Related papers: Dynamical Component Analysis (DyCA): Dimensionalit…
This paper introduces a novel methodology of adapting the representation of videos based on the dynamics of their scene content variation. In particular, we demonstrate how the clustering of dynamic mode decomposition eigenvalues can be…
Dimensionality reduction is a critical step in scaling machine learning pipelines. Principal component analysis (PCA) is a standard tool for dimensionality reduction, but performing PCA over a full dataset can be prohibitively expensive. As…
The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient…
Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
Recent advances in neuroscience data acquisition allow for the simultaneous recording of large populations of neurons across multiple brain areas while subjects perform complex cognitive tasks. Interpreting these data requires us to index…
Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…
These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…
In this work, we explore dimensionality reduction techniques for univariate and multivariate time series data. We especially conduct a comparison between wavelet decomposition and convolutional variational autoencoders for dimension…
Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…
Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide…
Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…
High-dimensional image data often require dimensionality reduction before further analysis. This paper provides a purely analytical comparison of two linear techniques-Principal Component Analysis (PCA) and Singular Value Decomposition…
One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…
Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…
In this paper, we present an online adaptive PCA algorithm that is able to compute the full dimensional eigenspace per new time-step of sequential data. The algorithm is based on a one-step update rule that considers all second order…
We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…
Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…