Research On Fast Algorithm For Subspace Segmentation In The Big Data Era

In recent years,big data is more and more in people's field of vision.The analysis,processing and representation of high-dimensional data are not only an important research content in the domain of data science,but also a key point for solving many problems.For a long time,the analysis of the intrinsic geometric structure of data has attracted the general attention.As a research hotspot in recent years,subspace segmentation is one of the fundamentals in computer vision and machine learning.It has a wide range of applications in the real-world problems.Although spectral clustering-based methods received more attention in the field of subspace segmentation,the subspace number in the past experiments was usually less than 10.Dense block and sparse representation and infinity norm minimization are two methods proposed in recent years for large subspace number subspace segmentation.Both methods can reduce the difference of affinity matrix,but there are still some shortcomings and limitations.For example,the dense block and sparse representation method minimized the combination of 1,1-norm and 2-norm,and induced equal density blocks by sparseness and dense block properties to achieve the low difference of the affinity matrix,but the computation speed was not fast enough for large subspace number subspace segmentation.The infinite norm minimization method introduced an infinite norm to control the difference of the diagonal blocks,thereby reducing the difference of the representation coefficient matrix,so it could effectively deal with large subspace number subspace segmentation.However,there was no theoretical guarantee for the independent subspaces,and there was room for increasing the computation speed.In this paper,a method named fast convex infinity norm minimization was proposed.By minimizing the combination of infinite norm and 1,1-norm,this method can not only reduce the difference of the representation matrix,but also provide the theoretical guarantee for the independent subspaces and enhance the computation speed,which has been testified by a large number of experiments.