Manifold öğrenme yöntemlerinin ileri seviye regresyon yöntemleri ile genelleştirilmesi

Recently, nonlinear dimensionality reduction, also called manifold learning methods, has been studied in the context of classification tasks. Manifold learning methods are graph-based methods, and they assume there is a nonlinear manifold with low dimensional space, that is hidden in the high dimensional data. They aim at preserving the neighborhoods between the samples lying in the high-dimensional space when projecting the data. Most of the manifold learning methods embed the training data into low dimensional space, but neither provide any projection matrix or an embedding function representing the nonlinear transformation. Due to this, the test data cannot be mapped to the same low dimensional space. To map the test data, the entire data, including the test and the previous training data, are given to the manifold learning method, then the learning process is rerun. However, it should be noted that this process needs to be repeated in each of the cases when the test data become available, resulting in a very high computational burden process. Therefore, especially for the classification tasks, one needs to have a generalized solution of manifold learning methods to transform the test data into previously learned low-dimensional space. In this study, advanced regression methods are utilized to solve this problem, also known as the out-of-the-sample problem in the literature. The embedding function, representing the transformation between the high and the low dimensional space, is provided by modeling the corresponding manifold learning method via regression methods. The quality of each embedding is evaluated based on the classification of hyperspectral images in detail.