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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F20%3APU133044" target="_blank" >RIV/00216305:26220/20:PU133044 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s10851-019-00902-2" target="_blank" >https://link.springer.com/article/10.1007/s10851-019-00902-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10851-019-00902-2" target="_blank" >10.1007/s10851-019-00902-2</a>

Result language
angličtina
Original language name
On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/LO1401" target="_blank" >LO1401: Interdisciplinary Research of Wireless Technologies</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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