Zheng Y., Greenleaf J.F., The effect of concave and convex weight adjustments on self-organizing maps, IEEE Transactions on Neural Networks, vol. 7, no. 1, pp. 87-96, January 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....techniques. As an example, here are some arguments recently developed: in [4] better clustering performances are shown with standard k means algorithm; in [5] the same argument is developed to justify the use of VQ algorithm with MDS (Muldi Dimensionnal Scaling) instead of Kohonen maps; in [6], the authors argue that there exists an exponent between the underlying density of vectors and centroids before and after VQ and propose to modify the algorithm to remedy to this problem . this non unity exponent is known as the magnification coefficient [7] Although different, this ....

....the reconstructed density is shown to be related to f(x) through an exponent as in (6) We insist on the fact that definitions of g(x) are different in [7] and [8] and that further investigation would be necessary to compare these two results. Finally, it must be mentioned that several authors [17, 6] proposed modifications of the algorithm to compensate the exponent in (6) and to obtain discrete densities of centroids closer fromf(x) To our opinion, the question is to know if the exponent in (6) must be considered as an undesired effect which must be compensated, or if the problem of ....

[Article contains additional citation context not shown here]

Zheng Y., Greenleaf J.F., The effect of concave and convex weight adjustments on self-organizing maps, IEEE Transactions on Neural Networks, vol. 7, no. 1, pp. 87-96, January 1996.

.... As an example, here are some arguments recently developed: in [4] better clustering performances are shown with standard k means algorithm; in [5] the same argument is developed to justify the use of VQ algorithm with MDS (Muldi Dimensionnal Scaling) instead of Kohonen maps; in [6], the authors argue that there exists an exponent between the underlying density of vectors and centroids before and after VQ and propose to modify the algorithm to remedy to this problem . this non unity exponent is known as the magnification coefficient [7] Although different, this coefficient ....

....the reconstructed density is shown to be related to f(x) through an exponent as in (6) We insist on the fact that definitions of g(x) are different in [7] and [8] and that further investigation would be necessary to compare these two results. Finally, it must be mentioned that several authors [17, 6] proposed modifications of the algorithm to compensate the exponent in (6) and to obtain discrete densities of centroids closer from f(x) To our opinion, the question is to know if the exponent in (6) must be considered as an undesired effect which must be compensated, or if the European ....

[Article contains additional citation context not shown here]

Zheng Y., Greenleaf J.F., The effect of concave and convex weight adjustments on self-organizing maps, IEEE Transactions on Neural Networks, vol. 7, no. 1, pp. 87-96, January 1996.

....quantizers is the main problem in vector quantization and requires the minimization of (1) which has many local minima. Thus, in general one can only provide suboptimal choices of the reference vectors [19] Several design algorithms have been developed for vector quantization [20] 19] 6] 1] [18], 17] The most widely used method for designing vector quantizers is the generalized Lloyd algorithm, known also as LBG scheme [10] 19] An alternative is Kohonen s learning algorithm [3] 4] 2] 5] which can be seen as a generalization of the LBG method [10] The mechanism of the ....

....the cluster units) of multidimensional space which tend to approximate to the density function of the input vectors. In his work [4] Kohonen indicates that linear SOM produce approximations of space filling curves, which mimick probability measures induced by data. In further studies [11] 10] [18] it was etabilished, that in fact this is true only for uniform density of data in one dimension. and the density of the SOM output units in the input space is proportional to the ff power of the input probability density (only in one dimension and if the number of units goes to the infinity) ....

[Article contains additional citation context not shown here]

YI ZHENG & GREENLEAF J.F., The effect of concave and convex weight adjustments on self-organizing maps, IEEE Trans. on Neural Networks 7, 87-- 96 (1996).

....In fact this is true only for uniform density of data in one dimension. Studies show that the density of the SOM output units in the input space is proportional to the 2=3 power of the input probability density (only in one dimension and if the number of units goes to the infinity) 25] 24] [36]. For some application the good output should be proportional exactly to the input probability density [36] The approach proposed in this paper allows to obtain space filling curves which tend to approximate to the density function of the input vectors in multidimensional 0.2 0.4 0.6 0.8 1 ....

.... the SOM output units in the input space is proportional to the 2=3 power of the input probability density (only in one dimension and if the number of units goes to the infinity) 25] 24] 36] For some application the good output should be proportional exactly to the input probability density [36]. The approach proposed in this paper allows to obtain space filling curves which tend to approximate to the density function of the input vectors in multidimensional 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Figure 2: Data driven Sierpinski space filling curve with 160 nodal points. ....

YI ZHENG & GREENLEAF J.F., The effect of concave and convex weight adjustments on self-organizing maps, IEEE Trans. on Neural Networks 7, 87--96 (1994).

.... empirically from one data set to another to achieve useful results [7] ffl Probability density function (pdf) estimation is not achieved [34] Attempts have been made to interpret the density of codebook vectors as a model of the input data distribution but with limited success [26] 27] 34] [51]. ffl It should not be employed in topology preserving mapping when the dimension of the input space is larger than three. In fact, SOM tries to form a neighborhood preserving inverse mapping OE Gamma1 S from lattice G to input manifold X, but not necessarily a neighborhood preserving mapping ....

Y. Zheng and J. F. Greenleaf, "The effect of concave and convex weight adjustments on self-organizing maps," IEEE Trans. on Neural Networks, vol. 7, no. 1, pp. 87-96, 1996.

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Zheng, Y. and Greenleaf, J. F. (1996). The effect of concave and convex weight adjustments of self-organising maps. IEEE Transactions on Neural Networks, 2(1):87--96.

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