Collaborative representation-based classification (CRC) has been extensively applied to various recognition fields due to its effectiveness and efficiency. Nevertheless, it is generally suboptimal for imbalanced learning. Previous studies have revealed that a class-imbalance distribution can lead CRC, and even most conventional classification methods, to ignore the minority class and prioritize the majority class. To address this deficiency, this paper proposes a hybrid density-based adaptive weighted collaborative representation model that incorporates a regularization technique and an adaptive weight generation mechanism into the CRC framework. A new regularization term, based on class-specific representation, is introduced to decrease the correlation between classes and enhance CRC’s discriminative ability. The sample distribution and density information within and between classes are employed to assign greater weights to minority samples, thereby strengthening the representation capabilities of minority samples and reducing the bias towards the majority class. Furthermore, it is theoretically demonstrated that this model has a closed-form solution. Its complexity is comparable to that of CRC, ensuring its efficiency. Extensive experiments on diverse data sets from the KEEL repository show the superiority of the proposed method compared to other state-of-the-art imbalanced classification methods.

基于协作表示的分类（CRC）由于其有效性和效率而被广泛应用于各个识别领域。然而，对于不平衡的学习来说，它通常不是最理想的。先前的研究表明，类别不平衡分布可能会导致 CRC，甚至大多数传统的分类方法，忽略少数类别并优先考虑多数类别。为了解决这一缺陷，本文提出了一种基于混合密度的自适应加权协作表示模型，该模型将正则化技术和自适应权重生成机制融入到 CRC 框架中。引入了基于类特定表示的新正则化项，以减少类之间的相关性并增强 CRC 的判别能力。利用类内和类间的样本分布和密度信息，为少数样本分配更大的权重，从而增强少数样本的表示能力，减少对多数类的偏差。此外，从理论上证明该模型具有闭式解。其复杂度与CRC相当，保证了其效率。对 KEEL 存储库中不同数据集的广泛实验表明，与其他最先进的不平衡分类方法相比，所提出的方法具有优越性。