Image Segmentation Based on Multi-Kernel Learning and Feature Relevance Analysis

Molina-Giraldo, S.; Álvarez-Meza, Andrés Marino; Peluffo-Ordóñez, Diego H.; Castellanos-Domínguez, Germán

doi:10.1007/978-3-642-34654-5_51

Cited by 12 publications

(7 citation statements)

References 9 publications

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“…This clustering technique has been widely used in a large amount of applications such as human motion analysis and people identification [1], image segmentation [2,3] and video analysis [4], among others. What makes spectral analysis applied to data clustering appealing is the use of the eigenvalue and eigenvector decomposition in order to obtain the local optima closest to the global continuous optima.…”

Section: Graph-based Approachesmentioning

confidence: 99%

“…Some of their remarkable applications to be mentioned are human motion analysis and people identification [1], image segmentation [2,3] and video analysis [4], among others. The spectral clustering techniques carry out the grouping task without any prior knowledge -indication or hints about the structure of data to be grouped-and then partitions are built from the information obtained by the clustering process itself.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Spectral Clustering for Dynamic Data

Peluffo-Ordóñez

Alvarado-Pérez

Castro-Ospina

2015

Lecture Notes in Computer Science

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Abstract. Spectral clustering has shown to be a powerful technique for grouping and/or rank data as well as a proper alternative for unlabeled problems. Particularly, it is a suitable alternative when dealing with pattern recognition problems involving highly hardly separable classes. Due to its versatility, applicability and feasibility, this clustering technique results appealing for many applications. Nevertheless, conventional spectral clustering approaches lack the ability to process dynamic or time-varying data. Within a spectral framework, this work presents an overview of clustering techniques as well as their extensions to dynamic data analysis.

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Section: Graph-based Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Spectral Clustering for Dynamic Data

Peluffo-Ordóñez

Alvarado-Pérez

Castro-Ospina

2015

Lecture Notes in Computer Science

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“…Indeed, local analysis provided by each kernel is of benefit to examine the structure of the whole data. Herein, we consider a MKL approach, in which each dimension of matrix X is considered as independent data matrix and then the resultant kernel is a linear combination of the set of obtained kernels [Molina-Giraldo et al, 2012]. We will denote the ℓ-th variable (column vector) as y (ℓ)…”

Section: Multiple-kernel Learningmentioning

confidence: 99%

“…Therefore, a kernel function enables learning methods to use similarities for representing the samples or data points, instead of using explicitly the input data matrix [Belanche Muñoz, 2013]. Kernel-based methods have been widely exploited for both supervised and unsupervised learning approaches showing their usability and versatility in several applications [Aldrich and Auret, 2013], such as image segmentation [Wu et al, 2015, Molina-Giraldo et al, 2012, time-varying data analysis and complex dynamic data clustering , Peluffo-Ordónez et al, 2013, and hypothesis testing [Harchaoui et al, 2013], among others. This article explores the benefit of using a kernel model within the design of spectral formulations of clustering and unsupervised dimensionality reduction methods.…”

Section: Introductionmentioning

confidence: 99%

Kernel-based framework for spectral dimensionality reduction and clustering formulation: A theoretical study

Valencia

Becerra

Castro-Ospina

et al. 2017

ADCAIJ

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Kernel PCA; Spectral clustering; Support vector machine.This work outlines a unified formulation to represent spectral approaches for both dimensionality reduction and clustering. Proposed formulation starts with a generic latent variable model in terms of the projected input data matrix. Particularly, such a projection maps data onto a unknown high-dimensional space. Regarding this model, a generalized optimization problem is stated using quadratic formulations and a least-squares support vector machine. The solution of the optimization is addressed through a primal-dual scheme. Once latent variables and parameters are determined, the resultant model outputs a versatile projected matrix able to represent data in a low-dimensional space, as well as to provide information about clusters. Particularly, proposed formulation yields solutions for kernel spectral clustering and weighted-kernel principal component analysis.On one side, kernel methods are of interest since they allow to incorporate prior knowledge into the clustering procedure [Filippone et al., 2008]. In case of unsupervised clustering methods (that is to say, when clusters are naturally formed by following a given partition criterion), a set of initial parameters should be properly selected to avoid any local optimum solution distant from the desired global optimum. Indeed, in spectral clustering (SC), such initial parameters are traditionally the number of clusters and the input kernel matrix itself. On the other side, the aim of dimensionality reduction (DR) is to extract a lower dimensional, relevant information from high-dim ensional data, being then a key stage for the design of pattern recognition systems. Indeed, when using adequate DR stages, the system performance can be enhanced as well as the data visualization can become more intelligible . Recent methods of DR are focused on the data topology preservation [Peluffo-Ordóñez et al., 2014b]. Mostly such a topology is driven by graph-based approaches where data are represented by a similarity matrix, and it is then susceptible to be expressed in terms of a kernel matrix [Ham et al., 2004], which means that a wide range of methods can be set within a kernel principal component analysis (KPCA) framework [Peluffo-Ordonez et al., 2014]. At the moment to choose a method for either SC or DR, aspects such as nature of data, complexity, aim to be reached and problem to be solved should be taken into consideration. In this regard, it must be quoted that there exists a variety of spectral methods making then the selection of a method a nontrivial task. In fact, some problems may require the combination of methods so that the properties of different methods are simultaneously exploited [Peluffo-Ordónez et al., 2015]. Some works have studied the benefit of taking advantage simultaneously of DR and SC techniques. For instance, in [Peluffo-Ordóñez et al., 2014a], a DR approach (linear feature extraction) is used to enhance the clustering performance by performing the grouping process over the projected data ...

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“…Furthermore, more elaborated approaches involving kernel models within support vector machines formulations have also been introduced [8,9]. Nonetheless, despite their applicability and performance [10,11], spectral approaches are prohibitive for some applications due to the high computational cost that often involves the calculation of eigenvectors, e.g. when dealing with large data.…”

Section: Introductionmentioning

confidence: 99%

Quadratic Problem Formulation with Linear Constraints for Normalized Cut Clustering

Peluffo-Ordóñez

Castro-Hoyos

Acosta-Medina

et al. 2014

Advanced Information Systems Engineering

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Abstract. This work describes a novel quadratic formulation for solving the normalized cuts-based clustering problem as an alternative to spectral clustering approaches. Such formulation is done by establishing simple and suitable constraints, which are further relaxed in order to write a quadratic functional with linear constraints. As a meaningful result of this work, we accomplish a deterministic solution instead of using a heuristic search. Our method reaches comparable performance against conventional spectral methods, but spending significantly lower processing time.

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Image Segmentation Based on Multi-Kernel Learning and Feature Relevance Analysis

Cited by 12 publications

References 9 publications

On the Spectral Clustering for Dynamic Data

On the Spectral Clustering for Dynamic Data

Kernel-based framework for spectral dimensionality reduction and clustering formulation: A theoretical study

Quadratic Problem Formulation with Linear Constraints for Normalized Cut Clustering

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