# Learning Extremal Representations with Deep Archetypal Analysis

@article{Keller2021LearningER, title={Learning Extremal Representations with Deep Archetypal Analysis}, author={Sebastian Mathias Keller and Maxim Samarin and Fabricio Arend Torres and Mario Wieser and Volker Roth}, journal={International Journal of Computer Vision}, year={2021}, volume={129}, pages={805 - 820} }

Archetypes represent extreme manifestations of a population with respect to specific characteristic traits or features. In linear feature space, archetypes approximate the data convex hull allowing all data points to be expressed as convex mixtures of archetypes. As mixing of archetypes is performed directly on the input data, linear Archetypal Analysis requires additivity of the input, which is a strong assumption unlikely to hold e.g. in case of image data. To address this problem, we propose…

## 11 Citations

### Consistency of Archetypal Analysis

- Mathematics, Computer ScienceSIAM J. Math. Data Sci.
- 2021

This paper proves a consistency result that shows if the data is independently sampled from a probability measure with bounded support, then the archetype points converge to a solution of the continuum version of the problem, of which it identifies and establishes several properties.

### Learning Invariances with Generalised Input-Convex Neural Networks

- Computer Science, MathematicsArXiv
- 2022

A novel and exible class of neural networks that generalise input-convex networks that represent functions that are guaranteed to have connected level sets forming smooth manifolds on the input space are introduced.

### Learning Conditional Invariance through Cycle Consistency

- Computer ScienceGCPR
- 2021

This work proposes a novel approach to cycle consistency based on the deep information bottleneck and, in contrast to other approaches, allows using continuous target properties and provides inherent model selection capabilities.

### Inverse Learning of Symmetries

- Computer ScienceNeurIPS
- 2020

This work proposes to learn the symmetry transformation with a model consisting of two latent subspaces, where the first subspace captures the target and the second subspace the remaining invariant information, based on the deep information bottleneck in combination with a continuous mutual information regulariser.

### 3DMolNet: A Generative Network for Molecular Structures

- Computer ScienceArXiv
- 2020

This work proposes a new approach to efficiently generate molecular structures that are not restricted to a fixed size or composition, based on the variational autoencoder which learns a translation-, rotation-, and permutation-invariant low-dimensional representation of molecules.

### Neural ADMIXTURE: rapid population clustering with autoencoders

- Computer Science, BiologybioRxiv
- 2021

Neural ADMIXTURE is presented, a neural network autoencoder that follows the same modeling assumptions as AD MIXTURE, providing similar (or better) clustering, while reducing the compute time by orders of magnitude.

### Inverse Learning of Symmetry Transformations

- Computer ScienceArXiv
- 2020

This work proposes learning two latent subspaces, where the first subspace captures the property and the second subspace the remaining invariant information, based on the deep information bottleneck principle in combination with a mutual information regulariser.

### Non-linear archetypal analysis of single-cell RNA-seq data by deep autoencoders

- Computer SciencebioRxiv
- 2021

The ability of scAAnet to extract biologically meaningful GEPs using publicly available scRNA-seq datasets including a pancreatic islet dataset, a lung idiopathic pulmonary fibrosis dataset and a prefrontal cortex dataset is demonstrated.

### Self-Supervised Representation Learning for High-Content Screening

- Computer Science
- 2022

A self-supervised triplet network is used to learn a phenotypic embedding which is used for visual inspection and top-down assay quality control and outperforms state-of-the-art unsupervised and supervised approaches.

### Archetypal Analysis of Geophysical Data illustrated by Sea Surface Temperature

- GeologyArtificial Intelligence for the Earth Systems
- 2022

The ability to find and recognize patterns in high-dimensional geophysical data is fundamental to climate science and critical for meaningful interpretation of weather and climate processes.…

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