Hybrid Methods in Pattern Recognition by H. Bunke, A. Kandel

By H. Bunke, A. Kandel

Choice of articles describing fresh development during this rising box. Covers themes akin to the mix of neural nets with fuzzy platforms or hidden Markov versions, neural networks for the processing of symbolic information constructions, hybrid tools in information mining, and others.

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The contour-tree algorithm and the corresponding representation for a company logo. Note that, unlike the typical pre-processing schemes adopted for neural networks, this representation is invariant under rotation. 1. Multilayer Perceptrons for Static Representations Feedforward neural networks 29 are directed acyclic graphs whose nodes carry out a forward computation based on any topological sort b S of the vertices. If we denote by pa[i>] be the parents of v, then the corresponding neural output is for eachv £ ] w v,zXzj where c(-) = tanh(-) is the node output.

One can use a d a t a flow computation model where the state of a given node can only be computed once all the states of its children are known. To some extent, the computation of the o u t p u t yv can be regarded as a transduction of the input graph u to an o u t p u t y with the same skeleton 6 as u. These IO-isomorph transductions are the direct generalisation of the classic concept of transduction of lists. When processing graphs, the concept of IO-isomorph transductions can also be extended to the case in which the skeleton of the graph is also modified.

The calculation of the confidence grade has already been described in Section 2. In this manner, we can determine the consequent class Cp and certainty grade CFP for the antecedent linguistic values api, . . , apn using the trained neural network. The value of CFP can be used to decrease the number of extracted linguistic rules. For example, we can specify a lower bound CFm-m for CFp. We extract the corresponding linguistic rule Rp only when CFP is larger than or equal to the lower bound ^ -^min- The antecedent part of each linguistic rule is specified as a combination of the given linguistic values.

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