Comparison of multidimensional swarm embedding techniques by potential fields

Comparison of multidimensional swarm embedding techniques by potential fields

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Multidimensional embedding is a technique useful for characterizing spectral signature relations in hyperspectral images. However, such images consist of disjoint similar spectral classes that are spatially sensitive, thus presenting challenges to existing graph embedding methods. In this chapter, the multidimensional embedding techniques are interpreted by the potential fields method, where a sum of attraction and repulsion potential functions is minimized to find optimal energy configuration of embedding. Repulsion dominates at short distances, thereby emphasizing local relations. On the other hand, attraction dominates at long distances, stressing global relations. The formulations capture long-rangeand short-range-distancerelated effects often associated with living organisms and help to establish algorithmic properties that mimic mutual behavior for the purpose of dimensionality reduction. Widely used tSNE (stochastic neighbor embedding) and its variations are compared in terms of the potential field methods and their sources of weakness are discussed. As part of the evaluation, the embedding maps are visualized, their trajectories are plotted, and their semisupervised classifications are conducted for image scenes acquired by multiple sensors at various spatial resolutions over different types of objects.

Chapter Contents:

  • Abstract
  • 6.1 Introduction
  • 6.1.1 Background
  • 6.1.2 Review of previous approaches
  • 6.1.3 Review of merits in force field framework
  • 6.1.4 Contributions
  • 6.2 Swarm intelligence and potential field methods
  • 6.2.1 Swarm intelligence
  • 6.2.2 Review of potential field methods
  • 6.2.3 Swarm intelligence and potential field methods
  • 6.3 Review of formulation of MAFE
  • 6.3.1 Graph embedding framework
  • 6.3.2 Force field functions for embedding
  • 6.4 Examples of swarm embedding by potential fields
  • 6.4.1 Stochastic neighbor embedding
  • 6.4.2 t-Stochastic neighbor embedding
  • 6.4.3 Spherical stochastic neighbor embedding
  • 6.4.4 Large margin nearest neighbor embedding
  • 6.5 Review of MAFE model
  • 6.5.1 MAFE model by embedding artificial potentials
  • 6.5.2 Bilateral kernel for spectral signature similarities
  • 6.6 Numerical analysis
  • 6.6.1 Data sets
  • 6.6.2 Method of experiments
  • 6.6.3 Trajectories in embedding space
  • 6.6.4 Visualization and embedding results
  • 6.6.5 Classification results
  • 6.7 Discussion
  • References

Inspec keywords: image sensors; hyperspectral imaging; embedded systems; stochastic processes; geophysical image processing; sensor fusion; image classification; graph theory; minimisation; image resolution

Other keywords: dimensionality reduction; semisupervised classifications; spectral signature relations; potential field methods; tSNE; multiple sensors; optimal energy configuration; multidimensional swarm embedding techniques; repulsion potential functions minimization; stochastic neighbor embedding; spatial resolutions; hyperspectral images; living organisms; graph embedding methods; embedding maps visualization; short-range-distance related effects; image scenes; long-range-distance related effects

Subjects: Image sensors; Other topics in statistics; Optical, image and video signal processing; Image sensors; Optimisation techniques; Probability theory, stochastic processes, and statistics; Combinatorial mathematics; Sensor fusion; Geophysics computing; Algebra, set theory, and graph theory; Optimisation techniques; Combinatorial mathematics; Instrumentation and techniques for geophysical, hydrospheric and lower atmosphere research; Computer vision and image processing techniques; Geophysical techniques and equipment; Other topics in statistics

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