Randomized Self-Organizing Map

Abstract We propose a variation of the self-organizing map algorithm by considering the random placement of neurons on a two-dimensional manifold, following a blue noise distribution from which various topologies can be derived. These topologies possess random (but controllable) discontinuities that allow for a more flexible self- organization, especially with high-dimensional data. The proposed algorithm is tested on one-, two- and three-dimensional tasks, as well as on the MNIST handwritten digits data set and validated using spectral analysis and topological data analysis tools. We also demonstrate the ability of the randomized self-organizing map to gracefully reorganize itself in case of neural lesion and/or neurogenesis.

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Self-Organizing Map Learning Nonlinearly Embedded Manifolds

Information Visualization ◽

10.1057/palgrave.ivs.9500088 ◽

2005 ◽

Vol 4 (1) ◽

pp. 22-31 ◽

Cited By ~ 8

Author(s):

Timo Similä

Keyword(s):

Learning Algorithm ◽

Image Data ◽

High Dimensional ◽

Locally Linear Embedding ◽

Complex Data ◽

Dimensional Manifold ◽

Self Organizing Map ◽

Training Strategy ◽

Low Dimensional ◽

Self Organizing

One of the main tasks in exploratory data analysis is to create an appropriate representation for complex data. In this paper, the problem of creating a representation for observations lying on a low-dimensional manifold embedded in high-dimensional coordinates is considered. We propose a modification of the Self-organizing map (SOM) algorithm that is able to learn the manifold structure in the high-dimensional observation coordinates. Any manifold learning algorithm may be incorporated to the proposed training strategy to guide the map onto the manifold surface instead of becoming trapped in local minima. In this paper, the Locally linear embedding algorithm is adopted. We use the proposed method successfully on several data sets with manifold geometry including an illustrative example of a surface as well as image data. We also show with other experiments that the advantage of the method over the basic SOM is restricted to this specific type of data.

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Exploratory data analysis and clustering of multivariate spatial hydrogeological data by means of GEO3DSOM, a variant of Kohonen’s Self-Organizing Map

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-3-1487-2006 ◽

2006 ◽

Vol 3 (4) ◽

pp. 1487-1516 ◽

Cited By ~ 9

Author(s):

L. Peeters ◽

F. Bação ◽

V. Lobo ◽

A. Dassargues

Keyword(s):

Data Analysis ◽

Exploratory Data Analysis ◽

Three Dimensional ◽

Spatial Knowledge ◽

Self Organizing Map ◽

Data Set ◽

Hydrochemical Data ◽

Som Algorithm ◽

Exploratory Data ◽

Self Organizing

Abstract. The use of unsupervised artificial neural network techniques like the self-organizing map (SOM) algorithm has proven to be a useful tool in exploratory data analysis and clustering of multivariate data sets. In this study a variant of the SOM-algorithm is proposed, the GEO3DSOM, capable of explicitly incorporating three-dimensional spatial knowledge into the algorithm. The performance of the GEO3DSOM is compared to the performance of the standard SOM in analyzing an artificial data set and a hydrochemical data set. The hydrochemical data set consists of 141 groundwater samples collected in two detritic, phreatic, Cenozoic aquifers in Central Belgium. The standard SOM proves to be more adequate in representing the structure of the data set and to explore relationships between variables. The GEO3DSOM on the other hand performs better in creating spatially coherent groups based on the data.

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A SOM PROJECTION TECHNIQUE WITH THE GROWING STRUCTURE FOR VISUALIZING HIGH-DIMENSIONAL DATA

International Journal of Neural Systems ◽

10.1142/s0129065703001662 ◽

2003 ◽

Vol 13 (05) ◽

pp. 353-365 ◽

Cited By ~ 8

Author(s):

ZHENG WU ◽

GARY G. YEN

Keyword(s):

Projection Method ◽

Cell Structure ◽

High Dimensional Data ◽

Network Size ◽

High Dimensional ◽

Data Sets ◽

Self Organizing Map ◽

Data Set ◽

Growing Cell ◽

Self Organizing

The Self-Organizing Map (SOM) is an efficient tool for visualizing high-dimensional data. In this paper, an intuitive and effective SOM projection method is proposed for mapping high-dimensional data onto the two-dimensional grid structure with a growing self-organizing mechanism. In the learning phase, a growing SOM is trained and the growing cell structure is used as the baseline framework. In the ordination phase, the new projection method is used to map the input vector so that the input data is mapped to the structure of the SOM without having to plot the weight values, resulting in easy visualization of the data. The projection method is demonstrated on four different data sets, including a 118 patent data set and a 399 checical abstract data set related to polymer cements, with promising results and a significantly reduced network size.

