This paper proposes a novel discriminative regression method, called adaptive locality preserving regression (ALPR) for classification. In particular, ALPR aims to learn a more flexible and discriminative projection that not only preserves the intrinsic structure of data, but also possesses the properties of feature selection and interpretability. To this end, we introduce a target learning technique to adaptively learn a more discriminative and flexible target matrix rather than the pre-defined strict zero-one label matrix for regression. Then a locality preserving constraint regularized by the adaptive learned weights is further introduced to guide the projection learning, which is beneficial to learn a more discriminative projection and avoid overfitting. Moreover, we replace the conventional `Frobenius norm' with the special l21 norm to constrain the projection, which enables the method to adaptively select the most important features from the original high-dimensional data for feature extraction. In this way, the negative influence of the redundant features and noises residing in the original data can be greatly eliminated. Besides, the proposed method has good interpretability for features owing to the row-sparsity property of the l21 norm. Extensive experiments conducted on the synthetic database with manifold structure and many real-world databases prove the effectiveness of the proposed method.
翻译:本文提出了一种新的歧视性回归法,称为适应性地方保留回归(ALPR),用于分类。特别是,ALPR旨在学习更灵活和更具歧视性的预测,不仅保存数据的内在结构,而且具有特征选择和可解释性特性的特性。为此,我们引入了一种有针对性的学习技术,以适应性地学习一种更具有歧视性和灵活性的目标矩阵,而不是预先定义的、严格的零一标签回归矩阵。然后,又引入了适应性学习重量规范的常规性地方保护制约,以指导预测学习,这有利于学习更具有歧视性的预测和避免过度调整。此外,我们用21世纪标准的特殊规范取代传统的“Frobenius规范”,以限制预测,从而使得能够从原有的高维度数据中适应性地选择最重要的特征的方法。这样,原数据中的冗余特征和噪音的负面影响就可以被大大消除。此外,拟议的方法对21世纪规范的行分属性具有很好的解释性。在合成数据库上进行的广泛实验,用多元结构和许多现实世界数据库证明拟议的有效性。