Large Amount Of Outliers Research Articles

An outlier-robust smoothness-based graph learning approach

Graph learning (GL) is a tool for finding direct relationships between the nodes of a network, and hence, inferring the graph topology from the data. Recently, many GL algorithms have been proposed in the field of graph signal processing, which are based on smoothness of the graph signals on the learned graph. However, although it is possible for the input graph signals to be contaminated by outliers, for example due to sensor failures or temporary faulty information records, existing techniques are very vulnerable to outliers. So, the goal is to infer a graph topology to be, as much as possible, insensitive to this kind of data corruptions. To this aim, due to the sparse nature of outlier data, we propose a new approach for robustifying GL algorithms by incorporating L1-norm or squared L1-norm terms into the objective function of smoothness based GL methods, yielding to a non-convex minimization problem. A novel iterative minimization method is introduced to solve the resulting non-convex problem. Moreover, the convergence of the algorithm is established despite of its non-convex nature. In simulations, the high performance of the proposed algorithm is demonstrated in presence of a considerably large amount of outliers.

Outlier data mining method considering the output distribution characteristics for photovoltaic arrays and its application

Sustainable growth of the installed capacity for photovoltaic (PV) power has brought greater challenges to the operation and maintenance of PV plants. As important functions of smart operation, the performance analysis, modeling, evaluation and fault diagnosis, are getting more demanding. However, large amount of outliers are generated during the running of the PV arrays in the plant, which brings many difficulties for the implement of above functions. To solve this problem, an outlier cleaning method considering the output distribution characteristics for PV arrays is proposed. First, the distribution characteristics of PV array operation data under different external environmental conditions are analyzed, and the distribution characteristics and laws of outliers are discussed. Next, based on the array output characteristics, a two-step quantile algorithm is used to modify the outliers. Subsequently, a case study shows that the proposed method can effectively identify different types of outliers. The main contributions of the paper are the explanation of the PV array outliers distribution affected by the external environment, and the first application of the data cleaning method to the thresholds setting of PV arrays operating and its fault diagnosis.

Clustering via fuzzy one-class quadratic surface support vector machine

This paper proposes a soft clustering algorithm based on a fuzzy one-class kernel-free quadratic surface support vector machine model. One main advantage of our new model is that it directly uses a quadratic function for clustering instead of the kernel function. Thus, we can avoid the difficult task of finding a proper kernel function and corresponding parameters. Besides, for handling data sets with a large amount of outliers and noise, we introduce the Fisher discriminant analysis to consider minimizing the within-class scatter. Our experimental results on some artificial and real-world data sets demonstrate that the proposed algorithm outperforms Bicego’s benchmark algorithm in terms of the clustering accuracy and efficiency. Moreover, this proposed algorithm is also shown to be very competitive with several state-of-the-art clustering methods.

Efficient algorithms for robust estimation of relative translation

One of the key challenges for structure from motion systems in order to make them robust to failure is the ability to handle outliers among the correspondences. In this paper we present two new algorithms that find the optimal solution in the presence of outliers when the camera undergoes a pure translation. The first algorithm has polynomial-time computational complexity, independently of the amount of outliers. The second algorithm does not offer such a theoretical complexity guarantee, but we demonstrate that it is magnitudes faster in practice. No random sampling approaches such as RANSAC are guaranteed to find an optimal solution, while our two methods do. We evaluate and compare the algorithms both on synthetic and real experiments. We also embed the algorithms in a larger system, where we optimize for the rotation angle as well (the rotation axis is measured by other means). The experiments show that for problems with a large amount of outliers, the RANSAC estimates may deteriorate compared to our optimal methods.

Fuzzy quadratic surface support vector machine based on fisher discriminant analysis

In this paper, using the concept of Fisher discriminant analysis and a new fuzzy membership function, a kernel-free fuzzy quadratic surface support vector machine model is proposed for binary classification. The membership function is specially designed to consider not only the ``quadratic-margin distance'' between a training point and its related ``quadratic center surface'' but also the affinity among training points. A decomposition algorithm is designed to solve the proposed model. Computational results on artificial and four real-world classifying data sets indicate that the proposed model outperforms fuzzy support vector machine models with Gaussian or Quadratic kernel and soft quadratic surface support vector machine model, especially, when the data sets contain a large amount of outliers and noises.

