Theoretical aspects of the SOM algorithm

Cottrell, Marie; Fort, Jean‐Claude; Pagès, Gilles

doi:10.1016/s0925-2312(98)00034-4

Cited by 189 publications

(116 citation statements)

References 49 publications

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“…As recommended (Cottrell et al, 1998;Mulier and Cherkassky, 1995;Song and Hopke, 1996), a twophase learning algorithm was applied. The first learning phase (rough learning) was characterized by a strongly decreasing learning rate and neighbourhood that allowed general mapping with large groups of neurons responding to similar data (Kohonen, 2001).…”

Section: Methodsmentioning

confidence: 99%

Extruded Bread Classification on the Basis of Acoustic Emission Signal With Application of Artificial Neural Networks

Świetlicka¹,

Muszyński²,

Marzec³

2015

International Agrophysics

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A b s t r a c t. The presented work covers the problem of developing a method of extruded bread classification with the application of artificial neural networks. Extruded flat graham, corn, and rye breads differening in water activity were used. The breads were subjected to the compression test with simultaneous registration of acoustic signal. The amplitude-time records were analyzed both in time and frequency domains. Acoustic emission signal parameters: single energy, counts, amplitude, and duration acoustic emission were determined for the breads in four water activities: initial (0.362 for rye, 0.377 for corn, and 0.371 for graham bread), 0.432, 0.529, and 0.648. For classification and the clustering process, radial basis function, and self-organizing maps (Kohonen network) were used. Artificial neural networks were examined with respect to their ability to classify or to cluster samples according to the bread type, water activity value, and both of them. The best examination results were achieved by the radial basis function network in classification according to water activity (88%), while the self-organizing maps network yielded 81% during bread type clustering.

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Section: Methodsmentioning

confidence: 99%

Extruded Bread Classification on the Basis of Acoustic Emission Signal With Application of Artificial Neural Networks

Świetlicka¹,

Muszyński²,

Marzec³

2015

International Agrophysics

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“…However, if the primary goal is clustering, a fixed topology puts restrictions on the map and topology preservation often cannot be achieved [30]. SOM does not possess a cost function in the continuous case and its mathematical investigation is difficult [9]. However, if the winner is chosen as the neuron i with minimum averaged distance n l=1 h λ (nd (i, l))d( x j , w l ), it optimizes the cost…”

Section: Neural Gasmentioning

confidence: 99%

“…However, a fixed prior lattice as chosen in SOM might be suboptimal for a given task depending on the data topology and topological mismatches can easily occur [30]. SOM does not possess a cost function in the continuous case, and the mathematical analysis is quite difficult unless variations of the original learning rule are considered for which cost functions can be found [9,16]. NG optimizes a cost function which, as a limit case, yields the quantization error [21].…”

Section: Introductionmentioning

confidence: 99%

Batch and median neural gas

et al. 2006

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Neural Gas (NG) constitutes a very robust clustering algorithm given euclidian data which does not suffer from the problem of local minima like simple vector quantization, or topological restrictions like the self-organizing map. Based on the cost function of NG, we introduce a batch variant of NG which shows much faster convergence and which can be interpreted as an optimization of the cost function by the Newton method. This formulation has the additional benefit that, based on the notion of the generalized median in analogy to Median SOM, a variant for non-vectorial proximity data can be introduced. We prove convergence of batch and median versions of NG, SOM, and k-means in a unified formulation, and we investigate the behavior of the algorithms in several experiments.

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“…This is possible because SOMs perform a non-linear projection of the input data onto the elements of a regular array, usually of low dimension [9]. The main characteristics of the projection is the preservation of neighborhood relations in the output space, which makes possible to see more clearly the structure hidden in the high-dimensional data, such as clusters [10,11].…”

Section: Introductionmentioning

confidence: 99%