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Development of Three-dimensional PTV with a Self-organizing Map

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B ◽

10.1299/kikaib.70.2584 ◽

2004 ◽

Vol 70 (698) ◽

pp. 2584-2590 ◽

Cited By ~ 1

Author(s):

Takafumi MORIHARA ◽

Shigeru MURATA

Keyword(s):

Three Dimensional ◽

Self Organizing Map ◽

Self Organizing

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GPU Accelerated Self-Organizing Map for High Dimensional Data

Neural Processing Letters ◽

10.1007/s11063-014-9383-4 ◽

2014 ◽

Vol 41 (3) ◽

pp. 341-355 ◽

Cited By ~ 5

Author(s):

Yi Xiao ◽

Rui-Bin Feng ◽

Zi-Fa Han ◽

Chi-Sing Leung

Keyword(s):

High Dimensional Data ◽

High Dimensional ◽

Self Organizing Map ◽

Self Organizing

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Unstructured borderline self-organizing map: Learning highly imbalanced, high-dimensional datasets for fault detection

Expert Systems with Applications ◽

10.1016/j.eswa.2021.116028 ◽

2022 ◽

Vol 188 ◽

pp. 116028

Author(s):

Jaeyeon Jang ◽

Chang Ouk Kim

Keyword(s):

Fault Detection ◽

High Dimensional ◽

Self Organizing Map ◽

Map Learning ◽

High Dimensional Datasets ◽

Self Organizing

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Self-Organizing Map and Relational Perspective Mapping for the Accurate Visualization of High-Dimensional Hyperspectral Data

Analytical Chemistry ◽

10.1021/acs.analchem.0c00986 ◽

2020 ◽

Vol 92 (15) ◽

pp. 10450-10459 ◽

Cited By ~ 2

Author(s):

Wil Gardner ◽

Ruqaya Maliki ◽

Suzanne M. Cutts ◽

Benjamin W. Muir ◽

Davide Ballabio ◽

...

Keyword(s):

Hyperspectral Data ◽

High Dimensional ◽

Self Organizing Map ◽

Relational Perspective ◽

Self Organizing

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A SELF-ORGANIZING MAP FOR MIXED CONTINUOUS AND CATEGORICAL DATA

International Journal of Computing ◽

10.47839/ijc.10.1.733 ◽

2011 ◽

pp. 24-32 ◽

Cited By ~ 1

Author(s):

Nicoleta Rogovschi ◽

Mustapha Lebbah ◽

Younès Bennani

Keyword(s):

Clustering Algorithm ◽

Clustering Algorithms ◽

Mixed Data ◽

Categorical Variables ◽

Data Sets ◽

Self Organizing Map ◽

Data Set ◽

Public Data ◽

Self Organizing

Most traditional clustering algorithms are limited to handle data sets that contain either continuous or categorical variables. However data sets with mixed types of variables are commonly used in data mining field. In this paper we introduce a weighted self-organizing map for clustering, analysis and visualization mixed data (continuous/binary). The learning of weights and prototypes is done in a simultaneous manner assuring an optimized data clustering. More variables has a high weight, more the clustering algorithm will take into account the informations transmitted by these variables. The learning of these topological maps is combined with a weighting process of different variables by computing weights which influence the quality of clustering. We illustrate the power of this method with data sets taken from a public data set repository: a handwritten digit data set, Zoo data set and other three mixed data sets. The results show a good quality of the topological ordering and homogenous clustering.

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Using an Extended Self-Organizing Map Network to Forecast Market Segment Membership

Neural Networks in Business Forecasting ◽

10.4018/978-1-59140-176-6.ch007 ◽

2011 ◽

pp. 142-157

Author(s):

Melody Y. Kiang ◽

Dorothy M. Fisher ◽

Michael Y. Hu ◽

Robert T. Chi

Keyword(s):

Input Data ◽

Self Organizing Map ◽

Market Segment ◽

Extended Version ◽

Extended Self ◽

Data Set ◽

Step Procedure ◽

Som Network ◽

Residential Market ◽

Self Organizing

This chapter presents an extended Self-Organizing Map (SOM) network and demonstrates how it can be used to forecast market segment membership. The Kohonen’s SOM network is an unsupervised learning neural network that maps n-dimensional input data to a lower dimensional (usually one- or two-dimensional) output map while maintaining the original topological relations. We apply an extended version of SOM networks that further groups the nodes on the output map into a user-specified number of clusters to a residential market data set from AT&T. Specifically, the extended SOM is used to group survey respondents using their attitudes towards modes of communication. We then compare the extended SOM network solutions with a two-step procedure that uses the factor scores from factor analysis as inputs to K-means cluster analysis. Results using AT&T data indicate that the extended SOM network performs better than the two-step procedure.

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