# On orthogonal projections for dimension reduction and applications in augmented target loss functions for learning problems

## TL;DR

This paper explores the use of orthogonal projections in high-dimensional data for dimension reduction and introduces augmented target loss functions in deep learning, improving accuracy in clinical imaging and music classification.

## Contribution

It analyzes the trade-offs in dimension reduction objectives and proposes a novel framework of augmented target loss functions for enhanced deep learning performance.

## Key findings

- Projections often do not satisfy variance and distance preservation simultaneously.
- Balanced projections improve classification results.
- Augmented target loss functions increase accuracy in real-world tasks.

## Abstract

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.