On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems

On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems

Článek WoS

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.

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.

orthogonal projections; dimension reduction; augmented target loss;

orthogonal projections; dimension reduction; augmented target loss;

BREGER, A.; ORLANDO, J.; HARÁR, P.; DÖRFLER, M.; KLIMSCHA, S.; GRECHENIG, C.; GERENDAS, B.; SCHMIDT-ERFURTH, U.; EHLER, M.

2021

23.08.2020

Springer

1573-7683

JOURNAL OF MATHEMATICAL IMAGING AND VISION

62

3

Nizozemsko

376

394

19

https://link.springer.com/article/10.1007/s10851-019-00902-2

http://hdl.handle.net/11012/187007

Breger2020_Article_OnOrthogonalProjectionsForDime