Kernel Trick Embedded Gaussian Mixture Model

Wang, Jingdong; Lee, Jianguo; Zhang, Changshui

doi:10.1007/978-3-540-39624-6_14

Cited by 24 publications

(8 citation statements)

References 12 publications

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“…Kernelized versions of Gaussian mixture models were introduced in the unsupervised (Wang et al 2003) and supervised (Xu et al 2009) classification contexts. These methods do not estimate the smallest eigenvalues of the kernel matrix from the data but use instead a constant threshold.…”

Section: Links With Existing Workmentioning

confidence: 99%

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Bouveyron¹,

Fauvel²,

Girard³

2014

Stat Comput

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International audienceThis work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the eigen-decomposition of the Gaussian processes modeling each class. This allows in particular to use non-linear mapping functions which project the observations into infinite dimensional spaces. It is also demonstrated that the building of the classifier can be directly done from the observation space through a kernel function. The proposed classification method is thus able to classify data of various types such as categorical data, functional data or networks. Furthermore, it is possible to classify mixed data by combining different kernels. The methodology is as well extended to the unsupervised classification case. Experimental results on various data sets demonstrate the effectiveness of the proposed method

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Section: Links With Existing Workmentioning

confidence: 99%

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Bouveyron¹,

Fauvel²,

Girard³

2014

Stat Comput

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“…. , L which is usually necessary in kernelized versions of Gaussian mixture models, see for instance [13,32,35,44,46]. In practice, d k is estimated thanks to the scree-test of Cattell [11] which looks for a break in the eigenvalues scree.…”

Section: Classi Cation With Binary Predictors Using a Kernel Functionmentioning

confidence: 99%

A classification method for binary predictors combining similarity measures and mixture models

Sylla

Girard

Diongue

et al. 2015

Dependence Modeling

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In this paper, a new supervised classification method dedicated to binary predictors is proposed. Its originality is to combine a model-based classification rule with similarity measures thanks to the introduction of new family of exponential kernels. Some links are established between existing similarity measures when applied to binary predictors. A new family of measures is also introduced to unify some of the existing literature. The performance of the new classification method is illustrated on two real datasets (verbal autopsy data and handwritten digit data) using 76 similarity measures.

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“…The kernel Gaussian mixture model [18] can also find non-Gaussian shaped clusters. This model estimates a GMM in the implicit high-dimensional feature space defined by the kernel mapping of the observed space.…”

Section: Related Workmentioning

confidence: 99%

Warped Mixtures for Nonparametric Cluster Shapes

Iwata¹,

Duvenaud²,

Ghahramani³

2012

Preprint

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A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allows us to summarize the properties of the high-dimensional clusters (or density manifolds) describing the data. The number of manifolds, as well as the shape and dimension of each manifold is automatically inferred. We derive a simple inference scheme for this model which analytically integrates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, performs better than infinite Gaussian mixture models at recovering the true number of clusters, and produces interpretable summaries of high-dimensional datasets.

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Kernel Trick Embedded Gaussian Mixture Model

Cited by 24 publications

References 12 publications

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

A classification method for binary predictors combining similarity measures and mixture models

Warped Mixtures for Nonparametric Cluster Shapes

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