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We consider the problem of image representation for the tasks of unsupervised learning and semi-supervised learning. In those learning tasks, the raw image vectors may not provide enough representation for their intrinsic structures due to…

Natural systems with emergent behaviors often organize along low-dimensional subsets of high-dimensional spaces. For example, despite the tens of thousands of genes in the human genome, the principled study of genomics is fruitful because…

In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions.Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder.…

Autoencoders and their variations provide unsupervised models for learning low-dimensional representations for downstream tasks. Without proper regularization, autoencoder models are susceptible to the overfitting problem and the so-called…

Linear autoencoder models learn an item-to-item weight matrix via convex optimization with L2 regularization and zero-diagonal constraints. Despite their simplicity, they have shown remarkable performance compared to sophisticated…

Manifold alignment (MA) involves a set of techniques for learning shared representations across domains, yet many traditional MA methods are incapable of performing out-of-sample extension, limiting their real-world applicability. We…

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…

Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…

Real-time data collection and analysis in large experimental facilities present a great challenge across multiple domains, including high energy physics, nuclear physics, and cosmology. To address this, machine learning (ML)-based methods…

Audio autoencoders learn useful, compressed audio representations, but their non-linear latent spaces prevent intuitive algebraic manipulation such as mixing or scaling. We introduce a simple training methodology to induce linearity in a…

Hyperspectral image analysis often requires selecting the most informative bands instead of processing the whole data without losing the key information. Existing band reduction (BR) methods have the capability to reveal the nonlinear…

Anomalies (or outliers) are prevalent in real-world empirical observations and potentially mask important underlying structures. Accurate identification of anomalous samples is crucial for the success of downstream data analysis tasks. To…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

This work presents a data-driven framework for fast forward and inverse analysis in topology optimization (TO) by combining Rank Reduction Autoencoders (RRAEs) with neural latent-space mappings. The methodology targets the efficient…

Variational autoencoders (VAEs) are one of the deep generative models that have experienced enormous success over the past decades. However, in practice, they suffer from a problem called posterior collapse, which occurs when the encoder…

Clustering single-cell RNA sequence (scRNA-seq) data poses statistical and computational challenges due to their high-dimensionality and data-sparsity, also known as `dropout' events. Recently, Regularized Auto-Encoder (RAE) based deep…

Inverse problems often involve matching observational data using a physical model that takes a large number of parameters as input. These problems tend to be under-constrained and require regularization to impose additional structure on the…

Using the information theory, this study provides insights into how the construction of latent space of autoencoder (AE) using deep neural network (DNN) training finds a smooth low-dimensional manifold in the stiff dynamical system. Our…

Latent diffusion models have established a new state-of-the-art in high-resolution visual generation. Integrating Vision Foundation Model priors improves generative efficiency, yet existing latent designs remain largely heuristic. These…

Autoencoders provide a powerful framework for learning compressed representations by encoding all of the information needed to reconstruct a data point in a latent code. In some cases, autoencoders can "interpolate": By decoding the convex…