Discriminative Graph Embedding Framework via Label-Free Marginal Fisher Analysis

Marginal Fisher Analysis (MFA) is a classical dimensionality reduction (DR) method that leverages dual graphs to capture intra-class compactness and inter-class separability. However, MFA's reliance on high-quality labels limits its practical application. For another, existing unsupervised DR methods neglect data's local manifold relationship, resulting in poor discriminativeness. To address these limitations, we propose a novel DR method named \textbf{D}iscriminative \textbf{G}raph \textbf{E}mbedding \textbf{F}ramework (DGEF) via Label-Free Marginal Fisher Analysis. Our approach uses the adjacency matrix and cluster indicator matrix derived from centerless K-Means to construct intrinsic graph and penalty graph, which preserve the local manifold structure of the data. Additionally, we have derived the convertible relationship between centerless K-Means and Manifold learning and unified them within a graph embedding framework. By adopting the intrinsic graph and penalty graph, our DGEF avoids centroid initialization and ensures robustness and discriminativeness. This method achieves dimensionality reduction adaptively without relying on labeled data. Extensive experiments on benchmark datasets show that our approach outperforms conventional methods in clustering performance.