Manifold constraint transfer for visual structure-driven optimization

Highlights：

• We leverage the manifold structure of visual data in order to improve performance in general optimization problems subject to linear constraints.

• As the main theoretical result, we show that manifold constraints can be transferred from the data to the optimized variables if these are linearly correlated.

• We also show that the resulting optimization problem can be solved with an efficient alternating direction method of multipliers that can consistently integrate the manifold constraints during the optimization process.

• We obtain a simple approach, which instead of directly optimizing on the manifold, and can iteratively recast the problem as the projection over the manifold via an embedding method.

摘要

•We leverage the manifold structure of visual data in order to improve performance in general optimization problems subject to linear constraints.•As the main theoretical result, we show that manifold constraints can be transferred from the data to the optimized variables if these are linearly correlated.•We also show that the resulting optimization problem can be solved with an efficient alternating direction method of multipliers that can consistently integrate the manifold constraints during the optimization process.•We obtain a simple approach, which instead of directly optimizing on the manifold, and can iteratively recast the problem as the projection over the manifold via an embedding method.

论文关键词：Manifold,Transfer learning,Alternating direction method of multipliers,Object tracking,Augmented lagrange multiplier,Image tracking,Image recognition,Object categorization

论文评审过程：Received 23 February 2017, Revised 20 October 2017, Accepted 5 November 2017, Available online 7 November 2017, Version of Record 27 December 2017.