K-associated optimal network for graph embedding dimensionality reduction

In machine learning, dimensionality reduction aims at reducing the dimension of the input data in order to achieve a small set of features that keeps the most important original relationships among data samples. In this paper, we investigate the usage of a non-parametric network formation algorithm into a graph embedding framework to perform supervised dimensionality reduction. Specifically, our technique maps data into networks and constructs two network adjacency matrices which convey information about intra-class components and inter-class penalty connections. Both matrices are inserted into an optimization framework in order to achieve a projection vector that is used to project high-dimension data samples into a low-dimensional space. One advantage of the technique is that no parameter is required, that is, there is no need to select a model for the input data. Computer simulations on real-world data sets have been performed to compare the proposed technique to some classical network formation methods such as k-NN and e-radius, and to well-known dimensionality reduction algorithms such as PCA and LDA. Statistical tests have shown that our approach outperforms those algorithms.