Related papers: Robust PCA for Anomaly Detection and Data Imputati…

This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to…

Robust Principal Component Analysis (RPCA) is a widely used method for recovering low-rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other…

In multivariate time series classification, although current sequence analysis models have excellent classification capabilities, they show significant shortcomings when dealing with long sequence multivariate data, such as prolonged…

In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…

In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…

In this paper we propose a novel optimization framework to systematically solve robust PCA problem with rigorous theoretical guarantee, based on which we investigate very computationally economic updating algorithms.

Due to their transient nature, clouds represent anomalies relative to the underlying landscape of interest. Hence, the challenge of cloud identification can be considered a specific case in the more general problem of anomaly detection. The…

In the current context of data explosion, online techniques that do not require storing all data in memory are indispensable to routinely perform tasks like principal component analysis (PCA). Recursive algorithms that update the PCA with…

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…

Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

The main shortage of principle component analysis (PCA) based anomaly detection models is their interpretability. In this paper, our goal is to propose an interpretable PCA-based model for anomaly detection and interpretation. The propose…

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

We design algorithms for Robust Principal Component Analysis (RPCA) which consists in decomposing a matrix into the sum of a low rank matrix and a sparse matrix. We propose a deep unrolled algorithm based on an accelerated alternating…

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…

Modal analysis techniques are used to identify patterns and develop reduced-order models in a variety of fluid applications. However, experimentally acquired flow fields may be corrupted with incorrect and missing entries, which may degrade…

Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…