In the Galerkin weak form technique based on various kernels that they do not have 8Kronecker property, in order to apply the essential boundary condition, there are two straight strategies that one of them is the Lag...
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In the Galerkin weak form technique based on various kernels that they do not have 8Kronecker property, in order to apply the essential boundary condition, there are two straight strategies that one of them is the Lagrange multiplier method and another one is the penalty method. In the penalty method the main boundary value problem (BVP) is converted to a new BVP with Robin boundary condition. So, we obtain a new BVP that it must be solved. The main purpose of this paper is to propose an error analysis to verify that the solutions of penalty method obtained by applying the essential boundary condition are convergent to the solution of main BVP with essential boundary condition. For this aim, we select fractional modified distributed-order anomalous sub-diffusion equation. At the first stage, we propose a second-order difference scheme for the temporal variable. The convergence and stability analysis for the time-discrete scheme are proposed. At the second stage, we derive the full-discrete scheme based on the Galerkin weak form and shape functions of reproducing kernel particle method (RKPM) as the mentioned shape functions do not have the 8-Kronecker property. Furthermore, it is shown that when the penalty parameter goes to infinity then the solutions of BVP with Robin boundary condition are convergent to the solutions of BVP based on the essential boundary condition. The proposed examples verify that the present error estimate is true. (c) 2020 Elsevier Inc. All rights reserved.
Several applications, like malicious URL detection and web spam detection, require classification on very high-dimensional data. In such cases anomalous data is hard to find but normal data is easily available. As suc...
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ISBN:
(纸本)9781450383325
Several applications, like malicious URL detection and web spam detection, require classification on very high-dimensional data. In such cases anomalous data is hard to find but normal data is easily available. As such it is increasingly common to use a one-class classifier (OCC). Unfortunately, most OCC algorithms cannot scale to datasets with extremely high dimensions. In this paper, we present Fast Random projection-based One-Class Classification (FROCC), an extremely efficient, scalable and easily parallelizable method for one-class classification with provable theoretical guarantees. Our method is based on the simple idea of transforming the training data by projecting it onto a set of random unit vectors that are chosen uniformly and independently from the unit sphere, and bounding the regions based on separation of the data. FROCC can be naturally extended with kernels. We provide a new theoretical framework to prove that that FROCC generalizes well in the sense that it is stable and has low bias for some parameter settings. We then develop a fast scalable approximation of FROCC using vectorization, exploiting data sparsity and parallelism to develop a new implementation called ParDFROCC. ParDFROCC achieves up to 2 percent points better ROC than the next best baseline, with up to 12x speedup in training and test times over a range of state-of-the-art benchmarks for the OCC task.
This paper proposes a novel approach to improve the kernel-based Word Sense Disambiguation (WSD). We first explain why linear kernels are more suitable to WSD and many other natural language processing problems than t...
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ISBN:
(纸本)9781424427796
This paper proposes a novel approach to improve the kernel-based Word Sense Disambiguation (WSD). We first explain why linear kernels are more suitable to WSD and many other natural language processing problems than translation-invariant kernels. based on the linear kernel, two external knowledge sources are integrated. One comprises a set of linguistic rules to find the crucial features. For the other, a distributional similarity thesaurus is used to alleviate data sparseness by generalizing crucial features when they do not match the word-form exactly. The experiments show that we have outperformed the state-of-the-art system on the benchmark data from English lexical sample task of SemEval-2007 and the improvement is statistically significant.
This paper presents a face detection methodbased on kernel Fisher Discriminant analysis (KFD). kernel based methods have been extensively investigated both in theories and applications, such as SVM and kernel PCA. Us...
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ISBN:
(纸本)0769521223
This paper presents a face detection methodbased on kernel Fisher Discriminant analysis (KFD). kernel based methods have been extensively investigated both in theories and applications, such as SVM and kernel PCA. Using the kernel trick, Linear Fisher Discriminant can be extended to non-linear case. Since the distribution of face patterns is very complex and highly nonlinear, using nonlinear classification tools can hopefully tackle the problem of face detection. We explore the application of KFD in the task of frontal face detection. The experimental results prove the effectiveness of KFD in the face detection problem.
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