Non-negative Local Coordinate Factorization And Its Applications

Non-negative matrix factorization(Non-negative Matrix Factorization,NMF)is a popular matrix decomposition technique and has widely applied in data minin.The inherent nonnegative constraints lead to parts-based representation.However,NMF does not always achieve this purpose.Non-negative local coordinate factorization(Non-negative Local Coordinate Factorization,NLCF)integrates the local coordinate constraint into NMF to ensure the resultant representation to be sparse;meanwhile,it makes the learned basis vectors close to data points.Benefitting from sparseness of data representation,NLCF has been used for feature extraction in various fields such as image clustering.Thus,NLCF can be exploited to expand the NMF-based model for various tasks.NLCF has attracted extension attention from machine learning community.However,it suffers from the following deficiencies: 1)it is unsupervised and completely neglects labels of the dataset,and often induces unsatisfactory clustering results,2)NLCF is designed for static data and unsuited to tackle stream data or large-scale dataset,and 3)NLCF is sensitive to noisy data or the outliers,and does not work well in clustering.Besides,it does not still handle the nonlinear data.To address the issues above,this paper focuses on the theoretical studies about NLCF and its applications.First of all,we propose a semi-supervised NLCF(Semi-supervised NLCF,SNLCF)which propagates labels of the labeled samples to the unlabeled by imposing the coefficients of the labeled dataset to be as close to the class indicator as possible.Moreover,to realize tracking task based on NLCF,we develop online NLCF(Online NLCF,ONLCF)tracker to model the target appearance and capture the best candidate with minimal reconstruction error in the frame of the particle filter framework.Last but not least,to remove the outliers and preserve nonlinear geometric structure of the dataset,we introduce a robust multiple kernel NLCF(Robust Multiple Kernel NLCF,RMKNLCF)using 2,1l-norm loss function in the kernel space.Particularly,multiple kernel learning can select the best linear combination of multiple input kernels.Experiments on the benchmark datasets demonstrate the effectiveness of the proposed methods in quantity.