Spatial partition-wise/region-wise/segmented/piecewise regression

Description

• This program automatically detects the change-points (boundaries) of a spatially varying coefficient linear model, i.e., the coefficients of a linear model varies among different spatial partitions/regions/segmentations.
• The algorithm used a greedy merging method to iteratively searching for the best pair of neighboring regions to merge until meeting stopping criteria.
• More details can refer to post@jay15summer.
• Note: the algorithm borrows ideas from a paper 'Fast Algorithms for Segmented Regression' and a GitHub repository DataDog/piecewise.

Usage

• Main function is: [partition_all, partiaion_slt] = spatial_partition_reg(S, X, y, h, v, T).
• The inputs of the algorithm are:
  • S: an N-by-2 matrix representing N spatial locations/coordinates;
  • X: an N-by-m matrix of m-dimension independent variables at locations S;
  • Y: an N-by-1 matrix of dependent variable at locations S;
  • h: an integer specifying the initial number of grids at horizontal direction (for initial grid-wise segmentation);
  • v: an integer specifying the initial number of grids at vertical direction (for initial grid-wise segmentation, the total number of rectangle shape of grid-wise segmentations is h*v);
  • T: a scalar specifying the threshold for stopping the merging. If merging a pair of neighboring regions results in the increase-percentage of the fitting error exceeding T, the algorithm will stop, i.e., optimal partitioning is found. Usually, 0<T<1, e.g., T = 0.05.
• The outputs of the algorithm are:
  • partition_all: a cell recording the segmentations of every iterations (partition_all.segments) and their fitting errors (partition_all.metric);
  • partition_slt: a map representing the selected partitions/segmentations (this program used 'map' to represent partitioning). The keys of the map can be obtained via cell2mat(keys(partition_slt)). The data [S X y] of every partition can be obtained via partition_slt(keys).data. The neighbor of the selected segmentation is partition_slt(keys).neighbor;
  • two plots: 1. percentage-increase of SSE (metric, sum of squared errors); 2. selected final partitioning.
• 'example1.m' gives a simulated example implementing the algorithm.