Research And Application Of Robust Locality Preserving Projections

Locality preserving projection is a classical manifold learning dimensionality reduction algorithm.It preserves local manifold structure while accomplishing dimensionality reduction.Since LPP employs the squared L2-norm to measure the similarity between data points,this distance measurement method will cause the influence of outliers to be amplified,which makes the algorithm less robust to noise.LPP adopts a non-adaptive method when constructing data similarity matrix,and the similarity matrix solved is often not optimal.Based on the deep analysis of LPP,a robust LPP is proposed.Taking advantages of the merits of LPP,a new clustering model is proposed by combining data dimension reduction and spectral clustering.The main research contents of this paper are as follows:LPP is sensitive to noise and outliers.To solve this problem,this paper propose a L21-norm based LPP,LPP-L21.The algorithm uses the L21 norm to define the objective function and employs L2-norm as the distance metric in spatial dimensions and L1-norm over different data points.This could alleviate the impact of noise and outliers,and LPP-L21 has rotation invariance.Experimental results on PIE,Extended Yale B,AR and COIL20 database show that the algorithm is more robust to noise and outliers.LPP adopts a non-adaptive method when constructing the similarity matrix.The similarity matrix obtained is not always optimal.As a result,the description of the local neighbor structure of data is not accurate enough.Then self-adaptive method is used to construct a similarity matrix,and the improved LPP dimension reduction method is combined with spectral clustering and integrated into the same objective function.A new clustering algorithm is proposed: Enhanced Constrained Laplacian Rank(ECLR),The algorithm learns a new similarity matrix for clustering.In the construction of the initial similarity matrix,the algorithm adopts an adaptive method to learn a more accurate similarity matrix,and the algorithm uses the LPP idea to extract the features of the data.This makes the expression of the data's neighbors more clear,which helps to learn a more accurate similarity matrix,thereby improving the clustering performance of the algorithm.Experimental results on some database show that the proposed algorithm has a good clustering effect.