Related papers: Using topological autoencoders as a filtering func…

While many phenomena in physics and engineering are formally high-dimensional, their long-time dynamics often live on a lower-dimensional manifold. The present work introduces an autoencoder framework that combines implicit regularization…

Autoencoders are neural network formulations where the input and output of the network are identical and the goal is to identify the hidden representation in the provided datasets. Generally, autoencoders project the data nonlinearly onto a…

A rapidly growing area of research is the use of machine learning approaches such as autoencoders for dimensionality reduction of data and models in scientific applications. We show that the canonical formulation of autoencoders suffers…

Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they…

Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for example, one can compute an attribute on each node of the tree and keep only…

The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a…

Conventional magneto-static finite element analysis of electrical machine design is time-consuming and computationally expensive. Since each machine topology has a distinct set of parameters, design optimization is commonly performed…

Acquiring plausible pathways on high-dimensional structural distributions is beneficial in several domains. For example, in the drug discovery field, a protein conformational pathway, i.e. a highly probable sequence of protein structural…

Feature selection is a dimensionality reduction technique that selects a subset of representative features from high dimensional data by eliminating irrelevant and redundant features. Recently, feature selection combined with sparse…

Autoencoders are a powerful and versatile tool often used for various problems such as anomaly detection, image processing and machine translation. However, their reconstructions are not always trivial to explain. Therefore, we propose a…

Feature maps, that preserve the global topology of arbitrary datasets, can be formed by self-organizing competing agents. So far, it has been presumed that global interaction of agents is necessary for this process. We establish that this…

An additive autoencoder for dimension reduction, which is composed of a serially performed bias estimation, linear trend estimation, and nonlinear residual estimation, is proposed and analyzed. Computational experiments confirm that an…

Autoencoders have achieved great success in various computer vision applications. The autoencoder learns appropriate low dimensional image representations through the self-supervised paradigm, i.e., reconstruction. Existing studies mainly…

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…

Tiered graph autoencoders provide the architecture and mechanisms for learning tiered latent representations and latent spaces for molecular graphs that explicitly represent and utilize groups (e.g., functional groups). This enables the…

The mapper algorithm is a popular tool from topological data analysis for extracting topological summaries of high-dimensional datasets. In this paper, we present Mapper Interactive, a web-based framework for the interactive analysis and…

With the increasing use of black-box Machine Learning (ML) techniques in critical applications, there is a growing demand for methods that can provide transparency and accountability for model predictions. As a result, a large number of…

It has been a long-standing goal in machine learning, as well as in AI more generally, to develop life-long learning systems that learn many different tasks over time, and reuse insights from tasks learned, "learning to learn" as they do…

Protein function is inherently linked to its localization within the cell, and fluorescent microscopy data is an indispensable resource for learning representations of proteins. Despite major developments in molecular representation…

Autoencoders have found widespread application in both their original deterministic form and in their variational formulation (VAEs). In scientific applications and in image processing it is often of interest to consider data that are…