Conformality in the self-organization network

Liou, Cheng-Yuan; Tai, Wen-Pin

doi:10.1016/s0004-3702(99)00093-4

Cited by 14 publications

(9 citation statements)

References 13 publications

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“…The SOM with finite neurons cannot be used for monitoring the continuous state. The folded mapping in the SOM can be indicated and resolved by the negative values of the Jacobian of the mapping function [11]. The CSM can save and accommodate fine textures in the plane map.…”

Section: Discussionmentioning

confidence: 99%

“…This is because q is a linear interpolation of jq 0 À a q 0 j=jb q 0 À a q 0 j, see its definition in Eq. (11). Therefore, v q must equal to zero.…”

Section: Appendix a Bijective Mappingmentioning

confidence: 99%

“…The conformal self-organizing map (CSM) [15,8,9] has been developed for modeling a continuous surface for the cloud patterns. It is a kind of self-organizing map with conformal contents [10,11]. The CSM is formed by a collection of connected simplices including points and edges.…”

Section: Introductionmentioning

confidence: 99%

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Conformal self-organizing map on curved seamless surface

Liou¹,

Kuo²,

Huang³

2008

Neurocomputing

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Section: Discussionmentioning

confidence: 99%

“…This is because q is a linear interpolation of jq 0 À a q 0 j=jb q 0 À a q 0 j, see its definition in Eq. (11). Therefore, v q must equal to zero.…”

Section: Appendix a Bijective Mappingmentioning

confidence: 99%

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Conformal self-organizing map on curved seamless surface

Liou¹,

Kuo²,

Huang³

2008

Neurocomputing

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“…Distortion analysis [12,21,23] has been introduced to study the formation mechanism of the self organizing map (SOM) [10]. The lack of a precise energy function for the SOM is studied in [7].…”

Section: Introductionmentioning

confidence: 99%

Manifold construction based on local distance invariance

Cheng

Liou

2010

Memetic Comp.

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This paper presents a distance invariant manifold that preserves the neighborhood relations among data patterns. All patterns have their corresponding cells in the manifold space. The constellation of neighborhood cells closely resembles that of patterns. The manifold is invariant under the translation, rotation and scale of the pattern coordinates. The neighborhood relations among cells are adjusted and improved in each iteration according to the reduction of the distance preservation energy.

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“…The another line is to combine the feature of Kohonen map with Gaussian mixture such as given in [7]. Another line that deserves to mention is applying certain advanced mathematical results on deformation analyses to interpret and evolve self-organization map [50].…”

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confidence: 99%