Related papers: Symmetry-Aware Autoencoders: s-PCA and s-nlPCA

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…

Linear latent variable models such as principal component analysis (PCA), independent component analysis (ICA), canonical correlation analysis (CCA), and factor analysis (FA) identify latent directions (or loadings) either ordered or…

In this paper, we introduce interpretable Siamese Neural Networks (SNN) for similarity detection to the field of theoretical physics. More precisely, we apply SNNs to events in special relativity, the transformation of electromagnetic…

Stack autoencoder (SAE), as a representative deep network, has unique and excellent performance in feature learning, and has received extensive attention from researchers. However, existing deep SAEs focus on original samples without…

An autoencoder is a self-supervised machine-learning network trained to output a quantity identical to the input. Owing to its structure possessing a bottleneck with a lower dimension, an autoencoder works to achieve data compression,…

The growing adoption of IoT systems in industries like transportation, banking, healthcare, and smart energy has increased reliance on sensor networks. However, anomalies in sensor readings can undermine system reliability, making real-time…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Many recent self-supervised frameworks for visual representation learning are based on certain forms of Siamese networks. Such networks are conceptually symmetric with two parallel encoders, but often practically asymmetric as numerous…

Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features. For example, latent factors may influence the data in a coordinated way, even though their effect is invisible…

Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample.…

This study explores the application of Convolutional Autoencoders (CAEs) for analyzing and reconstructing Scanning Tunneling Microscopy (STM) images of various crystalline lattice structures. We developed two distinct CAE architectures to…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…

Autoencoders are the simplest neural network for unsupervised learning, and thus an ideal framework for studying feature learning. While a detailed understanding of the dynamics of linear autoencoders has recently been obtained, the study…

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First,…

Geometric deep learning organises neural architectures around the symmetries of their data domain, with the choice of symmetry group serving as a geometric prior that determines what representations can be learned. Metric-Aware Principal…

The central aim of this paper is to implement Deep Autoencoder and Neighborhood Components Analysis (NCA) dimensionality reduction methods in Matlab and to observe the application of these algorithms on nine unlike datasets from UCI machine…

We propose a new supervised dimensionality reduction technique called Supervised Linear Centroid-Encoder (SLCE), a linear counterpart of the nonlinear Centroid-Encoder (CE) \citep{ghosh2022supervised}. SLCE works by mapping the samples of a…