Spectral clustering with the probabilistic cluster kernel

Izquierdo‐Verdiguier, Emma; Jenssen, Robert; Gómez-Chova, Luis; Camps‐Valls, Gustau

doi:10.1016/j.neucom.2014.08.068

Cited by 20 publications

(31 citation statements)

References 10 publications

(12 reference statements)

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“…Thus, we are able to construct a kernel function that is robust with regards to parameter choice. This way of constructing a robust kernel is similar to the methodology used in ensemble clustering and recent work in spectral clustering [6]. However, such recent methods are not able to explicitly handle missing data.…”

Section: Pckid -A Probabilistic Cluster Kernel For Incomplete Datamentioning

confidence: 97%

“…In this paper, we propose as a new approach to integrate in a synergistic manner recent advances in spectral clustering and kernel methods with existing probabilistic methods for dealing with incomplete data. In particular, we exploit the Probabilistic Cluster Kernel (PCK) framework [6], which combines posterior distributions of Gaussian Mixture Models (GMMs) on different scales to learn a robust kernel function, capturing similarities on both a global and local scale. This kernel function is robust with regards to hyperparameter choices, since instead of assuming some structure in the data, the ensemble of GMMs adapt to the data manifold.…”

Section: Introductionmentioning

confidence: 99%

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Spectral Clustering Using PCKID – A Probabilistic Cluster Kernel for Incomplete Data

et al. 2017

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Abstract. In this paper, we propose PCKID, a novel, robust, kernel function for spectral clustering, specifically designed to handle incomplete data. By combining posterior distributions of Gaussian Mixture Models for incomplete data on different scales, we are able to learn a kernel for incomplete data that does not depend on any critical hyperparameters, unlike the commonly used RBF kernel. To evaluate our method, we perform experiments on two real datasets. PCKID outperforms the baseline methods for all fractions of missing values and in some cases outperforms the baseline methods with up to 25 percentage points.

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Section: Pckid -A Probabilistic Cluster Kernel For Incomplete Datamentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Spectral Clustering Using PCKID – A Probabilistic Cluster Kernel for Incomplete Data

et al. 2017

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“…To stress this fact, in our experiments we consider the probabilistic cluster kernel (PCK), a kernel function that is the result of a feature generation procedure. PCK is robust with respect to hyperparameter choices and has been shown to often outperform counterparts such as the radial basis function (RBF) kernel [23].…”

Section: Contribution and Paper Organizationmentioning

confidence: 99%

“…The Probabilistic Cluster Kernel (PCK) [23] is a robust kernel function, which automatically adapts to the inherent structures in the data. Its robustness comes from the fact that it does not depend on any critical user-specified hyperparameters, like the width in Gaussian kernels.…”

Section: Probabilistic Cluster Kernelmentioning

confidence: 99%

The deep kernelized autoencoder

Kampffmeyer¹,

Løkse²,

Bianchi³

et al. 2018

Applied Soft Computing

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Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel machines have experienced great success by operating via inner-products in a theoretically well-defined reproducing kernel Hilbert space, hence capturing topological properties of input data. In this paper, we enhance the autoencoder's ability to learn effective data representations by aligning inner products between codes with respect to a kernel matrix. By doing so, the proposed kernelized autoencoder allows learning similarity-preserving embeddings of input data, where the notion of similarity is explicitly controlled by the user and encoded in a positive semi-definite kernel matrix. Experiments are performed for evaluating both reconstruction and kernel alignment performance in classification tasks and visualization of high-dimensional data. Additionally, we show that our method is capable to emulate kernel principal component analysis on a denoising task, obtaining competitive results at a much lower computational cost.

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“…Additionally, our method applies to arbitrary kernel functions, even the ones computed through ensemble methods. To stress this fact, we consider in our experiments the probabilistic cluster kernel, a kernel function that is robust with regards to hyperparameter choices and has been shown to often outperform counterparts such as the RBF kernel [14].…”

Section: Introductionmentioning

confidence: 99%

Deep Kernelized Autoencoders

et al. 2017

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Abstract. In this paper we introduce the deep kernelized autoencoder, a neural network model that allows an explicit approximation of (i) the mapping from an input space to an arbitrary, user-specified kernel space and (ii) the back-projection from such a kernel space to input space. The proposed method is based on traditional autoencoders and is trained through a new unsupervised loss function. During training, we optimize both the reconstruction accuracy of input samples and the alignment between a kernel matrix given as prior and the inner products of the hidden representations computed by the autoencoder. Kernel alignment provides control over the hidden representation learned by the autoencoder. Experiments have been performed to evaluate both reconstruction and kernel alignment performance. Additionally, we applied our method to emulate kPCA on a denoising task obtaining promising results.

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Spectral clustering with the probabilistic cluster kernel

Cited by 20 publications

References 10 publications

Spectral Clustering Using PCKID – A Probabilistic Cluster Kernel for Incomplete Data

Spectral Clustering Using PCKID – A Probabilistic Cluster Kernel for Incomplete Data

The deep kernelized autoencoder

Deep Kernelized Autoencoders

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