Composite kernel learning

Szafranski, Marie; Grandvalet, Yves; Rakotomamonjy, Alain

doi:10.1145/1390156.1390287

Cited by 30 publications

(11 citation statements)

References 28 publications

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“…Kernel learning machines have been widely used in machine learning and pattern recognition [69], [70], [71], [72], it has been proven that the kernel machines have a stronger mathematical slant than earlier machine learning method (e.g., neural networks) and also attract significant interest from the statistics and mathematics community [17]. Meanwhile, these kernel machines are becoming particularly popular in target tracking; exceptionally in complex environment that kernel based tracking cannot give good performance.…”

Section: Kernel-based Learningmentioning

confidence: 99%

Review on Kernel based Target Tracking for Autonomous Driving

Wang

Yue

Dong

et al. 2016

Journal of Information Processing

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Significant progress has been made in the field of autonomous driving during the past decades. However, fully autonomous driving in urban traffic is still extremely difficult in the near future. Visual tracking of vehicles or pedestrians is an essential part of autonomous driving. Among these tracking methods, kernel-based object tracking is an effective means of tracking in video sequences. This paper reviews the kernel theory adopted in target tracking of autonomous driving and makes a qualitative and quantitative comparison among several well-known kernel based methods. The theoretical and experimental analysis allow us to conclude that the kernel based online subspace learning algorithm achieves a good trade-off between the stability and real-time processing for target tracking in the practical application environments of autonomous driving. This paper reports on the result of evaluating the performances of five algorithms by using seven video sequences.

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Section: Kernel-based Learningmentioning

confidence: 99%

Review on Kernel based Target Tracking for Autonomous Driving

Wang

Yue

Dong

et al. 2016

Journal of Information Processing

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“…To overcome this problem, non-sparse MK-SVMs based on 2 regularisation and the general case of p (p ≥ 1) regularisation have been proposed in [14,15]. Other works on the regularisation norm in MK-SVM include composite kernel learning [29] and mixed norm kernel learning [21].…”

Section: Related Work: Multiple Kernel Learningmentioning

confidence: 99%

“…Note that putting an p constraint on β or penalizing w by an q norm are equivalents with p = q/(2 − q) [15,29]. When p = 1 we have the 1 MK-FDA; while p = ∞ leads to q = 2, and MK-FDA reduces to the regular kernel FDA with concatenation of feature spaces.…”

Section: Binary Casementioning

confidence: 99%

ℓ<inf>p</inf> norm multiple kernel Fisher discriminant analysis for object and image categorisation

Yan

Mikolajczyk

Barnard

et al. 2010

2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition

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In this paper, we generalise multiple kernel Fisher discriminant analysis (MK-FDA) such that the kernel weights can be regularised with an p norm for any p ≥ 1, in contrast to existing MK-FDA that uses either l1 or l2 norm. We present formulations for both binary and multiclass cases and solve the associated optimisation problems efficiently with semi-infinite programming. We show on three object and image categorisation benchmarks that by learning the intrinsic sparsity of a given set of base kernels using a validation set, the proposed p MK-FDA outperforms its fixed-norm counterparts, and is capable of producing stateof-the-art performance. Moreover, we show that our p MK-FDA outperforms the p multiple kernel support vector machine ( p MK-SVM) which has been recently proposed. Based on this observation and our experience with single kernel FDA and SVM, we argue that the almost century-old FDA is still a strong competitor of the popular SVM.

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“…Rakotomamonjy et al (2007Rakotomamonjy et al ( , 2008 proposed simple MKL by exploring an adaptive 2-norm regularization formulation. Szafranski et al (2010), Xu et al (2010) and Subrahmanya and Shin (2010) constructed the connection between MKL and group-LASSO to model group structure. Most of them were based on implicit kernel mapping (IKM) (Muller et al 2001).…”

Section: Introductionmentioning

confidence: 99%

Reduced multiple empirical kernel learning machine

2014

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Multiple kernel learning (MKL) is demonstrated to be flexible and effective in depicting heterogeneous data sources since MKL can introduce multiple kernels rather than a single fixed kernel into applications. However, MKL would get a high time and space complexity in contrast to single kernel learning, which is not expected in real-world applications. Meanwhile, it is known that the kernel mapping ways of MKL generally have two forms including implicit kernel mapping and empirical kernel mapping (EKM), where the latter is less attracted. In this paper, we focus on the MKL with the EKM, and propose a reduced multiple empirical kernel learning machine named RMEKLM for short. To the best of our knowledge, it is the first to reduce both time and space complexity of the MKL with EKM. Different from the existing MKL, the proposed RMEKLM adopts the Gauss Elimination technique to extract a set of feature vectors, which is validated that doing so does not lose much information of the original feature space. Then RMEKLM adopts the extracted feature vectors to span a reduced orthonormal subspace of the feature space, which is visualized in terms of the geometry structure. It can be demonstrated that the spanned subspace is isomorphic to the original feature space, which means that the dot product of two vectors in the original feature space is equal to that of the two corresponding vectors in the generated orthonormal subspace. More importantly, the proposed RMEKLM brings a simpler computation and meanwhile needs a less storage space, especially in the processing of testing. Finally, the experimental results show that RMEKLM owns a much efficient and effective performance in terms of both complexity and classification. The contributions of this paper can be given as follows: (1) by mapping the input space into an orthonormal subspace, the geometry of the generated subspace is visualized; (2) this paper first reduces both the time and space complexity of the EKM-based MKL; (3) this paper adopts the Gauss Elimination, one of the on-the-shelf techniques, to generate a basis of the original feature space, which is stable and efficient.

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Composite kernel learning

Cited by 30 publications

References 28 publications

Review on Kernel based Target Tracking for Autonomous Driving

Review on Kernel based Target Tracking for Autonomous Driving

ℓ<inf>p</inf> norm multiple kernel Fisher discriminant analysis for object and image categorisation

Reduced multiple empirical kernel learning machine

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Composite kernel learning

Cited by 30 publications

References 28 publications

Review on Kernel based Target Tracking for Autonomous Driving

Review on Kernel based Target Tracking for Autonomous Driving

&#x2113;<inf>p</inf> norm multiple kernel Fisher discriminant analysis for object and image categorisation

Reduced multiple empirical kernel learning machine

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Product

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ℓ<inf>p</inf> norm multiple kernel Fisher discriminant analysis for object and image categorisation