English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Following the seminal work of Nesterov, accelerated optimization methods havebeen used to powerfully boost the performance of first-order, gradient-basedparameter estimation in scenarios where second-order optimization strategiesare either inapplicable or impractical. Not only does accelerated gradientdescent converge considerably faster than traditional gradient descent, but italso performs a more robust local search of the parameter space by initiallyovershooting and then oscillating back as it settles into a finalconfiguration, thereby selecting only local minimizers with a basis ofattraction large enough to contain the initial overshoot. This behavior hasmade accelerated and stochastic gradient search methods particularly popularwithin the machine learning community. In their recent PNAS 2016 paper,Wibisono, Wilson, and Jordan demonstrate how a broad class of acceleratedschemes can be cast in a variational framework formulated around the Bregmandivergence, leading to continuum limit ODE's. We show how their formulation maybe further extended to infinite dimension manifolds (starting here with thegeometric space of curves and surfaces) by substituting the Bregman divergencewith inner products on the tangent space and explicitly introducing adistributed mass model which evolves in conjunction with the object of interestduring the optimization process. The co-evolving mass model, which isintroduced purely for the sake of endowing the optimization with helpfuldynamics, also links the resulting class of accelerated PDE based optimizationschemes to fluid dynamical formulations of optimal mass transport.

Accelerated Optimization in the PDE Framework: Formulations for the Active Contour Case