Online data visualization using the neural gas network

Estévez, P. A.; Figueroa, Cristian

doi:10.1016/j.neunet.2006.05.024

Cited by 46 publications

(17 citation statements)

References 18 publications

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“…Several improvements have since been made to the ViSOM for improved stability, flexibility and scalability [30,66,67]. In Ref.…”

Section: Visom As Metric Scaling Manifoldmentioning

confidence: 99%

Advances in adaptive nonlinear manifolds and dimensionality reduction

Yin

2011

Front. Electr. Electron. Eng. China

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Recent decades have witnessed a much increased demand for advanced, effective and efficient methods and tools for analyzing, understanding and dealing with data of increasingly complex, high dimensionality and large volume. Whether it is in biology, neuroscience, modern medicine and social sciences or in engineering and computer vision, data are being sampled, collected and cumulated in an unprecedented speed. It is no longer a trivial task to analyze huge amounts of high dimensional data. A systematic, automated way of interpreting data and representing them has become a great challenge facing almost all fields and research in this emerging area has flourished. Several lines of research have embarked on this timely challenge and tremendous progresses and advances have been made recently. Traditional and linear methods are being extended or enhanced in order to meet the new challenges. This paper elaborates on these recent advances and discusses various state-of-the-art algorithms proposed from statistics, geometry and adaptive neural networks. The developments mainly follow three lines: multidimensional scaling, eigen-decomposition as well as principal manifolds. Neural approaches and adaptive or incremental methods are also reviewed. In the first line, traditional multidimensional scaling (MDS) has been extended not only to be more adaptive such as neural scale, curvilinear component analysis (CCA) and visualization induced self-organizing map (ViSOM) for online learning, but also to be more local scaling such as Isomap for enhanced flexibility for nonlinear data sets. The second line extends linear principal component analysis (PCA) and has attracted a huge amount of interest and enjoyed flourishing advances with methods like kernel PCA (KPCA), locally linear embedding (LLE) and Laplacian eigenmap. The advantage is obvious: a nonlinear problem is transformed into a linear one and a unique solution can then be sought. The third line starts with the nonlinear principal curve and surface and links up with adaptive neural network approaches such as self-organizing map (SOM) and ViSOM. Many of these frameworks have been further improved and enhanced for incremental learning and mapping function generalization. This paper discusses these recent advances and their connections. Their application issues and implementation matters will also be briefly enlightened and commented on.

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“…Several improvements have since been made to the ViSOM for improved stability, flexibility and scalability [30,66,67]. In Ref.…”

Section: Visom As Metric Scaling Manifoldmentioning

confidence: 99%

Advances in adaptive nonlinear manifolds and dimensionality reduction

Yin

2011

Front. Electr. Electron. Eng. China

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“…Several improvements have since been made to the ViSOM for improved stability and flexibility [13,60]. A growing ViSOM (gViSOM) has been proposed recently to effectively extract a highly nonlinear manifold [65].…”

Section: Visom As Metric-scaling Manifoldmentioning

confidence: 99%

Adaptive nonlinear manifolds and their applications to pattern recognition

Yin¹,

Huang²

2010

Information Sciences

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a b s t r a c tDimensionality reduction has long been associated with retinotopic mapping for understanding cortical maps. Multisensory information is processed, fused and mapped to an essentially 2-D cortex in an information preserving manner. Data processing and projection techniques inspired by this biological mechanism are playing an increasingly important role in pattern recognition, computational intelligence, data mining, information retrieval and image recognition. Dimensionality reduction involves reduction of features or volume of data and has become an essential step of information processing in many fields. The topic of manifold learning has recently attracted a great deal of attention, and a number of advanced techniques for extracting nonlinear manifolds and reducing data dimensions have been proposed from statistics, geometry theory and adaptive neural networks. This paper provides an overview of this challenging and emerging topic and discusses various recent methods such as self-organizing map (SOM), kernel PCA, principal manifold, isomap, local linear embedding, and Laplacian eigenmap. Many of them can be considered in a learning manifold framework. The paper further elaborates on the biologically inspired SOM model and its metric preserving variant ViSOM under the framework of adaptive manifold; and their applications in dimensionality reduction with face recognition are investigated. The experiments demonstrate that adaptive ViSOM-based methods produce markedly improved performance over the others due to their metric scaling and preserving properties along the nonlinear manifold.

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“…The resulting SOM has a clearer connection to an MDS cost function. Estévez and Figueora extend the ViSOM to an arbitrary, neural gas type of map structure [21]. Various other variants of SOM, such as hierarchical, growing, and hierarchical and growing structures are readily extendable to the ViSOM for various application needs.…”

Section: Visualization Induced Som (Visom)mentioning

confidence: 99%