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Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
Kernel Principal Component Analysis (KPCA) is a key machine learning algorithm for extracting nonlinear features from data. In the presence of a large volume of high dimensional data collected in a distributed fashion, it becomes very…
Principal Component Analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
Spatiotemporal traffic data (e.g., link speed/flow) collected from sensor networks can be organized as multivariate time series with additional spatial attributes. A crucial task in analyzing such data is to identify and detect anomalous…
Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…
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…
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
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…
We have obtained the first time-resolved, disc-integrated observations of Earth's poles with the Deep Impact spacecraft as part of the EPOXI Mission of Opportunity. These data mimic what we will see when we point next-generation space…
Motivated by risk assessment of coastal flooding, we consider time-consuming simulators with a spatial output. The aim is to perform sensitivity analysis (SA), quantifying the influence of input parameters on the output. There are three…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
Astronomy has evolved almost exclusively by the use of spectroscopic and imaging techniques, operated separately. With the development of modern technologies it is possible to obtain datacubes in which one combines both techniques…
Recurrence plots (RPs) are powerful tools for visualizing time series dynamics; however, traditional Recurrence Quantification Analysis (RQA) often relies on global metrics, such as line counting, that can overlook system-specific,…
Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin…
Molecular dynamics simulations produce huge datasets of temporal sequences of molecules. It is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such…
The $k$-principal component analysis ($k$-PCA) problem is a fundamental algorithmic primitive that is widely-used in data analysis and dimensionality reduction applications. In statistical settings, the goal of $k$-PCA is to identify a top…
The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…
We introduce Adaptive Subspace PCA (AS-PCA), a framework for principal component analysis of random elements in a general separable Hilbert space. AS-PCA projects the covariance operator onto a data-adaptive finite-dimensional subspace…
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…