Related papers: Closed-Form, Provable, and Robust PCA via Leverage…
We present an algorithm for L1-norm kernel PCA and provide a convergence analysis for it. While an optimal solution of L2-norm kernel PCA can be obtained through matrix decomposition, finding that of L1-norm kernel PCA is not trivial due to…
We provide a new robust convergence analysis of the well-known power method for computing the dominant singular vectors of a matrix that we call the noisy power method. Our result characterizes the convergence behavior of the algorithm when…
Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…
This work studies the recursive robust principal components' analysis(PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers. If the outlier is the signal-of-interest, this problem can be…
Principal component analysis (PCA) is a classical and widely used method for dimensionality reduction, with applications in data compression, computer vision, pattern recognition, and signal processing. However, PCA is designed for…
High-dimensional data poses unique challenges in outlier detection process. Most of the existing algorithms fail to properly address the issues stemming from a large number of features. In particular, outlier detection algorithms perform…
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…
In this paper, we propose a novel approach for outlier detection, called local projections, which is based on concepts of Local Outlier Factor (LOF) (Breunig et al., 2000) and RobPCA (Hubert et al., 2005). By using aspects of both methods,…
Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…
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.
We derive a convex optimization problem for the task of segmenting sequential data, which explicitly treats presence of outliers. We describe two algorithms for solving this problem, one exact and one a top-down novel approach, and we…
Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…
Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be…
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…
We propose a general approach to handle data contaminations that might disrupt the performance of feature selection and estimation procedures for high-dimensional linear models. Specifically, we consider the co-occurrence of mean-shift and…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
In this paper, we propose an optimization-based method for robust phase retrieval problem where the goal is to estimate an unknown signal from a quadratic measurement corrupted by outliers. To enhance the robustness of existing optimization…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
Outlier detection is an important problem occurring in a wide range of areas. Outliers are the outcome of fraudulent behaviour, mechanical faults, human error, or simply natural deviations. Many data mining applications perform outlier…
Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…