Topology Preservation in Self-Organizing Maps

Villmann, T.

doi:10.1016/b978-044450270-4/50022-x

Cited by 14 publications

(11 citation statements)

References 14 publications

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“…Various coloring methods have been proposed to account for this drawback, including. [11][12][13][14][15][16][17] In particular, Kaski et al 14,15 display neurons in a CIELab colorimetric space; 16 Johan Himberg 17 uses a hierarchical classification in order to find clusters and use a cut-off function in the resulting tree so as to linking neurons to a LUT (thanks to a method close to the Fuas' one). 5,6 However, the SOM context differs from the one of our present objective, despite approaches that are connected.…”

Section: Introductionmentioning

confidence: 99%

ColorPhylo: A Color Code to Accurately Display Taxonomic Classifications

Lespinats

Fertil²

2011

Evol Bioinform Online

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Color may be very useful to visualise complex data. As far as taxonomy is concerned, color may help observing various species’ characteristics in correlation with classification. However, choosing the number of subclasses to display is often a complex task: on the one hand, assigning a limited number of colors to taxa of interest hides the structure imbedded in the subtrees of the taxonomy; on the other hand, differentiating a high number of taxa by giving them specific colors, without considering the underlying taxonomy, may lead to unreadable results since relationships between displayed taxa would not be supported by the color code. In the present paper, an automatic color coding scheme is proposed to visualise the levels of taxonomic relationships displayed as overlay on any kind of data plot. To achieve this goal, a dimensionality reduction method allows displaying taxonomic “distances” onto a Euclidean two-dimensional space. The resulting map is projected onto a 2D color space (the Hue, Saturation, Brightness colorimetric space with brightness set to 1). Proximity in the taxonomic classification corresponds to proximity on the map and is therefore materialised by color proximity. As a result, each species is related to a color code showing its position in the taxonomic tree. The so called ColorPhylo displays taxonomic relationships intuitively and can be combined with any biological result. A Matlab version of ColorPhylo is available at http://sy.lespi.free.fr/ColorPhylo-homepage.html. Meanwhile, an ad-hoc distance in case of taxonomy with unknown edge lengths is proposed.

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Section: Introductionmentioning

confidence: 99%

ColorPhylo: A Color Code to Accurately Display Taxonomic Classifications

Lespinats

Fertil²

2011

Evol Bioinform Online

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“…The topology preservation implicates into the equivalence between the generated map and the entry space for all represented points and its neighbourhoods (Vilmann, 1999). Definition 1: A graph together its nodes associated to points forms a topology preserving map of a entry space (manifold) , if exists a mapping function leading neighbour signals in to neighbour nodes in ; and its inverse mapping leading nodes that are neighbour in to neighbour places in (Martinetz, 1994).…”

Section: Topology Preservationmentioning

confidence: 99%

Growing Topology Learning Self-Organizing Map

Mole¹,

Araújo²

2011

Self Organizing Maps - Applications and Novel Algorithm Design

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“…The SOM can be summarized as where output neuron is the winner neuron and neighbor neurons to the winner at the iteration and the learning coefficient at iteration defines a decaying constant with an iteration such as with predetermined constant and total number of iterations [3], [4]. The SOM holds the very advantageous topology preserving property that can capture the probability distribution density of the input data without help of external supervision [11], [12]. As mentioned in literature including [13], however, the required parameter selection prior to learning is very important in achieving useful results.…”

Section: Self-organizing Mapmentioning

confidence: 99%

Centroid neural network for unsupervised competitive learning

Park

2000

IEEE Trans. Neural Netw.

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Abstract-An unsupervised competitive learning algorithm based on the classical -means clustering algorithm is proposed. The proposed learning algorithm called the centroid neural network (CNN) estimates centroids of the related cluster groups in training date. This paper also explains algorithmic relationships among the CNN and some of the conventional unsupervised competitive learning algorithms including Kohonen's self-organizing map (SOM) and Kosko's differential competitive learning (DCL) algorithm. The CNN algorithm requires neither a predetermined schedule for learning coefficient nor a total number of iterations for clustering. The simulation results on clustering problems and image compression problems show that CNN converges much faster than conventional algorithms with compatible clustering quality while other algorithms may give unstable results depending on the initial values of the learning coefficient and the total number of iterations.

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Topology Preservation in Self-Organizing Maps

Cited by 14 publications

References 14 publications

ColorPhylo: A Color Code to Accurately Display Taxonomic Classifications

ColorPhylo: A Color Code to Accurately Display Taxonomic Classifications

Growing Topology Learning Self-Organizing Map

Centroid neural network for unsupervised competitive learning

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