Discriminative Projection with Flexible Marginal and Local Relationships Learning for Feature Extraction and Classification

Feature extraction effectively captures meaningful information from raw signals or data to improve the accuracy and real-time performance of detection, classification, and prediction. The selection of an effective discriminant projection method is crucial for extracting discriminant features from the raw signals or data. However, some existing discriminative projection methods face two major limitations. First, the fixed graph structure adopted by some of the methods during feature extraction makes them susceptible to noise or outliers. Second, the predefined zero-one label matrix used by some of the methods to guide the model in learning the discriminative projection matrix leads to the loss of some intrinsic information inherent in the data. To overcome these limitations, we propose a framework called discriminative projection with flexible marginal and local relationship learning (DP-FRL). The key innovations of DP-FRL are primarily reflected in three aspects: (1) utilizing a flexible target matrix to guide the projection matrix in learning marginally structured relationships in the data; (2) employing permutation matrices in the local relationship regularization term reduces the dependence of the projection matrix on the order of features, effectively enhancing its ability to flexibly capture local relationships in the data; and (3) introducing a rank-one quadratic penalty to constrain the projection matrix, which helps learn more discriminative projections. To effectively solve the proposed framework model, we designed an iterative optimization algorithm. Finally, the classification experiments conducted on real-world datasets demonstrate that, compared to related methods, the features extracted by the DP-FRL method are more effective for classification tasks.