Assignment flows for data labeling on graphs: convergence and stability
نویسندگان
چکیده
The assignment flow recently introduced in the J. Math. Imaging and Vision 58/2 (2017), constitutes a high-dimensional dynamical system that evolves on an elementary statistical manifold performs contextual labeling (classification) of data given any metric space. Vertices graph index points define neighborhoods. These neighborhoods together with nonnegative weight parameters regularization evolution label assignments to points, through geometric averaging induced by affine e-connection information geometry. Regarding evolutionary game dynamics, may be characterized as large replicator equations are coupled averaging. This paper establishes conditions guarantee convergence continuous-time integral (labelings), up negligible subset situations will not encountered when working real practice. Furthermore, we classify attractors quantify corresponding basins attraction. provides guarantees for which extended discrete-time results from applying Runge-Kutta-Munthe-Kaas scheme numerical integration flow. Several counter-examples illustrate violating entail unfavorable behavior regarding classification.
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ژورنال
عنوان ژورنال: Information geometry
سال: 2021
ISSN: ['2511-2481', '2511-249X']
DOI: https://doi.org/10.1007/s41884-021-00060-8