Unsupervised and Semi-supervised Dimensionality Reduction with Self-Organizing Incremental Neural Network and Graph Similarity Constraints

The complexity of optimizations in semi-supervised dimensionality reduction methods has limited their usage. In this paper, an unsupervised and semi-supervised nonlinear dimensionality reduction method that aims at lower space complexity is proposed. First, a positive and negative competitive learning strategy is introduced to the single layered Self-Organizing Incremental Neural Network (SOINN) to process partially labeled datasets. Then, we formulate the dimensionality reduction of SOINN weight vectors as a quadratic programming problem with graph similarities calculated from previous step as constraints. Finally, an approximation of distances between newly arrived samples and the SOINN weight vectors is proposed to complete the dimensionality reduction task. Experiments are carried out on two artificial datasets and the NSL-KDD dataset comparing with Isomap, Transductive Support Vector Machine etc. The results show that the proposed method is effective in dimensionality reduction and an efficient alternate transductive learner.