Feature Selection for Incomplete Hierarchical Data by Positive Weight Recovery and Implicit Hierarchical Information

In real-world applications, hierarchical data with complex category structures pose significant challenges due to high dimensionality and potential incompleteness. Existing studies on hierarchical feature selection assume data are complete, without considering incomplete hierarchical data. However, in practice, obtaining a complete and uncorrupted feature space can be challenging due to physical, technical, and cost constraints in data collection. To address this issue, we propose a hierarchical feature selection method for incomplete hierarchical data. First, weight amendment matrices are introduced to shift the primary missing-data compensation from the feature space to the projection-weight space under hierarchical structural guidance. Second, we establish a hierarchical interaction framework that explicitly captures the implicit relationship between the weight amendment matrix and the hierarchical weight matrix via constrained optimization. Third, we design a sparse hierarchical regularization term that adaptively adjusts feature weights based on hierarchy levels. Extensive experiments on benchmark datasets demonstrate the proposed approach's superior performance over state-of-the-art methods, validating its enhanced effectiveness and progress in addressing the target problem domain.