Batch kernel SOM and related Laplacian methods for social network analysis

Boulet, Romain; Jouve, Bertrand; Rossi, Fabrice; Villa, Nathalie

doi:10.1016/j.neucom.2007.12.026

Cited by 75 publications

(51 citation statements)

References 44 publications

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“…More precisely, kernel -means and batch kernel SOM [53] were processed as implemented in the R package yasomi (development version available at https://r-forge.r-project.org/projects/yasomi). …”

Section: Methodsmentioning

confidence: 99%

The Structure of a Gene Co-Expression Network Reveals Biological Functions Underlying eQTLs

Villa-Vialaneix¹,

Liaubet

Laurent

et al. 2013

PLoS ONE

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What are the commonalities between genes, whose expression level is partially controlled by eQTL, especially with regard to biological functions? Moreover, how are these genes related to a phenotype of interest? These issues are particularly difficult to address when the genome annotation is incomplete, as is the case for mammalian species. Moreover, the direct link between gene expression and a phenotype of interest may be weak, and thus difficult to handle. In this framework, the use of a co-expression network has proven useful: it is a robust approach for modeling a complex system of genetic regulations, and to infer knowledge for yet unknown genes. In this article, a case study was conducted with a mammalian species. It showed that the use of a co-expression network based on partial correlation, combined with a relevant clustering of nodes, leads to an enrichment of biological functions of around 83%. Moreover, the use of a spatial statistics approach allowed us to superimpose additional information related to a phenotype; this lead to highlighting specific genes or gene clusters that are related to the network structure and the phenotype. Three main results are worth noting: first, key genes were highlighted as a potential focus for forthcoming biological experiments; second, a set of biological functions, which support a list of genes under partial eQTL control, was set up by an overview of the global structure of the gene expression network; third, pH was found correlated with gene clusters, and then with related biological functions, as a result of a spatial analysis of the network topology.

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Section: Methodsmentioning

confidence: 99%

The Structure of a Gene Co-Expression Network Reveals Biological Functions Underlying eQTLs

Villa-Vialaneix¹,

Liaubet

Laurent

et al. 2013

PLoS ONE

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“…This approach is very similar to the batch kernel SOM described in [12,13]. In kernel SOM, the Euclidean framework is justified by the definition of a kernel K : G × G → R that implicitly maps the data into a Hilbert space where the inner product is directly available via the kernel.…”

Section: Som For Dissimilarity Datamentioning

confidence: 99%

“…This method is based on the idea that prototypes may be expressed as linear combinations of the original input data. In kernel SOM framework, this setting is made natural by the use of the kernel, which maps the original data into a (large dimensional) Euclidean space (see [10,11,12] for on-line versions and [13] for the batch version). Several kernels may then be used to handle complex data such as strings, nodes in a graph or graphs themselves [14].…”

Section: Introductionmentioning

confidence: 99%

On-line relational and multiple relational SOM

Olteanu¹,

Villa-Vialaneix²

2015

Neurocomputing

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In some applications and in order to address real-world situations better, data may be more complex than simple numerical vectors. In some examples, data can be known only through their pairwise dissimilarities or through multiple dissimilarities, each of them describing a particular feature of the data set. Several variants of the Self Organizing Map (SOM) algorithm were introduced to generalize the original algorithm to the framework of dissimilarity data. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual linear combination of all elements in the data set, referring to a pseudo-euclidean framework. In the present article, an on-line version of relational SOM is introduced and studied. Similarly to the situation in the Euclidean framework, this on-line algorithm provides a better organization and is much less sensible to prototype initialization than standard (batch) relational SOM. In a more general case, this stochastic version allows us to integrate an additional stochastic gradient descent step in the algorithm which can tune the respective weights of several dissimilarities in an optimal way: the resulting multiple relational SOM thus has the ability to integrate several sources of data of different types, or to make a consensus between several dissimilarities describing the same data. The algorithms introduced in this manuscript are tested on several data sets, including categorical data and graphs. On-line relational SOM is currently available in the R package SOMbrero that can be downloaded at http://sombrero.r-forge.r-project.org/ or directly tested on its Web User Interface at http://shiny.nathalievilla.org/sombrero.

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“…exactly as in equation (22). While the earliest kernel SOM (STMK) in [17] is optimized using deterministic annealing (as the SMTP presented in Section 5), the kernel trick enables the more traditional online SOM [31] and batch SOM [5,32,49] derived from the previous equations. It should be noted for the sake of completeness that another kernel SOM was proposed in [2].…”

Section: The Kernel Trick For the Sommentioning

confidence: 99%

How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?

Rossi

2014

Advances in Self-Organizing Maps and Learning Vector Quantization

Self Cite

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Abstract. In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel that measures how different or similar two objects are. This approach has been used to define several variants of the Self Organizing Map (SOM). This paper reviews those variants in using a common set of notations in order to outline differences and similarities between them. It discusses the advantages and drawbacks of the variants, as well as the actual relevance of the dissimilarity/kernel SOM for practical applications.

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Batch kernel SOM and related Laplacian methods for social network analysis

Cited by 75 publications

References 44 publications

The Structure of a Gene Co-Expression Network Reveals Biological Functions Underlying eQTLs

The Structure of a Gene Co-Expression Network Reveals Biological Functions Underlying eQTLs

On-line relational and multiple relational SOM

How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?

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