A new kernelization framework for Mahalanobis distance learning algorithms

Chatpatanasiri, Ratthachat; Korsrilabutr, Teesid; Tangchanachaianan, Pasakorn; Kijsirikul, Boonserm

doi:10.1016/j.neucom.2009.11.037

Cited by 68 publications

(58 citation statements)

References 20 publications

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“…Many existing distance learning methods are not intuitively kernelizable. Recently, Chatpatanasiri et al, [16] showed various techniques of kernelizing some popular metric learning approaches. Their results are easily extended to this approach in order to learn nonlinear metrics.…”

Section: Mirror Descent For Metric Learningmentioning

confidence: 99%

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Mirror Descent for Metric Learning: A Unified Approach

Kunapuli

Shavlik

2012

Machine Learning and Knowledge Discovery in Databases

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Abstract. Most metric learning methods are characterized by diverse loss functions and projection methods, which naturally begs the question: is there a wider framework that can generalize many of these methods? In addition, ever persistent issues are those of scalability to large data sets and the question of kernelizability. We propose a unified approach to Mahalanobis metric learning: an online regularized metric learning algorithm based on the ideas of composite objective mirror descent (comid). The metric learning problem is formulated as a regularized positive semidefinite matrix learning problem, whose update rules can be derived using the comid framework. This approach aims to be scalable, kernelizable, and admissible to many different types of Bregman and loss functions, which allows for the tailoring of several different classes of algorithms. The most novel contribution is the use of the trace norm, which yields a sparse metric in its eigenspectrum, thus simultaneously performing feature selection along with metric learning.

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Section: Mirror Descent For Metric Learningmentioning

confidence: 99%

“…There are two primary approaches to kernelizing metric learning algorithms: one based on the direct application of the kernel trick, and the other based on the application of the Kernel Principal Components Analysis (KPCA) framework [16]. We use the first approach here.…”

Section: Kernel Mdmlmentioning

confidence: 99%

Mirror Descent for Metric Learning: A Unified Approach

Kunapuli

Shavlik

2012

Machine Learning and Knowledge Discovery in Databases

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“…Since we have n = ℓ + u total examples, the span of {φ i } has dimensionality n by our assumption. According to [16], each example φ i can be represented as ϕ i ∈ R n with respect to a new…”

Section: The Kpca-trick Algorithmmentioning

confidence: 99%

A unified semi-supervised dimensionality reduction framework for manifold learning

Chatpatanasiri

Kijsirikul

2010

Neurocomputing

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We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived under our framework are able to employ both labeled and unlabeled examples and are able to handle complex problems where data form separate clusters of manifolds. Our framework offers simple views, explains relationships among existing frameworks and provides further extensions which can improve existing algorithms. Furthermore, a new semi-supervised kernelization framework called "KPCA trick" is proposed to handle non-linear problems.

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“…The success of SVMs is therefore, highly dependent on the choice of kernels and usual ones, such the linear, the gaussian and the histogram intersection, may not be appropriate in order to capture the actual and the semantic similarity between images for some specific concepts. Better kernels based on tuning Mahalanobis distances were obtained by minimizing the ratio between intra and inter class distances [7,24,28] while others were designed using semidefinite programming [30]. In order to take extra advantage from different settings, multiple kernels (MKL) were also introduced [1,2,39,43,51] and consider convex (and possibly sparse) linear combinations of elementary kernels and proved to be more suitable [47].…”

Section: Introductionmentioning

confidence: 99%

Transductive Kernel Map Learning and Its Application Image Annotation

Vo¹,

Sahbi²

2012

Procedings of the British Machine Vision Conference 2012

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We introduce in this paper a novel image annotation approach based on maximum margin classification and a new class of kernels. The method goes beyond the naive use of existing kernels and their restricted combinations in order to design "model-free" transductive kernels applicable to interconnected image databases. The main contribution of our method includes the minimization of an energy function mixing i) a reconstruction term that factorizes a matrix of interconnected image data as a product of a learned dictionary and a learned kernel map ii) a fidelity term that ensures consistent label predictions with those provided in a training set and iii) a smoothness term which guarantees similar labels for neighboring data and allows us to iteratively diffuse kernel maps and labels from labeled to unlabeled images. Solving this minimization problem makes it possible to learn both a decision criterion and a kernel map that guarantee linear separability in a high dimensional space and good generalization performance. Experiments conducted on image annotation, show that our obtained kernel achieves at least comparable results with related state of the art methods on the MSRC and the Corel5k databases.

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A new kernelization framework for Mahalanobis distance learning algorithms

Cited by 68 publications

References 20 publications

Mirror Descent for Metric Learning: A Unified Approach

Mirror Descent for Metric Learning: A Unified Approach

A unified semi-supervised dimensionality reduction framework for manifold learning

Transductive Kernel Map Learning and Its Application Image Annotation

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