Research On Algorithms Of Locality Preserving Projection Based On Anchorgraph For Dimensionality Reduction

Data is often represented by a high dimensional vector in many practical research and applications, which is called "high-dimensional data". And these high-dimensional data can often be represented by a few factors, which indicates that the high-dimensional data contain a large amount of redundant information, but also shows that using a low dimensional vector to reflect the essential characteristics of these high-dimensional data is meaningful. Dimensionality reduction is the process of finding the low-dimensional structure which is embedded in the high-dimensional data set, and it plays an important role in many research fields.Many dimensionality reduction methods based on manifold learning have been studied and successfully applied in machine learning and pattern recognition, due to their ability of well capture the underlying relationship between data points, such as Isomap, LLE and LPP. LPP is a method of linear subspace dimensionality reduction, it can deal with the known training set and new data points effectively. However, with the rapid increase of the size of data, these methods impose restrictions on the memory consumption and computational complexity.We propose an improved dimensionality reduction algorithm called Anchorgraph-based Locality Preserving Projection (AgLPP), trying to cope with the limitations via a novel estimation of the relationship between data points. Firstly, we use the clustering algorithm to produce a small number of cluster centers as the virtual anchors. A small amount of anchors can retain the characteristics of the skeleton of the original data sets have been proved in this paper. Secondly, we construct an adjacency weight matrix which is based on the anchor point. Finally, we can get the method of AgLPP which is based on the adjacency weight matrix.Besides, We extend AgLPP into a kernel version, and reformulate it into a novel sparse representation. We can see that it has nothing to do with the bandwidth of kernel function. The experiments on several real-world datasets have demonstrated the effectiveness and efficiency of our methods.