Related papers: Detecting Anomaly in Chemical Sensors via L1-Kerne…
Anomalous change detection (ACD) is an important problem in remote sensing image processing. Detecting not only pervasive but also anomalous or extreme changes has many applications for which methodologies are available. This paper…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…
We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…
We present a method to compute the Shapley values of reconstruction errors of principal component analysis (PCA), which is particularly useful in explaining the results of anomaly detection based on PCA. Because features are usually…
A variety of interstellar complex organic molecules (COMs) have been detected in various physical conditions. However, in the protostellar and protoplanetary environments, their complex kinematics make line profiles blend each other and the…
Cyber-physical control systems are critical infrastructures designed around highly responsive feedback loops that are measured and manipulated by hundreds of sensors and controllers. Anomalous data, such as from cyber-attacks, greatly risk…
L1-norm Principal-Component Analysis (L1-PCA) of real-valued data has attracted significant research interest over the past decade. However, L1-PCA of complex-valued data remains to date unexplored despite the many possible applications…
Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…
Our main objective is to develop a denoising strategy to increase the signal to noise ratio of individual spectral lines of stellar spectropolarimetric observations. We use a multivariate statistics technique called Principal Component…
We present a novel approach to anomaly detection by integrating Generalized Hyperbolic (GH) processes into kernel-based methods. The GH distribution, known for its flexibility in modeling skewness, heavy tails, and kurtosis, helps to…
In this work we introduce a new residual for normal linear models that are suitable for situations in which we are dealing with heteroskedasticity of unknown form, they are referred to by principal component analysis (PCA) residuals. These…
We propose an anomaly detection method for multi-variate scientific data based on analysis of high-order joint moments. Using kurtosis as a reliable measure of outliers, we suggest that principal kurtosis vectors, by analogy to principal…
The challenge of efficiently identifying anomalies in data sequences is an important statistical problem that now arises in many applications. Whilst there has been substantial work aimed at making statistical analyses robust to outliers,…
As modern software systems continue to grow in terms of complexity and volume, anomaly detection on multivariate monitoring metrics, which profile systems' health status, becomes more and more critical and challenging. In particular, the…
We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In simple, homogeneous missingness settings with a noise level of constant order, we show that an existing inverse-probability weighted…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
We apply local laws of random matrices and free probability theory to study the spectral properties of two kernel-based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), for two…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…