The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well as numerical experiments show that a projection does usually not satisfy both objectives at once. In a standard classification problem, we determine projections on the input data that balance the objectives and compare subsequent results. Next, we extend our application of orthogonal projections to deep learning tasks and introduce a general framework of augmented target loss functions. These loss functions integrate additional information via transformations and projections of the target data. In two supervised learning problems, clinical image segmentation and music information classification, the application of our proposed augmented target loss functions increases the accuracy.

中文翻译：

---

关于降维的正交投影及其在学习问题的增强目标损失函数中的应用

研究了在学习框架中正交投影对高维输入和目标数据的使用。首先，我们研究了两个标准目标之间在减少尺寸，保留方差和成对相对距离方面的关系。对它们的渐近相关性的研究以及数值实验表明，投影通常不能同时满足两个目标。在标准分类问题中，我们确定对输入数据的预测，以平衡目标并比较后续结果。接下来，我们将正交投影的应用扩展到深度学习任务，并介绍增强目标损失函数的一般框架。这些损失函数通过目标数据的转换和投影来集成其他信息。在两个监督学习问题中，