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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…

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

Outliers are ubiquitous in modern data sets. Distance-based techniques are a popular non-parametric approach to outlier detection as they require no prior assumptions on the data generating distribution and are simple to implement. Scaling…

Euclidean embedding from noisy observations containing outlier errors is an important and challenging problem in statistics and machine learning. Many existing methods would struggle with outliers due to a lack of detection ability. In this…

Classical discriminant analysis (DA) is based on the mean and empirical covariance matrix of each class, both of which are sensitive to outliers in the data. In the past the focus was on casewise outliers, that is, datapoints that lie far…

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…

The accuracy of machine learning interatomic potentials suffers from reference data that contains numerical noise. Often originating from unconverged or inconsistent electronic-structure calculations, this noise is challenging to identify.…

Outlier detection refers to the identification of rare items that are deviant from the general data distribution. Existing approaches suffer from high computational complexity, low predictive capability, and limited interpretability. As a…

Reliable outlier detection in high-dimensional data is crucial in modern science, yet it remains a challenging task. Traditional methods often break down in these settings due to their reliance on asymptotic behaviors with respect to sample…

This study concerns the issue of high dimensional outliers which are challenging to distinguish from inliers due to the special structure of high dimensional space. We introduce a new notion of high dimensional outliers that embraces…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

The goal of Continual Learning (CL) task is to continuously learn multiple new tasks sequentially while achieving a balance between the plasticity and stability of new and old knowledge. This paper analyzes that this insufficiency arises…

Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…

The well-known Lee-Carter model uses a bilinear form $\log(m_{x,t})=a_x+b_xk_t$ to represent the log mortality rate and has been widely researched and developed over the past thirty years. However, there has been little attention being paid…

Dimensionality reduction methods are very common in the field of high dimensional data analysis. Typically, algorithms for dimensionality reduction are computationally expensive. Therefore, their applications for the analysis of massive…

Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…

At the crossway of machine learning and data analysis, anomaly detection aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…