Modeling Anisotropic Preference Manifolds for Robust Graph-based Fashion Recommendation

Graph Convolutional Networks (GNNs) have established themselves as the leading paradigm for collaborative filtering; however, their efficacy in complex domains like fashion is often hindered by a fundamental geometric mismatch between model assumptions and data reality. Conventional methods typically rely on scalar aggregation and Euclidean metrics, which implicitly assume that user interest clusters are isotropic (spherical) and uniformly dense. This assumption fails to capture the complexity of fashion preferences, where style distributions exhibit significant anisotropic variance—ranging from sparse, broad categories to dense, niche trends. To bridge this gap, we propose the Multi-Interest Mahalanobis Denoising Graph Convolutional Network (MIMD-GCN), a framework that synergizes structural disentanglement with geometry-aware denoising. We introduce a Poly-Attention mechanism to disentangle user representations into multiple latent interest centers, thereby resolving the collapse of diverse preferences into single vectors. Furthermore, we construct an anisotropic denoising module based on a learnable Mahalanobis distance barrier. Unlike static Euclidean thresholds, this mechanism dynamically adapts to the covariance structure of specific interest manifolds, establishing elliptical boundaries that effectively isolate spurious interactions while preserving valid niche signals. Extensive experiments on Amazon Fashion and Taobao datasets demonstrate that MIMD-GCN achieves statistically significant improvements over state-of-the-art baselines and maintains high robustness under severe synthetic noise, validating the geometric necessity of non-Euclidean modeling in recommender systems.