On orthogonal projections for dimension reduction and applications in augmented target loss functions for learning problems
This work addresses dimension reduction trade-offs and enhances supervised learning accuracy in specific domains like medical imaging and music analysis.
The paper investigates orthogonal projections for dimension reduction, showing they typically cannot simultaneously preserve variance and pairwise distances, and introduces augmented target loss functions that integrate projected target data to improve accuracy in clinical image segmentation and music classification tasks.
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 increase the accuracy.