  In order to meet the requirements of practical applications, a model of
deforming manifold in the embedded space is proposed. The deforming vector and
deforming field are presented to precisely describe the deforming process,
which have clear physical meanings. The proposed model is a modification of the
general differential dynamic model, with constraints of spatial and temporal
continuity on the deforming field. The deformation integral and derivative are
presented as compact expressions of manifold deforming process. Moreover, a
specific autonomous deforming field with flattening effect is defined, which
provides a novel geometric viewpoint on data dimension reduction. The
effectiveness of this autonomous deforming field is proved by numerical
computation simulations, which indicate the promising potential of the proposed
model in practical dimension reduction tasks.
