Principal Component Analysis (PCA) is the most widely used unsupervised dimensionality reduction approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, the existing robust PCA methods incorrectly center the data using the `2-norm distance to calculate the mean, which actually is not the optimal mean due to the `1-norm used in ...

In this paper, we present a nonconvex alternating minimization optimization algorithm for low-rank and sparse structure pursuit. Compared with convex relaxation based methods, the proposed algorithm is computationally more e cient for large scale problems. In our study, we define a notion of bounded di↵erence of gradients, based on which we rigorously prove that with suitable initialization, th...

In this paper, we propose a robust principal component analysis (PCA) to overcome the problem that PCA is prone to outliers included in the training set. Different from the other alternatives which commonly replace L2-norm by other distance measures, the proposed method alleviates the negative effect of outliers using the characteristic of the generalized mean keeping the use of the Euclidean d...

Principal Component Analysis (PCA) is very sensitive in presence of outliers. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit based method for principal component analysis ...

Principal Component Analysis (PCA) is the problem of finding a lowrank approximation to a matrix. It is a central problem in statistics, but it is sensitive to sparse errors with large magnitudes. Robust PCA addresses this problem by decomposing a matrix into the sum of a low-rank matrix and a sparse matrix, thereby separating out the sparse errors. This paper provides a background in robust PC...

Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel rob...

Electrical capacitance tomography (ECT) attempts to reconstruct the permittivity distribution of the cross-section of measurement objects from the capacitance measurement data, in which reconstruction algorithms play a crucial role in real applications. Based on the robust principal component analysis (RPCA) method, a dynamic reconstruction model that utilizes the multiple measurement vectors i...

Xisha waters are considered to be in pristine condition, while facing the fast increasing stress under anthropogenic activities. Water quality around Yongxing Island (YX) has been measured in May, 2012. The results show that the water quality is of the first class standards as compared to the water quality of China, with insignificant difference among the monitoring stations. Robust principal c...

Latency is one of the most critical performance metrics for a wide range of applications. Therefore, it is important to understand the underlying mechanisms that give rise to the observed latency values and diagnose the ones that are unexpectedly high. In this paper, we study the Internet delay space via robust principal component analysis (RPCA). Using RPCA, we show that the delay space, i.e. ...

the species of dioscorea (yam) are regarded as a staple food crop for millions of people in the tropical and subtropical regions of the world. it is regarded as an important food crop next to cereals and grains due to high yield storage of carbohydrates. economically, only few species are recognized for cultivation from agricultural point of view, in spite of its large species diversity. the sp...