Related papers: Thresholding based Efficient Outlier Robust PCA

Sparse principal component analysis (SPCA) methods have proven to efficiently analyze high-dimensional data. Among them, threshold-based SPCA (TSPCA) is computationally more cost-effective than regularized SPCA, based on L1 penalties. We…

Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the…

This work studies the recursive robust principal components analysis (PCA) problem. If the outlier is the signal-of-interest, this problem can be interpreted as one of recursively recovering a time sequence of sparse vectors, $S_t$, in the…

We propose a novel unsupervised outlier detection method based on Randomized Principal Component Analysis (PCA). Motivated by the performance of Randomized PCA (RPCA) Forest in approximate K-Nearest Neighbor (KNN) search, we develop a novel…

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…

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…

In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…

The task of outlier detection is to find small groups of data objects that are exceptional when compared with rest large amount of data. In [38], the problem of outlier detection in categorical data is defined as an optimization problem and…

The task of robust linear estimation in the presence of outliers is of particular importance in signal processing, statistics and machine learning. Although the problem has been stated a few decades ago and solved using classical…

The Projection Congruent Subset (PCS) Outlyingness is a new index of multivariate outlyingness obtained by considering univariate projections of the data. Like many other outlier detection procedures, PCS searches for a subset which…

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…

Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the…

We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional…

This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…

Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank…

The idea of Innovation Search, which was initially proposed for data clustering, was recently used for outlier detection. In the application of Innovation Search for outlier detection, the directions of innovation were utilized to measure…

Impulsed noise outliers are data points that differs significantly from other observations.They are generally removed from the data set through local regression or Kalman filter algorithm.However, these methods, or their generalizations,…

Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…