Conditionally Positive Definite Kernels for SVM Based Image Recognition

The One-Shot similarity measure has recently been introduced in the context of face recognition where it was used to produce state-of-the-art results. Given two vectors, their One-Shot similarity score reflects the likelihood of each vector belonging in the same class as the other vector and not in a class defined by a fixed set of "negative" examples. The potential of this approach has thus far been largely unexplored. In this paper we analyze the One-Shot score and show that: (1) when using a version of LDA as the underlying classifier, this score is a Conditionally Positive Definite kernel and may be used within kernel-methods (e.g., SVM), (2) it can be efficiently computed, and (3) that it is effective as an underlying mechanism for image representation. We further demonstrate the effectiveness of the One-Shot similarity score in a number of applications including multiclass identification and descriptor generation.

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“…CPD kernels can be used directly in translation invariant kernel-methods [32], specifically within SVM [5]. Moreover, as Prop.…”

Section: Analysis Of the Os Similaritymentioning

confidence: 99%

The One-Shot similarity kernel

Wolf

Hassner

Taigman

2009

2009 IEEE 12th International Conference on Computer Vision

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“…Since, conventional SVM also requires positive definite kernels, it is not possible to evaluate it using these kernels. However, in [3], conditionally positive definite kernels are used with SVM under some assumptions and we will investigate then in future. Furthermore, the modified SR-KDA is also compared with state-of-theart methods for multi-label classification namely BR-SVM [4], CMPLC-LP [13] …”

Section: Benchmark Methodsmentioning

confidence: 99%

“…That means positive definiteness has to be checked for kernels to be suitable in this method. But there are alternative kernels called conditional positive definite or indefinite kernels that have drawn attention during the last decade and proved successful in image recognition [3]. LDL T decomposition is applicable to symmetric matrices which are not positive definite.…”

Section: Introductionmentioning

confidence: 99%

Kernel Discriminant Analysis Using Triangular Kernel for Semantic Scene Classification

Tahir

Kittler

Yan

et al. 2009

2009 Seventh International Workshop on Content-Based Multimedia Indexing

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Semantic scene classification is a challenging research problem that aims to categorise images into semantic classes such as beaches, sunsets or mountains. This problem can be formulated as multi-labeled classification problem where an image can belong to more than one conceptual class such as sunsets and beaches at the same time. Recently, Kernel Discriminant Analysis combined with spectral regression (SR-KDA) has been successfully used for face, text and spoken letter recognition. But SR-KDA method works only with positive definite symmetric matrices. In this paper, we have modified this method to support both definite and indefinite symmetric matrices. The main idea is to use LDL T decomposition instead of Cholesky decomposition. The modified SR-KDA is applied to scene database involving 6 concepts. We validate the advocated approach and demonstrate that it yields significant performance gains when conditionally positive definite triangular kernel is used instead of positive definite symmetric kernels such as linear, polynomial or RBF. The results also indicate performance gains when compared with the state-of-the art multi-label methods for semantic scene classification.

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“…We further extended our experiments to use the Hyperbolic tangent kernel [22] for its resemblance with neural networks, and even being already demonstrated as less preferable than RBF kernels [10] have been found to perform well in practice. We also used the long-tailed Cauchy kernel from Basak [23] and the Log kernel [24]. Though there are studies involving the development and adaptations of new kernels using heuristics [25,26], we intended to evaluate current literature's kernels and not to create dataset-specific kernels.…”

Section: Methodsmentioning

confidence: 99%

On the parameter optimization of Support Vector Machines for binary classification

Gaspar

Carbonell

Oliveira

2012

Journal of Integrative Bioinformatics

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SummaryClassifying biological data is a common task in the biomedical context. Predicting the class of new, unknown information allows researchers to gain insight and make decisions based on the available data. Also, using classification methods often implies choosing the best parameters to obtain optimal class separation, and the number of parameters might be large in biological datasets. Support Vector Machines provide a well-established and powerful classification method to analyse data and find the minimal-risk separation between different classes. Finding that separation strongly depends on the available feature set and the tuning of hyper-parameters. Techniques for feature selection and SVM parameters optimization are known to improve classification accuracy, and its literature is extensive. In this paper we review the strategies that are used to improve the classification performance of SVMs and perform our own experimentation to study the influence of features and hyper-parameters in the optimization process, using several known kernels.

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Conditionally Positive Definite Kernels for SVM Based Image Recognition

Cited by 49 publications

References 3 publications

The One-Shot similarity kernel

The One-Shot similarity kernel

Kernel Discriminant Analysis Using Triangular Kernel for Semantic Scene Classification

On the parameter optimization of Support Vector Machines for binary classification

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