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This study introduces the concept of finite element network analysis (FENA) which is a physics-informed, machine-learning-based, computational framework for the simulation of complex physical systems. The framework leverages the extreme…

Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within…

A network supporting deep unsupervised learning is presented. The network is an autoencoder with lateral shortcut connections from the encoder to decoder at each level of the hierarchy. The lateral shortcut connections allow the higher…

Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

Canonical Correlation Analysis (CCA) is a statistical technique used to extract common information from multiple data sources or views. It has been used in various representation learning problems, such as dimensionality reduction, word…

Independent component analysis (ICA) is a powerful computational tool for separating independent source signals from their linear mixtures. ICA has been widely applied in neuroimaging studies to identify and characterize underlying brain…

Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…

Multiview analysis aims at extracting shared latent components from data samples that are acquired in different domains, e.g., image, text, and audio. Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles this…

Independent Component Analysis (ICA) is a fundamental unsupervised learning technique foruncovering latent structure in data by separating mixed signals into their independent sources. While substantial progress has been made in…

Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful…

Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least…

We introduce the use of two machine learning algorithms to create an empirical model of an experimental apparatus, which is able to reduce the number of measurements necessary for generic optimisation tasks exponentially as compared to…

A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from…

As a widely used method in machine learning, principal component analysis (PCA) shows excellent properties for dimensionality reduction. It is a serious problem that PCA is sensitive to outliers, which has been improved by numerous Robust…

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…

The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine…

Computing the excited states of a given Hamiltonian is computationally hard for large systems, but methods that do so using quantum computers scale tractably. This problem is equivalent to the PCA problem where we are interested in…

Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…

Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…