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Finding overcomplete latent representations of data has applications in data analysis, signal processing, machine learning, theoretical neuroscience and many other fields. In an overcomplete representation, the number of latent features…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…

Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it…

We perform a Koopman spectral analysis of elementary cellular automata (ECA). By lifting the system dynamics using a one-hot representation of the system state, we derive a matrix representation of the Koopman operator as a transpose of the…

Autoencoders (AE) provide a useful method for nonlinear dimensionality reduction but are ill-suited for low data regimes. Conversely, Principal Component Analysis (PCA) is data-efficient but is limited to linear dimensionality reduction,…

Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…

Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies by finding maximally correlated embeddings of pairs of random variables. CA has found applications in fields ranging from…

We study a distributed Principal Component Analysis (PCA) framework where each worker targets a distinct eigenvector and refines its solution by updating from intermediate solutions provided by peers deemed as "superior". Drawing intuition…

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

Principal Component Analysis (PCA) and its exponential family extensions have three components: observations, latents and parameters of a linear transformation. We consider a generalised setting where the canonical parameters of the…

Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lend to the possibility of automatically discovering structures in…

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

Linear principal component analysis (PCA) learns (semi-)orthogonal transformations by orienting the axes to maximize variance. Consequently, it can only identify orthogonal axes whose variances are clearly distinct, but it cannot identify…

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

Elementary cellular automata (ECA) are one-dimensional discrete models of computation with a small memory set that have gained significant interest since the pioneer work of Stephen Wolfram, who studied them as time-discrete dynamical…

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…