A Frequency Domain Kernel Function-Based Manifold Dimensionality Reduction and Its Application for Graph-Based Semi-Supervised Classification

With the increasing demand for high-resolution images, handling high-dimensional image data has become a key aspect of intelligence algorithms. One effective approach is to preserve the high-dimensional manifold structure of the data and find the accurate mappings in a lower-dimensional space. However, various non-sparse, high-energy occlusions in real-world images can lead to erroneous calculations of sample relationships, invalidating the existing distance-based manifold dimensionality reduction techniques. Many types of noise are difficult to capture and filter in the original domain but can be effectively separated in the frequency domain. Inspired by this idea, a novel approach is proposed in this paper, which obtains the high-dimensional manifold structure according to the correlationships between data points in the frequency domain and accurately maps it to a lower-dimensional space, named Frequency domain-based Manifold Dimensionality Reduction (FMDR). In FMDR, samples are first transformed into frequency domains. Then, interference is filtered based on the distribution in the frequency domain, thereby emphasizing discriminative features. Subsequently, an innovative kernel function is proposed for measuring the similarities between samples according to the correlationships in the frequency domain. With the assistance of these correlationships, a graph structure can be constructed and utilized to find the mapping in a low-dimensional space. To further demonstrate the effectiveness of the proposed algorithm, FMDR is employed for the semi-supervised classification problems in this paper. Experiments using public image datasets indicate that, compared to baseline algorithms and state-of-the-art methods, our approach achieves superior recognition performance. Even with very few labeled data, the advantages of FMDR are still maintained. The effectiveness of FMDR in dimensionality reduction and feature extraction of images makes it widely applicable in fields such as image processing and image recognition.