Universum linear discriminant analysis was recently proposed to improve linear discriminant analysis by incorporating Universum information. However, it obtains each of the discriminant directions by just using samples from two classes, while other class samples are considered as Universum. This not only leads to the ignoring of some discriminant information, but also restricts its number of extracted features to at most \(0.5k(k-1)\), where k is the number of classes. To fully explore discriminant information from all classes, this paper studies a novel Universum linear discriminant analysis by considering a unified model that simultaneously uses all classes. Compared to the existing Universum linear discriminant analysis, all Universum information is fully utilized in the proposed model when obtaining each discriminant direction, where the Universum can be self-constructed as well can be given advanced of any types. The constrained “concave-convex" procedure can be used to solve the proposed method, which makes the algorithm convergent to a local minimum. By employing a recursive technique, arbitrary number of discriminant directions can be obtained. Experimental results on real-world benchmark datasets and image datasets illustrate the advantages of the proposed method.

最近提出了 Universum 线性判别分析，通过合并 Universum 信息来改进线性判别分析。然而，它仅使用两个类的样本来获得每个判别方向，而其他类样本则被视为Universum。这不仅导致忽略了一些判别信息，而且将其提取的特征数量限制为最多\(0.5k(k-1)\)，其中k是班级数量。为了充分探索所有类别的判别信息，本文通过考虑同时使用所有类别的统一模型，研究了一种新颖的 Universum 线性判别分析。与现有的Universum线性判别分析相比，该模型在获得每个判别方向时充分利用了所有Universum信息，其中Universum可以自构造，也可以预先给出任何类型。可以使用约束“凹凸”过程来求解所提出的方法，这使得算法收敛到局部最小值。通过采用递归技术，可以获得任意数量的判别方向。在真实世界基准数据集上的实验结果和图像数据集说明了所提出方法的优点。