Outliers In Training Samples Research Articles

Fuzzy SVM-Based Coding Unit Decision in HEVC

The latest video compression standard, High Efficiency Video Coding (HEVC), has greatly improved the coding efficiency compared to the predecessor H.264/AVC. However, equipped with the quadtree structure of coding tree unit partition and other sophisticated coding tools, HEVC brings a significant increase in the computational complexity. To address this issue, a coding unit (CU) decision method based on fuzzy support vector machine (SVM) is proposed for rate-distortion-complexity (RDC) optimization, where the process of CU decision is formulated as a cascaded multi-level classification task. The optimal feature set is selected according to a defined misclassification cost and a risk area is introduced for an uncertain classification output. To further improve the RDC performance, different regulation parameters in SVM are adopted and outliers in training samples are eliminated. Additionally, the proposed CU decision method is incorporated into a joint RDC optimization framework, where the width of risk area is adaptively adjusted to allocate flexible computational complexity to different CUs, aiming at minimizing computational complexity under a configurable constraint in terms of RD performance degradation. Experimental results show that the proposed approach can reduce 58.9% and 55.3% computational complexity on average with the values of Bjønteggard delta peak-signal-to-noise ratio as -0.075 dB and -0.085 dB and the values of Bjøntegaard delta bit rate as 2.859% and 2.671% under low delay P and random access configurations, respectively, which has outperformed the state-of-the-art fast algorithms based on statistical information and machine learning.

Multimode Process Fault Detection Based on Local Density Ratio-Weighted Support Vector Data Description

Industrial process fault detection plays an important role for process security, and data-based process monitoring is an effective way to detect fault. Industrial processes typically have multiple operating modes with different data distribution and outliers. This paper proposes a novel multimode process fault detection method based on local density ratio-weighted support vector data description (LDR-wSVDD) to address the multimodal process monitoring with different density and outliers in training samples. By considering both global density distribution and local data structure, this method provides a weight for each training sample based on its density information to make sure that the outliers with lower weight have less influence on the normal sample model. Meanwhile, it maintains the efficiency of SVDD single hypersphere model for multimode processes. The feasibility and validity of the LDR-wSVDD approach for multimode multidensity process monitoring are demonstrated through a numerical example and T...

Breakdown Point of Robust Support Vector Machines

Support vector machine (SVM) is one of the most successful learning methods for solving classification problems. Despite its popularity, SVM has the serious drawback that it is sensitive to outliers in training samples. The penalty on misclassification is defined by a convex loss called the hinge loss, and the unboundedness of the convex loss causes the sensitivity to outliers. To deal with outliers, robust SVMs have been proposed by replacing the convex loss with a non-convex bounded loss called the ramp loss. In this paper, we study the breakdown point of robust SVMs. The breakdown point is a robustness measure that is the largest amount of contamination such that the estimated classifier still gives information about the non-contaminated data. The main contribution of this paper is to show an exact evaluation of the breakdown point of robust SVMs. For learning parameters such as the regularization parameter, we derive a simple formula that guarantees the robustness of the classifier. When the learning parameters are determined with a grid search using cross-validation, our formula works to reduce the number of candidate search points. Furthermore, the theoretical findings are confirmed in numerical experiments. We show that the statistical properties of robust SVMs are well explained by a theoretical analysis of the breakdown point.

Adaptive weighted least square support vector machine regression integrated with outlier detection and its application in QSAR

In order to eliminate the influence of unavoidable outliers in training sample on a model's performance, a novel least square support vector machine regression, which combines outlier detection approach and adaptive weight value for the training sample, is proposed and named as adaptive weighted least square support vector machine regression (AWLS-SVM). Firstly, the effective robust 3 σ principle is used to detect marked outliers for the training sample. Secondly, based on the training sample without marked outliers, least square support vector machine regression is employed to develop the model and the fitting error of each sample data is obtained. Thirdly, according to the fitting error of each sample data, the initial weight is calculated. The bigger the fitting error of sample data is, the smaller the weight value of the sample data. Thus, the potential outliers, which are not detected by the robust 3 σ principle and have bigger fitting errors, have smaller weight values to reduce the influence of the potential outliers on the performance of model. Then, LS-SVM is applied for the weighted sample to develop the model again. Finally, via the proposed weight value iterative method, the weight values of the training sample are converged, and the model with good predicting performance is obtained. To illustrate the performance of AWLS-SVM, simulation experiment is designed to produce the training sample with marked outlier and some non-marked outliers. AWLS-SVM, AWLS-SVM without the robust 3 σ principle, LS-SVM with the robust 3 σ principle, LS-SVM, and radial basis function network are applied to develop the model based on the designed sample. The results show that the influence of marked and un-marked outliers on the model's performance is eliminated by AWLS-SVM, and that the predicting performance of AWLS-SVM is the best. Furthermore, the AWLS-SVM method was applied to develop the quantitative structure–activity relationships (QSAR) model of HIV-1 protease inhibitors, and the satisfactory result was obtained.