By Cesar F. Caiafa, Emanuele Salerno, Araceli N. Proto (auth.), Bruno Apolloni, Robert J. Howlett, Lakhmi Jain (eds.)

This ebook is a part of a three-volume set that constitutes the refereed lawsuits of the eleventh overseas convention on Knowledge-Based clever info and Engineering platforms, KES 2007, held in Vietri sul Mare, Italy, September 2007. The 409 revised papers offered have been rigorously reviewed and chosen from approximately 1,203 submissions. The papers current a wealth of unique learn effects from the sector of clever details processing within the broadest sense.

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**Additional info for Knowledge-Based Intelligent Information and Engineering Systems: 11th International Conference, KES 2007, XVII Italian Workshop on Neural Networks, Vietri sul Mare, Italy, September 12-14, 2007, Proceedings, Part III**

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CfαK (x))). Random Germs and Stochastic Watershed 19 A limited number K of factorial axes is usually chosen. It is smaller than the channels number L. Therefore FCA can be seen as a projection of initial vector pixels in a factor space with a lower dimension. Moreover FCA can be used to reduce noise in the image [5,7]. Consequently, we have two spaces for the multivariate segmentation: the multispectral image space (MIS) and the factor image space (FIS). Fig. 1 gives an example of a ﬁve bands satellite simulated image PLEIADES, acquired by the CNES (Centre National d’Etudes Spatiales, the French space agency) and provided by Flouzat [4], and its corresponding FCA representation.

As for PCA, from selected factorial FCA axes the image can be partially reconstructed. The metric used in FCA is the chi-squared, which is adapted to probability laws and normalized by channels weight. FCA can be seen as a transformation going from image space to factorial space. In factorial space the coordinates of the pixels vector on each factorial axis are called pixels factors. The pixels factors can be considered as another multispectral image whose channels correspond to factorial axes: ζ : T L → T K /K < L (fλ (x) → cfα (x) = (cfα1 (x), .

The concluding section looks at some future developments in astrophysical source separation. 2 FD-CCA Model Learning Before describing our algorithm, we briefly formalize the separation problem and introduce the notation used throughout this paper. In our model, the measured data x at a generic pixel i are generated from the underlying components s through a linear, space-invariant, noisy, convolutional mixture operator described as follows [1]: x(i) = (H*As)(i) + n(i), (1) where x and s are N-dimensional and M-dimensional vectors, respectively, with N≥M, A is an unknown N×M space-invariant matrix, n is the N-dimensional, signalindependent, noise vector, the asterisk means convolution, and H is an N×N diagonal matrix whose entries are known convolutional kernels that model the telescope radiation patterns at the related measurement channels.