By Stephen Grossberg (auth.), Georg Dorffner, Horst Bischof, Kurt Hornik (eds.)
This e-book is predicated at the papers awarded on the overseas convention on Arti?cial Neural Networks, ICANN 2001, from August 21–25, 2001 on the - enna collage of know-how, Austria. The convention is geared up by means of the A- trian learn Institute for Arti?cal Intelligence in cooperation with the development acceptance and photograph Processing crew and the heart for Computational - telligence on the Vienna college of know-how. The ICANN meetings have been initiated in 1991 and became the key eu assembly within the ?eld of neural networks. From approximately three hundred submitted papers, this system committee chosen 171 for booklet. each one paper has been reviewed via 3 application committee m- bers/reviewers. we want to thank the entire participants of this system comm- tee and the reviewers for his or her nice e?ort within the reviewing approach and aiding us to establish a scienti?c software of top of the range. furthermore, we now have invited 8 audio system; 3 in their papers also are incorporated within the lawsuits. we wish to thank the eu Neural community Society (ENNS) for his or her aid. We recognize the ?nancial help of Austrian airways, A- trian technology origin (FWF) less than the agreement SFB 010, Austrian Society ¨ for Arti?cial Intelligence (OGAI), financial institution Austria, and the Vienna conference Bureau. we want to precise our honest due to A. Flexer, W. Horn, okay. Hraby, F. Leisch, C. Schittenkopf, and A. Weingessel. The convention and the court cases do not need been attainable with no their huge, immense contri- tion.
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Extra resources for Artificial Neural Networks — ICANN 2001: International Conference Vienna, Austria, August 21–25, 2001 Proceedings
3 A Numerical Illustration We will illustrate the preceding techniques on a toy synthetic problem with 2 unidimensional classes. 25). 5. 48 %. On the other hand, the class distributions are not unimodal, and neither linearly separable. NLDA networks will thus realize feature enhancing rather than feature extraction. We shall work ˆdh the sample with the sample versions I, H of I, H and we denote by w ˆh , w derived weights. We start with a minimal network with all units being relevant and shall “grow” the network’s hidden layers.
These results are given in the next section, while the third one contains an illustration of these procedures on a synthetic problem. 2 Unit Relevance in NLDA Networks We shall study unit relevance, working with sets of weights related to a concrete unit. To do so we could consider either input or output weights. However, and as it happens with MLPs, NLDA networks may present identiﬁability problems. For instance, if all the weights wkl starting at a given hidden unit k are zero, the weights whk leading to that unit can take any value without aﬀecting network outputs.
C Springer-Verlag Berlin Heidelberg 2001 28 Jos´e R. Dorronsoro, Ana M. Gonz´ alez, and Carlos Santa Cruz As with MLPs, optimal NLDA network architectures have to be somehow decided upon. We shall analyze here how this can be done. In our setting we have to decide on the number of hidden units. If the relevance of the original features is also to be decided, the number of input units cannot be taken to be ﬁxed in advance and may have to be lowered. Architecture selection is a long studied question for MLPs, and many approaches, such as bootstrapping, pruning, regularization, stopped training or information criteria have been proposed (see [3,6,8] for an overview of these approaches).
Artificial Neural Networks — ICANN 2001: International Conference Vienna, Austria, August 21–25, 2001 Proceedings by Stephen Grossberg (auth.), Georg Dorffner, Horst Bischof, Kurt Hornik (eds.)