Backpropagation

Just as was the case with simple perceptrons, the multi-layer perceptron s fundamental problem is to learn to associate given inputs with desired outputs. The input layer consists of as many neurons as are necessary to set up some natural 

The output layer likewise consists of as many neurons as are necessary to set up a natural cori espondence between the output neurons and the output-fact set. Using the same example of learning the alphabet, the output space might consist of 26 neurons, one for each letter of the alphabet. A perfect association between input and output facts would be to have - for each input letter - the value of the output neuron corresponding to the letter equal one and all other output neurons equal zero. 

One or more hidden layers are sandwiched between the input and output layers and, for the moment, consist of an arbitrary number of neurons. There are unfortunately no theorems dictating what number should be used for a given problem, but useful heuristics do exist. We will comment on some of these heuristics a bit later on. 

Given pattern p, the hidden neuron receives a weighted input equal to 

Note that the derivative / (x) also takes a rather simple form  

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Neuronal networks are nowadays predominantly applied in classification tasks. Here, three kind of networks are tested First the backpropagation network is used, due to the fact that it is the most robust and common network. The other two networks which are considered within this study have special adapted architectures for classification tasks. The Learning Vector Quantization (LVQ) Network consists of a neuronal structure that represents the LVQ learning strategy. The Fuzzy Adaptive Resonance Theory (Fuzzy-ART) network is a sophisticated network with a very complex structure but a high performance on classification tasks. Overviews on this extensive subject are given in [2] and [6]. 

The architecture of a backpropagation neuronal network is comparatively simple. The network consists of different neurone layers. The layer connected to the network input is called input layer while the layer at the network output is called the output layer. The different layers between input and output are named hidden layers. The number of neurones in the layers is determined by the developer of the network. Networks used for classification have commonly as much input neurones as there are features and as much output neurones as there are classes to be separated. 

In a backpropagation network each neurone of a layer is coimected to each neurone in the previous and in the next layer. Connections spanning over one layer are forbidden in this architecture. 

The three introduced network structures were trained with the training data set and tested with the test dataset. The backpropagation network reaches its best classification result after 70000 training iterations ... 

Table 2 Classification results of the Backpropagation Network in percent...

In many cases, structure elucidation with artificial neural networks is limited to backpropagation networks [113] and, is therefore performed in a supervised man-... 

T. J. McAvoy and co-workers, "Interpreting Biosensor Data via Backpropagation," in Proceedings of the InternationalJoint Conf. on Neural Networks, Washington, D.C., 1989. 

Numeric-to-numeric transformations are used as empirical mathematical models where the adaptive characteristics of neural networks learn to map between numeric sets of input-output data. In these modehng apphcations, neural networks are used as an alternative to traditional data regression schemes based on regression of plant data. Backpropagation networks have been widely used for this purpose. 

We are now ready to introduce the backpropagation learning rule (also called the generalized delta rule) for multidayercd perceptrons, credited to Rumelhart and McClelland [rumel86a]. Figure 10.12 shows a schematic of the multi-layered per-ceptron s structure. Notice that the design shown, and the only kind we will consider in this chapter, is strictly feed-forward. That is to say, information always flows from the input layer to each hidden layer, in turn, and out into the output layer. There are no feedback loops anywhere in the system. 

The previous section introduced the backpropagation rule for multi-layer percep-trons. This section briefly discusses tfie model development cycle necessary ftu-obtaining a properly functioning net. It also touches upon some of the available heuristics for determining the proper size of hidden layers. 

Fundamentally, all feed-forward backpropagating nets follow the same five basic steps of a model development cycle ... 

The obvious lesson to be taken away from this amusing example is that how well a net learns the desired associations depends almost entirely on how well the database of facts is defined. Just as Monte Carlo simulations in statistical mechanics may fall short of intended results if they are forced to rely upon poorly coded random number generators, so do backpropagating nets typically fail to ac hieve expected re.sults if the facts they are trained on are statistically corrupt. 

Garrido L, Gomez S, Roca J. Improved multidimensional scaling analysis using neural networks with distance-error backpropagation. Neural Comput 1999 11 595-600. 

In the bottom-up approach the initiative to start the learning process is taken by one of the infimal decision units. Since solutions found at this unit may include connection variables, the request for given values of these variables is propagated backward, to unit A + 1, through temporary loss functions. After successive backpropagation steps, the participation of several other fhe operators associated with them, a final decision... 

The bottom-up approach contains two distinct stages. First, by successive backpropagation steps one builds a decision policy. Then, this uncovered policy is evaluated and refined, and its expected benefits confirmed before any implementation actually takes place. This two-stage process is conceptually similar to dynamic programming solution strategies, where first a decision policy is constructed by backward induction, and then one finds a realization of the process for the given policy, in order to check its expected performance (Bradley et al., 1977). 

Although the minimization of the objective function might run to convergence problems for different NN structures (such as backpropagation for multilayer perceptrons), here we will assume that step 3 of the NN algorithm unambiguously produces the best, unique model, g(x). The question we would like to address is what properties this model inherits from the NN algorithm and the specific choices that are forced. 

Hernandez, E., and Arkun, Y., A study of the control relevant properties of backpropagation neural net models of nonlinear dynamical systems. Comput. Chem. Eng. 16, 227 (1992). 

B.J. Wythoff, Backpropagation neural networks — a tutorial. Chemom. Intell. Lab. Syst., 18 (1993) 115-155. 

B. Walczak, Neural networks with robust backpropagation learning algorithm. Anal. Chim. Acta, 322 (1996) 21-30. 

By design, ANNs are inherently flexible (can map nonlinear relationships). They produce models well suited for classification of diverse bacteria. Examples of pattern analysis using ANNs for biochemical analysis by PyMS can be traced back to the early 1990s.4fM7 In order to better demonstrate the power of neural network analysis for pathogen ID, a brief background of artificial neural network principles is provided. In particular, backpropagation artificial neural network (backprop ANN) principles are discussed, since that is the most commonly used type of ANN. 

Wythoff BJ (1993) Backpropagation neural networks. A tutorial. Chemom Intell Lab Syst 18 115... 

Both cases can be dealt with both by supervised and unsupervised variants of networks. The architecture and the training of supervised networks for spectra interpretation is similar to that used for calibration. The input vector consists in a set of spectral features yt(Zj) (e.g., intensities at selected wavelengths zi). The output vector contains information on the presence and absence of certain structure elements and groups fixed by learning rules (Fig. 8.24). Various types of ANN models may be used for spectra interpretation, viz mainly such as Adaptive Bidirectional Associative Memory (BAM) and Backpropagation Networks (BPN). The correlation... 

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