High-dimensionality graph data reduction based on proposing a new algorithm

In recent years, graph data analysis has become very important in modeling data distribution or structure in many applications, for example, social science, astronomy, computational biology or social networks with a massive number of nodes and edges. However, high-dimensionality of the graph data remains a difficult task, mainly because the analysis system is not used to dealing with large graph data. Therefore, graph-based dimensionality reduction approaches have been widely used in many machine learning and pattern recognition applications. This paper offers a novel dimensionality reduction approach based on the recent graph data. In particular, we focus on combining two linear methods: Neighborhood Preserving Embedding (NPE) method with the aim of preserving the local neighborhood information of a given dataset, and Principal Component Analysis (PCA) method with aims of maximizing the mutual information between the original high-dimensional data sets. The combination of NPE and PCA contributes to proposing a new Hybrid dimensionality reduction technique (HDR). We propose HDR to create a transformation matrix, based on formulating a generalized eigenvalue problem and solving it with Rayleigh Quotient solution. Consequently, therefore, a massive reduction is achieved compared to the use of PCA and NPE separately. We compared the results with the conventional PCA, NPE, and other linear dimension reduction methods. The proposed method HDR was found to perform better than other techniques. Experimental results have been based on two real datasets.