Contrastive Learning Dimensionality Reduction Method Based on Manifold Learning

 With the development of the times, more and more high-dimensional datasets come into people's view. In order to reduce the time complexity and space complexity of downstream tasks, data dimensionality reduction becomes the primary choice. Classical dimensionality reduction algorithms are mainly divided into linear dimensionality reduction algorithms and nonlinear dimensionality reduction algorithms. Some of the traditional dimensionality reduction methods have the problems of not considering the nonlinear structure of the original dataset and the existence of weak generalisation, which makes the dimensionality reduction effect not good or model need to be recalculated because of the addition of new samples. In order to solve these problems, the research in this paper is a comparative learning dimensionality reduction method based on manifold learning. The idea of manifold learning using geodesic distance can fully consider the nonlinear structure of the original dataset. In this paper, comparative learning is the main framework. When the neural network completes the training, it only need to take the new data as input to calculate, the result can be obtained, no need to reconstruct the model which means the generality is high. Starting from the related work, this paper briefly introduces manifold learning, comparative learning and neural network algorithms. Subsequently, an innovative model is proposed, including three modules, Isomap to extract nonlinear structure, expanding neighbourhood to make pseudo-labels, and comparative learning training. Detailed analyses are carried out through experiments, comparing with PCA and LLE algorithms with the geodetic distance retention rate as an indicator, which proves that the data dimensionality reduction method of this model is more effective and ubiquitous.