is smaller then threshold or number of iterations exceeds limit:
    save current points position and STOP calculations

maszdev/dist2location documentation built on June 11, 2025, 11:55 a.m.