2019
DOI: 10.1007/s10851-019-00902-2
|View full text |Cite|
|
Sign up to set email alerts
|

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

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 o… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
2

Citation Types

0
12
0

Year Published

2019
2019
2024
2024

Publication Types

Select...
4
1
1
1

Relationship

0
7

Authors

Journals

citations
Cited by 10 publications
(12 citation statements)
references
References 44 publications
0
12
0
Order By: Relevance
“…In the following we want to investigate possible enhancement with alternative output/target data representations. To do so, we use an augmented target loss function, a general framework is introduced in [3]. It allows to integrate known characteristics of the target space via informed transformations on the output and target data.…”
Section: Augmented Target Loss Functionmentioning
confidence: 99%
See 3 more Smart Citations
“…In the following we want to investigate possible enhancement with alternative output/target data representations. To do so, we use an augmented target loss function, a general framework is introduced in [3]. It allows to integrate known characteristics of the target space via informed transformations on the output and target data.…”
Section: Augmented Target Loss Functionmentioning
confidence: 99%
“…It allows to integrate known characteristics of the target space via informed transformations on the output and target data. We now recall a general formulation of AT from [3] and describe subsequently in detail, how it can be applied on the studied audio data.…”
Section: Augmented Target Loss Functionmentioning
confidence: 99%
See 2 more Smart Citations
“…The CNN is trained using high quality and coregistered anatomical and dMRI data (from the HCP), and then predicts tissue segmentation of new subjects directly from dMRI data, without the need for anatomical MRI data nor inter-modality registration. To further improve accuracy we trained the CNN using a novel augmented target loss function (Breger et al, 2020) that penalizes segmentation errors in tissue boundary regions. The dMRI input includes seven DKI and DTI parameter maps that have been corrected for implausible values using MK-Curve and three additional MK-Curve-derived maps (Zhang et al, 2019).…”
Section: Introductionmentioning
confidence: 99%