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While variational autoencoders have been successful in several tasks, the use of conventional priors are limited in their ability to encode the underlying structure of input data. We introduce an Encoded Prior Sliced Wasserstein AutoEncoder…
A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…
Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart…
Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel…
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned…
Measuring the similarity between data points often requires domain knowledge, which can in parts be compensated by relying on unsupervised methods such as latent-variable models, where similarity/distance is estimated in a more compact…
To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density…
One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…
High dimensional data is often assumed to be concentrated on or near a low-dimensional manifold. Autoencoders (AE) is a popular technique to learn representations of such data by pushing it through a neural network with a low dimension…
An autoencoder is a neural network which data projects to and from a lower dimensional latent space, where this data is easier to understand and model. The autoencoder consists of two sub-networks, the encoder and the decoder, which carry…
We present the self-encoder, a neural network trained to guess the identity of each data sample. Despite its simplicity, it learns a very useful representation of data, in a self-supervised way. Specifically, the self-encoder learns to…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an…
In this article, we will look at autoencoders. This article covers the mathematics and the fundamental concepts of autoencoders. We will discuss what they are, what the limitations are, the typical use cases, and we will look at some…
A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…
What do auto-encoders learn about the underlying data generating distribution? Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of data. This paper clarifies some of these previous…
Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…
Deep generative models have made tremendous advances in image and signal representation learning and generation. These models employ the full Euclidean space or a bounded subset as the latent space, whose flat geometry, however, is often…
Brain encoding and decoding aims to understand the relationship between external stimuli and brain activities, and is a fundamental problem in neuroscience. In this article, we study latent embedding alignment for brain encoding and…
Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…