Tractable Algorithms for Robust Model Estimation

What is the computational complexity of geometric model estimation in the presence of noise and outliers? We show that the number of outliers can be minimized in polynomial time with respect to the number of measurements, although exponential in the model dimension. Moreover, for a large class of problems, we prove that the statistically more desirable truncated $$L_2$$L2-norm can be optimized with the same complexity. In a similar vein, it is also shown how to transform a multi-model estimation problem into a purely combinatorial one--with worst-case complexity that is polynomial in the number of measurements but exponential in the number of models. We apply our framework to a series of hard fitting problems. It gives a practical method for simultaneously dealing with measurement noise and large amounts of outliers in the estimation of low-dimensional models. Experimental results and a comparison to random sampling techniques are presented for the applications rigid registration, triangulation and stitching.

Robust hair capture using simulated examples

We introduce a data-driven hair capture framework based on example strands generated through hair simulation. Our method can robustly reconstruct faithful 3D hair models from unprocessed input point clouds with large amounts of outliers. Current state-of-the-art techniques use geometrically-inspired heuristics to derive global hair strand structures, which can yield implausible hair strands for hairstyles involving large occlusions, multiple layers, or wisps of varying lengths. We address this problem using a voting-based fitting algorithm to discover structurally plausible configurations among the locally grown hair segments from a database of simulated examples. To generate these examples, we exhaustively sample the simulation configurations within the feasible parameter space constrained by the current input hairstyle. The number of necessary simulations can be further reduced by leveraging symmetry and constrained initial conditions. The final hairstyle can then be structurally represented by a limited number of examples. To handle constrained hairstyles such as a ponytail of which realistic simulations are more difficult, we allow the user to sketch a few strokes to generate strand examples through an intuitive interface. Our approach focuses on robustness and generality. Since our method is structurally plausible by construction, we ensure an improved control during hair digitization and avoid implausible hair synthesis for a wide range of hairstyles.

Discovery of Anomalous Windows through a Robust Nonparametric Multivariate Scan Statistic (RMSS)

This paper studies unusual phenomena by discovering anomalous windows in multivariate spatial data. Such an anomalous window is a group of contiguous spatial objects indicating the occurrence of unusual phenomenon in terms of multiple variables. The paper presents a novel Robust non-parametric Multivariate Scan Statistic (RMSS). In contrast to the existing work, the authors’ approach is designed to deal with anomalous window discovery in multivariate data. They propose their multivariate scan statistic that employs the robust Mahalanobis distance which enables taking into account multiple behavioral attributes at the same time and their correlations for the discovery of significant anomalous windows. The proposed multivariate scan statistic is non-parametric such that it does not rely on any prior assumption about the data distribution. It is robust such that it can handle data with large amount of outliers, up to 50% of the overall data size. It is also affine equivariant such that affine transformation such as stretch or rotation of the data would not affect the results. The authors evaluate their approach with (a) real-world multivariate climate data for discovering natural disasters and climate changes, (b) real-world multivariate traffic accident data for identifying accident hubs, which are route segments with underlying accident-prone issues, and (c) synthetic data of both continuous and discrete multivariate distribution for identifying clusters of known outliers under different outlier percentage in data. They compare their results to state of the art multivariate scan statistic method (Kulldorff et al., 2007). The evaluation shows the detection power of the authors’ method, and the significant improvement over the existing methods.

