[HP 42S] [DM42] Multidimensional Scaling (MDS) - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: General Software Library (/forum-13.html) +--- Thread: [HP 42S] [DM42] Multidimensional Scaling (MDS) (/thread-20137.html) |
[HP 42S] [DM42] Multidimensional Scaling (MDS) - rawi - 07-02-2023 02:41 PM Multidimensional Scaling is a method that places elements for which distances are given in a space of lower dimensions, normally in two dimensions (as is done by this program). It can be used to place products in a map for which distances in image dimensions are given. Method: The method used is described in German Wikipedia (unfortunately not in English Wikipedia) here: https://de.wikipedia.org/wiki/Multidimensionale_Skalierung Instruction: Save the matrix of distances in matrix M1 (it has to be symmetric with zeroes in the diagonal). You can put a seed for the random number generator (used to compute eigenvectors). XEQ ”MDS” Result: X-register (also Reg 03): R² of distances. Matrix of coordinates of data points in 2-dimensional space: M2 Matrix of reproduced distances: M4 Example (from Backhaus et.al.: Multivariate Analysen, 2016, p. 613): Distances for six margarine brands: 0 1 7 6 11 13 1 0 8 5 10 12 7 8 0 9 15 14 6 5 9 0 4 3 11 10 15 4 0 2 13 12 14 3 2 0 Save matrix in M1. Pi 3 – seed. XEQ MDS X-register: 0,9896 (distances in 2-dimensional space can explain the variance of distances between brands by 98.96%). RCL “M2” -> Coordinates of brands in 2-dimensional space: 4.7924 -2.6139 3.5854 -2.9794 7.0880 4.3450 -1.6941 0.4239 -6.6191 -1.8237 -7.1527 2.6428 Use of registers (n=number of elements): M1 (n x n), M2 (n x 2), M4 (n x n), M5 (n x 1), M6 (n x 1), Reg 00-03 Program: Code: 00 { 414-Byte Prgm } |