Research On Dimensionality Reduction Algorithms Based On Locality Preserving Projections

Nowadays,the development of information technology is advancing rapidly,and huge amounts of data are constantly appearing in fields such as pattern recognition and machine learning.The fast update rate,high dimensionality,complex structure,and redundant information have led to a series of problems such as difficulties in storing highdimensional data,and a large amount of data computation.Currently,dimensionality reduction is one of the effective ways to solve these problems.Dimensionality reduction not only reduces the dimensions of the raw high-dimensional data and enables the data to be stored easily,but also discovers the intrinsic regulations and connections hidden in the high-dimensional data.Locality preserving projection is a typical example of dimensionality reduction methods,which can preserve the local nearest relationships in the raw high-dimensional data in the process of dimensionality reduction.Although locality preserving projection has been applied in fields such as classification and face recognition,there are still problems that are sensitive to parameters,do not utilize the label information in the data effectively,and only consider the local structure information of the data.To address these problems,this paper takes locality preserving projection as the basis for an extended study of dimensionality reduction methods and proposes three improvement methods,the main research of the paper is described as follows.(1)An orthogonal globality and locality preserving projection method is proposed.To preserve both the local intrinsic connections and the global linear relationships of highdimensional data in the reduced subspace,this paper combines the advantages of linear and non-linear dimensionality reduction methods,introduces an orthogonality criterion to enhance the robustness of the method,and proposes an orthogonal global and local preserving projection method.The global geometric and local undirected nearest neighbor graphs constructed by this method allow the global linear relationships and local intrinsic connections in the data to be preserved in the reduced subspace.At the same time,by introducing an orthogonality criterion,the method is more resistant to noise,etc.Excellent experimental results on the SEMEION handwritten digital dataset,the COIL-20 object image dataset,the UMIST face dataset,and the ORL face image dataset demonstrate the effectiveness of the method.(2)A coupled locality discriminative analysis method with globality preserving is proposed.To address the limitations of modal finiteness,sensitivity to parameters,and ineffective use of labeling information in locality preserving projection,this paper extends the local hold projection and proposes a coupled local discriminative analysis method with globality preserving.The method gives a novel local similarity self-learning strategy to explore local manifold shapes of data.Unlike the previous artificially set ranges of local nearest neighbor regions,the strategy analyses the local nearest neighbor regions of samples by measuring the similarity between them and the class label information,thus effectively avoiding the interference of external factors and obtaining local features with strong discriminative classification capability.Excellent projection results on an artificial Swiss roll dataset and extensive experimental results on several common image datasets demonstrate the robustness and classification capability of the method.(3)An elastic discriminative graph embedding based on adaptive kernel parameters is proposed.The kernel function is often used to measure the inter-sample distance in dimensionality reduction methods due to its excellent non-linear separability,but its performance has heavily relied on the selection of the kernel parameter.The use of multiple cross-validations to select suitable kernel parameters is a common way of selecting kernel parameters,which is simple and effective,but the time cost is very high when dealing with large-scale data.Therefore,an elastic discriminative graph embedding based on adaptive kernel parameters is proposed in this paper.The method distinguishes global graphs previously constructed by using label information as part of the judgment basis,which can effectively enhance the ability to extract the global contour information of the original data;The local topology preservation capability of the method is enhanced by edge weights during local intrinsic graph construction,thus improving the analysis of local intrinsic structural information of the original data.In addition,the adaptive kernel parameters are used to measure the distance of sample points in space when calculating the edge weights on the corresponding adjacency matrix of the graph,greatly reducing the time cost associated with previous multiple calculations.Experimental results on several publicly available image datasets also demonstrate the feasibility of this method.Figure [14] Table [13] Reference [64]...