Non-Mercer Kernels for SVM Object Recognition

Boughorbel, Sabri; Tarel, Jean-Philippe; Fleuret, François

doi:10.5244/c.18.16

Cited by 53 publications

(46 citation statements)

References 15 publications

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“…Our experimental evaluation is similar to that reported in [2], also showing that the match kernel satisfies the three conditions above.…”

Section: Exact Recognition With Local Features: the Match Kernelsupporting

confidence: 74%

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A Performance Evaluation of Exact and Approximate Match Kernels for Object Recognition

Caputo¹,

Luo²

2010

ELCVIA

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Local features have repeatedly shown their effectiveness for object recognition during the last years, and they have consequently become the preferred descriptor for this type of problems. The solution of the correspondence problem is traditionally approached with exact or approximate techniques. In this paper we are interested in methods that solve the correspondence problem via the definition of a kernel function that makes it possible to use local features as input to a support vector machine. We single out the match kernel, an exact approach, and the pyramid match kernel, that uses instead an approximate strategy. We present a thorough experimental evaluation of the two methods on three different databases. Results show that the exact method performs consistently better than the approximate one, especially for the object identification task, when training on a decreasing number of images. Based on these findings and on the computational cost of each approach, we suggest some criteria for choosing between the two kernels given the application at hand.

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“…Our experimental evaluation is similar to that reported in [2], also showing that the match kernel satisfies the three conditions above.…”

Section: Exact Recognition With Local Features: the Match Kernelsupporting

confidence: 74%

“…Boughorbel et al [2] introduced a new definition of kernel positiveness based on a statistical approach. Their definition is such that includes most of Mercer kernels, and it shows that matching kernels are statistically positive definite.…”

Section: Exact Recognition With Local Features: the Match Kernelmentioning

confidence: 99%

A Performance Evaluation of Exact and Approximate Match Kernels for Object Recognition

Caputo¹,

Luo²

2010

ELCVIA

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“…This behavior might be due to several factors: to begin with, the matching kernel is not a Mercer kernel [5], which might affect the algorithm. Also, the algorithm does not reach a plateau in the SVs growth because, in the induced space of the matching kernel, there seems to be a high probability that pair of training points are orthogonal, or almost orthogonal, to each other (notice that, as the kernel is not a Mercer one, the geometric interpretation might not be valid).…”

Section: Place Recognition Via Oisvmsmentioning

confidence: 99%

“…In the experiments, we consider both exponential χ 2 kernel for SVM (when use CRFH), and local kernels [30] (SIFT). Note the kernel in [30] is not always positive semidefinite [5], so this is also a test on non-Mercer kernels that have proved useful for visual recognition. The kernels used are infinite-dimensional, so for both kernels we run the OISVM using different values of η.…”

Section: Place Recognition Via Oisvmsmentioning

confidence: 99%

Indoor Place Recognition using Online Independent Support Vector Machines

Orabona¹,

Castellini²,

Caputo³

et al. 2007

Procedings of the British Machine Vision Conference 2007

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In the framework of indoor mobile robotics, place recognition is a challenging task, where it is crucial that self-localization be enforced precisely, notwithstanding the changing conditions of illumination, objects being shifted around and/or people affecting the appearance of the scene. In this scenario online learning seems the main way out, thanks to the possibility of adapting to changes in a smart and flexible way. Nevertheless, standard machine learning approaches usually suffer when confronted with massive amounts of data and when asked to work online. Online learning requires a high training and testing speed, all the more in place recognition, where a continuous flow of data comes from one or more cameras. In this paper we follow the Support Vector Machines-based approach of Pronobis et al. [26], proposing an improvement that we call Online Independent Support Vector Machines. This technique exploits linear independence in the image feature space to incrementally keep the size of the learning machine remarkably small while retaining the accuracy of a standard machine. Since the training and testing time crucially depend on the size of the machine, this solves the above stated problems. Our experimental results prove the effectiveness of the approach.

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“…Counter examples can be found to prove that such kernels are actually not positive definite, see [10]. Although Matching kernels have been successfully applied for recognitions tasks [8], [10], their use is risky since we no longer insure that the SVM maximizes the margin in some space. Moreover, there is always a potential risk that SVM does not converge.…”

Section: Matching Kernelmentioning

confidence: 99%