Accurate CT/MR vessel‐guided nonrigid registration of largely deformed livers

Computer tomography (CT) scans are used for designing radiotherapy treatment plans. However, the tumor is often better visible in magnetic resonance (MR) images. For liver stereotactic body radiation therapy (SBRT), the planning CT scan is acquired while abdominal compression is applied to reduce tumor motion induced by breathing. However, diagnostic MR scans are acquired under voluntary breath-hold without the compression device. The resulting large differences in liver shape hinder the alignment of CT and MR image sets, which severely limits the integration of the information provided by these images. The purpose of the current study is to develop and validate a nonrigid registration method to align breath-hold MR images with abdominal-compressed CT images, using vessels that are automatically segmented within the liver. Contrast-enhanced MR and CT images of seven patients with liver cancer were used for this study. The registration method combines automatic vessel segmentation with an adapted version of thin-plate spline robust point matching. The vessel segmentation uses a multiscale vesselness measure, which allows vessels of various thicknesses to be segmented. The nonrigid registration is point-based, and progressively improves the correspondence and transformation between two point sets. Moreover, the nonrigid registration is capable of identifying and handling outliers (points with no counterpart in the other set). We took advantage of the strengths of both methods and created a multiscale registration algorithm. First, thick vessels are registered, then with each new iteration thinner vessels are included in the registration (strategy A). We compared strategy A to a straightforward approach where vessels of various diameters are segmented and subsequently registered (strategy B). To assess the transformation accuracy, residual distances were calculated for vessel bifurcations. For anatomical validation, residual distances were calculated for additional anatomical landmarks within the liver. To estimate the extent of deformation, the residual distances for the aforementioned anatomical points were calculated after rigid registration. Liver deformations in the range of 2.8-10.7 mm were found after rigid registration of the CT and MR scans. Low residual distances for vessel bifurcations (average 1.6, range 1.3-1.9 mm) and additional anatomical landmarks (1.5, 1.1-2.4 mm) were found after nonrigid registration. A large amount of outliers were identified (25%-55%) caused by vessels present in only one of the image sets and false positives in the vesselness measure. The nonrigid registration was capable of handling these outliers as was demonstrated by the low residual distances. Both strategies yielded very similar results in registration accuracy, but strategy A was faster than strategy B (≥2.0 times). An accurate CT∕MR vessel-guided nonrigid registration for largely deformed livers was developed, tested, and validated. The method, combining vessel segmentation and point matching, was robust against differences in the segmented vessels. The authors conclude that nonrigid registration is required for accurate alignment of abdominal-compressed and uncompressed liver anatomy. Alignment of breath-hold MR and abdominal-compressed CT images can be used to improve tumor localization for liver SBRT.

Quick outlier-resilient entropy coder for space missions

More than a decade has passed since the Consultative Committee for Space Data Systems (CCSDS) made its recommendation for lossless data compression. The CCSDS standard is commonly used for scientific missions because it is a general-purpose lossless compression technique with a low computational cost which results in acceptable compression ratios. At the core of this compression algorithm it is the Rice coding method. Its performance rapidly degrades in the presence of outliers, as the Rice coder is conceived for noiseless data following geometric distributions. To overcome this problem we present here a new entropy coder, the so-called Prediction Error Coder (PEC), as well as its fully adaptive version (FAPEC) which we show is a reliable alternative to the CCSDS standard. We show that PEC and FAPEC achieve high compression ratios even when a large amount of outliers are present in the data. This is done by testing our compressors with synthetic and real data, comparing the compression ratios and processor requirements with those obtained using the CCSDS standard.

Weighting Method for a Linear Mixed Model

Maximum likelihood is a widely used estimation method in statistics. This method is model dependent and as such is criticized as being non robust. In this article, we consider using weighted likelihood method to make robust inferences for linear mixed models where weights are determined at both the subject level and the observation level. This approach is appropriate for problems where maximum likelihood is the basic fitting technique, but a subset of data points is discrepant with the model. It allows us to reduce the impact of outliers without complicating the basic linear mixed model with normally distributed random effects and errors. The weighted likelihood estimators are shown to be robust and asymptotically normal. Our simulation study demonstrates that the weighted estimates are much better than the unweighted ones when a subset of data points is far away from the rest. Its application to the analysis of deglutition apnea duration in normal swallows shows that the differences between the weighted and unweighted estimates are due to large amount of outliers in the data set.

A fast and automatic stereotactic registration with a single CT-slice

The paper presents an algorithm for the automatic registration of a stereotactic frame from a single slice captured by a computed tomography (CT) scanner. Such registration is needed in interventional radiology for CT-image guidance of a robotic assistant. Stereotactic registration is based on a set of line fiducials that produce a set of image points. Our objective is to achieve the automatic registration of a stereotactic frame in the presence of noisy data and outliers. To this end, a new formulation of the stereotactic registration problem with a single image is proposed, for any configuration of the fiducials. With very few fiducials, closed-form and numerical solutions are presented. This comes in useful for building a robust automatic line to point matching algorithm based on the RANSAC statistical method. Simulation and experimental results are presented and highlight the robustness properties of the algorithm. They show that the registration is accurate with moderate computing requirements even for a large amount of outliers.