Evaluation of graph embedding approach for dimensionality reduction using different kernels

Abstract

By passing of time, the size of data such as fMRI scans, speech signals and digital photographs becomes very high and it takes large amount of time for data processing. To overcome this problem, the dimensionality of data should be reduced. Whereas graph embedding introduces a successful framework for dimensionality reduction, we use it as the base of our proposed method. In this framework, similarity and penalty graphs are constructed based on data relations. These graphs characterize the statistical or geometric property of the data that should be kept or avoided during dimensionality reduction. Our proposed method constructs these two graphs on data using Euclidean distance, in which similarity graph connects each data point with its neighboring points on the same class and characterizes compactness of within class data, while penalty graph connects the marginal points and characterizes separability out of classes. These two graphs show the geometry of the neighboring space of each data and are able to describe whole data space. Two extensions of graph embedding are discussed in this paper which are called as linearization and kernelization of graph embedding. In kernel extension, the impression of different kernel functions is evaluated on different databases. Obtained results show that the proposed method improves the accuracy of classification on data such as face and digit databases.