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Transporte óptimo supervisado Gromov-Wasserstein con restricciones de preservación métrica

Zixuan Cang1, Yaqi Wu2, Yanxiang Zhao2

  • 1Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695 USA.

SIAM journal on mathematics of data science
|September 2, 2025
PubMed
Resumen

Introducimos el método supervisado Gromov-Wasserstein (sGW), un nuevo método de transporte óptimo que hace cumplir las restricciones de preservación de la distancia. Este enfoque mejora la alineación de datos, particularmente para conjuntos de datos parcialmente superpuestos, como los datos de secuenciación de ARN de una sola célula.

Palabras clave:
28A33 Se incluyen los siguientes:49Q22 y65K10 Se refiere a:cobertura mínima de los vérticesDescenso espejo-COptimización no convexabajo la supervisión de GromovWassersteinsolucionador de transporte óptimo bajo supervisión

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Área de la Ciencia:

  • Teoría del transporte óptimo
  • Geometría computacional
  • Ciencia de los datos

Sus antecedentes:

  • Gromov-Wasserstein (GW) es una herramienta poderosa para comparar espacios métricos.
  • Los métodos GW existentes pueden no preservar adecuadamente las distancias en pares bajo ciertas restricciones.
  • Alinear conjuntos de datos, especialmente datos de secuenciación de ARN de una sola célula, a menudo requiere una sólida preservación de la distancia.

Objetivo del estudio:

  • Introducir el transporte óptimo bajo supervisión Gromov-Wasserstein (sGW).
  • Incorporar entradas de infinito en el tensor de costos para hacer cumplir las restricciones de preservación de distancia.
  • Desarrollar y validar un solucionador numérico para el problema sGW.

Principales métodos:

  • Extendido Gromov-Wasserstein mediante la incorporación de entradas de infinito potencial en el tensor de costos.
  • Las restricciones de orden superior se transforman en restricciones de matriz de acoplamiento a través de la cobertura mínima de vértices.
  • Se empleó la iteración de descenso espejo-C junto con un solucionador de transporte óptimo supervisado.

Principales resultados:

  • Demostró la eficacia de la SGM a través de varios experimentos numéricos.
  • Validación del marco sobre conjuntos de datos sintéticos y datos de secuenciación de ARN de una sola célula.
  • Mostró la capacidad de sGW para controlar la preservación de la distancia y estimar automáticamente la superposición de conjuntos de datos.

Conclusiones:

  • El sistema supervisado Gromov-Wasserstein (sGW) proporciona un mayor control sobre la preservación de la distancia en el transporte óptimo.
  • sGW mejora la estabilidad y la flexibilidad en aplicaciones basadas en datos, incluida la alineación de datos de una sola celda.
  • El método facilita la estimación automática de las porciones superpuestas en los conjuntos de datos.