Development of a dimensionality reduction algorithm applicable for out of sample problem

Dimensionality Reduction provides advantages for time complexity and storage. Traditional Manifold Learning, on the other hand, is an important proven field of Dimensionality Reduction study for feature extraction, but it is not applicable for the Out of Sample Problem, so they cannot work quickly and practically. Afterwards, in the literature, linear methods applicable for out of sample problem on Manifold Learning are presented. In the study, it is aimed to develop a Linear Manifold Learning-based Dimension Reduction method that is both applicable to the Out of Sample Problem and superior to its competitors in feature learning capability and demonstrate its effectiveness. The proposed method forms the coefficient that carries scattering information among the data and give it to a special function required to create a weight matrix in a supervised way. This method is applied to the Locality Preserving Projection and Orthogonal Locality Preserving Projection algorithms. Experiments are performed comparatively on the Locality Preserving Projection, Orthogonal Locality Preserving Projection, Neighborhood Preserving Embedding, and Orthogonal Neighborhood Preserving Embedding algorithms applicable to the Out of Sample Problem. In the findings obtained from the experiments of face recognition and hyperspectral imaging fields, it was seen that the proposed method showed superior classification accuracy performance compared to its competitors. In addition, the changes in weight matrices, scatterplots, band graphs, correlation matrices and significance matrices showed that the discrimination information between classes improved. As a result, a Dimensionality Reduction method has been presented for the Out of Sample problem, which has a superior feature learning capacity compared to its competitors, and the effectiveness of this method has been proven in both face recognition and hyperspectral imaging.