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Software FindGraph Procrustes analysis

Least-squares orthogonal mapping

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A least-squares orthogonal generalized Procrustes analysis
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FindGraph performs a least-squares orthogonal generalized Procrustes analysis (least-squares orthogonal mapping). Procrustes analysis is a method of comparing two sets of data. The method is based on matching corresponding points (landmarks) from each of the two data sets. Procrustes analysis

Procrustes analysis is a rigid shape analysis that uses isomorphic scaling, translation, and rotation to find the “best” fit between two or more landmarked shapes. See wikipedia for generalized orthogonal Procrustes analysis, and 'Procrustes Analysis' by Amy Ross, www.cse.sc.edu.

Landmarks are points that accurately describe a shape. Corresponding landmarks would be the same landmark on two different shapes. landmarks

To define a reference cluster of landmarks with FindGraph we select the data series and define N marks. There are different ways to define an experimental cluster of landmarks:
  select landmarks select the points by hand;
  take N landmarks take first N points in series;
  find bestlandmarks find best pattern of N points in series.

FindGraph uses scaling, translation, rotation, and additionally stretching/compressing and shearing transformations.
nonlinear mapping It applies nonlinear mapping algorithm to find best fit, i.e. to find a reference cluster of landmarks, so that the distance of each reference landmark to it's corresponding experimental landmark is minimised.

Data points can be given greater or less influence over the Procrustes analysis by assigning a weight to each point.

Read more about:

Digitizing Digitizing
Graphing Graphing
Curve fitting Curve fitting
Best-fit Best-fit equation
Closed curves Closed curves
Library Library
Analysis Analysis
Tools Tools
Filters Filters
Convolution Convolution
Extract of periodic signals Periodic signals
Multi-peak fitting Multi-peak fitting
SSA forecasting SSA forecasting




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