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We review a multiple kernel learning (MKL) technique called lp regularised multiple kernel Fisher discriminant analysis (MK-FDA), and investigate the effect of feature space denoising on MKL. Experiments show that with both the or...
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We review a multiple kernel learning (MKL) technique called lp regularised multiple kernel Fisher discriminant analysis (MK-FDA), and investigate the effect of feature space denoising on MKL. Experiments show that with both the original kernels or denoised kernels, ip MK-FDA outperforms its fixed-norm counterparts. Experiments also show that feature space denoising boosts the performance of both single kernel FDA and £p MK-FDA, and that there is a positive correlation between the learnt kernel weights and the amount of variance kept by feature space denoising. Based on these observations, we argue that in the case where the base feature spaces are noisy, linear combination of kernels cannot be optimal. An MKL objective function which can take care of feature space denoising automatically, and which can learn a truly optimal (non-linear) combination of the base kernels, is yet to be found.
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摘要 :
We review a multiple kernel learning (MKL) technique called lp regularised multiple kernel Fisher discriminant analysis (MK-FDA), and investigate the effect of feature space denoising on MKL. Experiments show that with both the or...
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We review a multiple kernel learning (MKL) technique called lp regularised multiple kernel Fisher discriminant analysis (MK-FDA), and investigate the effect of feature space denoising on MKL. Experiments show that with both the original kernels or denoised kernels, ip MK-FDA outperforms its fixed-norm counterparts. Experiments also show that feature space denoising boosts the performance of both single kernel FDA and £p MK-FDA, and that there is a positive correlation between the learnt kernel weights and the amount of variance kept by feature space denoising. Based on these observations, we argue that in the case where the base feature spaces are noisy, linear combination of kernels cannot be optimal. An MKL objective function which can take care of feature space denoising automatically, and which can learn a truly optimal (non-linear) combination of the base kernels, is yet to be found.
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Kernel method is one of the promising approaches to learning with tree-structured data, and various efficient tree kernels have been proposed to capture informative structures in trees. In this paper, we propose a new tree kernel ...
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Kernel method is one of the promising approaches to learning with tree-structured data, and various efficient tree kernels have been proposed to capture informative structures in trees. In this paper, we propose a new tree kernel function based on "subpath sets" to capture vertical structures in rooted unordered trees, since such tree-structures are often used to code hierarchical information in data. We also propose a simple and efficient algorithm for computing the kernel by extending the multikey quicksort algorithm used for sorting strings. The time complexity of the algorithm is O((|T1| + |T2|)log(|T1| + |T2|)) time on average, and the space complexity is O([T1| + |T2|), where |T1| and |T2| are the numbers of nodes in two trees T1 and T2. We apply the proposed kernel to two supervised classification tasks, XML classification in web mining and glycan classification in bioinformatics. The experimental results show that the predictive performance of the proposed kernel is competitive with that of the existing efficient tree kernel for unordered trees proposed by Vishwanathan et al. [1], and is also empirically faster than the existing kernel.
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摘要 :
Kernel method is one of the promising approaches to learning with tree-structured data, and various efficient tree kernels have been proposed to capture informative structures in trees. In this paper, we propose a new tree kernel ...
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Kernel method is one of the promising approaches to learning with tree-structured data, and various efficient tree kernels have been proposed to capture informative structures in trees. In this paper, we propose a new tree kernel function based on "subpath sets" to capture vertical structures in rooted unordered trees, since such tree-structures are often used to code hierarchical information in data. We also propose a simple and efficient algorithm for computing the kernel by extending the multikey quicksort algorithm used for sorting strings. The time complexity of the algorithm is O((|T1| + |T2|)log(|T1| + |T2|)) time on average, and the space complexity is O([T1| + |T2|), where |T1| and |T2| are the numbers of nodes in two trees T1 and T2. We apply the proposed kernel to two supervised classification tasks, XML classification in web mining and glycan classification in bioinformatics. The experimental results show that the predictive performance of the proposed kernel is competitive with that of the existing efficient tree kernel for unordered trees proposed by Vishwanathan et al. [1], and is also empirically faster than the existing kernel.
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Successful clustering of multiple objects using kernels, heavily relies on the proper selection of kernel parameters. This can be a computationally complex process and may necessitate prior knowledge of label information. In this ...
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Successful clustering of multiple objects using kernels, heavily relies on the proper selection of kernel parameters. This can be a computationally complex process and may necessitate prior knowledge of label information. In this paper, a novel method has been introduced that is computationally efficient and requires no prior information. The method relies on the eigenvalues of each kernel matrix to determine a proper linear combination of kernels among a dictionary of kernels that results in good clustering. A difference of convex functions formulation is proposed and solved via an algorithmically simple method which is extremely cost-effective in implementation. Comparisons using various forms of real-world data with two popular supervised methods show its superior performance.
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We present novel kernels that measure similarity of two RNA sequences, taking account of their secondary structures. Two types of kernels are presented. One is for RNA sequences with known secondary structures, the other for those...
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We present novel kernels that measure similarity of two RNA sequences, taking account of their secondary structures. Two types of kernels are presented. One is for RNA sequences with known secondary structures, the other for those without known secondary structures. The latter employs stochastic context-free grammar (SCFG) for estimating the secondary structure. We call the latter the marginalized count kernel (MCK). We show computational experiments for MCK using 74 sets of human tRNA sequence data:(i) kernel principal component analysis (PCA) for visualizing tRNA similarities, (ii) supervised classification with support vector machines (SVMs). Both types of experiment show promising results for MCKs.
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Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this wo...
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Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we focus our attention on the complex gaussian kernel and its possible application in the complex Kernel LMS algorithm. In order to derive the gradients needed to develop the complex kernel LMS (CKLMS), we employ the powerful tool of Wirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, the notion of Writinger's calculus is extended to include complex RKHSs. Experiments verify that the CKLMS offers significant performance improvements over the traditional complex LMS or Widely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities.
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摘要 :
Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this wo...
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Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we focus our attention on the complex gaussian kernel and its possible application in the complex Kernel LMS algorithm. In order to derive the gradients needed to develop the complex kernel LMS (CKLMS), we employ the powerful tool of Wirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, the notion of Writinger's calculus is extended to include complex RKHSs. Experiments verify that the CKLMS offers significant performance improvements over the traditional complex LMS or Widely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities.
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In this paper, we introduce a unified String Kernel. Based on this unified string kernel, we construct improved sparse kernel and composite kernel. Using the same target families and the same test and training set splits as in the...
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In this paper, we introduce a unified String Kernel. Based on this unified string kernel, we construct improved sparse kernel and composite kernel. Using the same target families and the same test and training set splits as in the protein classification experiments from We-ston, we do experiments with these new kernels. The results show that our kernels are superior to previously developed string kernel.
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