Counter-propagation

Now, one may ask, what if we are going to use Feed-Forward Neural Networks with the Back-Propagation learning rule Then, obviously, SVD can be used as a data transformation technique. PCA and SVD are often used as synonyms. Below we shall use PCA in the classical context and SVD in the case when it is applied to the data matrix before training any neural network, i.e., Kohonen s Self-Organizing Maps, or Counter-Propagation Neural Networks. 

To understand neural networks, especially Kohonen, counter-propagation and back-propagation networks, and their applications... 

Kohonen network Conceptual clustering Principal Component Analysis (PCA) Decision trees Partial Least Squares (PLS) Multiple Linear Regression (MLR) Counter-propagation networks Back-propagation networks Genetic algorithms (GA)... 

Supeiwised learning strategies are applied in counter-propagation and in back-propagation neural networks (see Sections 9.5.5 and 9.5,7, ... 

Besides the artihcial neural networks mentioned above, there are various other types of neural networks. This chapter, however, will confine itself to the three most important types used in chemoinformatics Kohonen networks, counter-propagation networks, and back-propagation networks. 

A counter-propagation network is a method for supervised learning which can be used for prediction, It has a two-layer architecture where each netiron in the upper layer, the Kohonen layer, has a corresponding netiron in the lower layer, the output layer (sec Figure 9-21). A trained counter-propagation network can be used as a look-up tabic a neuron in one layer is used as a pointer to the other layer. 

The architecture of a counter-propagation network resembles that of a Kohonen network, but in addition to the cubic Kohonen layer (input layer) it has an additional layer, the output layer. Thus, an input object consists of two parts, the m-dimeiisional input vector (just as for a Kohonen network) plus a second k-dimensional vector with the properties for the object. 

Tt provides unsupervised (Kohonen network) and supervised (counter-propagation network) learning techniques with planar and toroidal topology of the network. 

The usage of a neural network varies depending on the aim and especially on the network type. This tutorial covers two applications on the one hand the usage of a Kohonen network for classification, and on the other hand the prediction of object properties with a counter-propagation network,... 

Counter-propagation network this network also needs the input dimension. It gives the columns that arc used for the upper layer of the network. 

Kohonen network Counter-propagation Back-propagation... 

Association deals with the extraction of relationships among members of a data set. The methods applied for association range from rather simple ones, e.g., correlation analysis, to more sophisticated methods like counter-propagation or back-propagation neural networks (see Sections 9.5.5 and 9.5.7). 

A counter-propagation neural network is a method for supervised learning which can be used for predictions. 

The objective of this study is to show how data sets of compounds for which dif-ferent biological activities have been determined can be studied. It will be shown how the use of a counter-propagation neural networb can lead to new insights [46]. The cmpha.si.s in this example is placed on the comparison of different network architectures and not on quantitative results. 

The data set was then sent into a counter-propagation (CPG) network consisting of 13 X 9 neurons with 10 layers (one for each descriptor) in the input block and one layer in the output block (figure 10.1-9), with the output values having nine different values corresponding to the nine different MOA. 

Rather than making this statement, one should consider first whether the representation of the Y-variablc is appropriate. What wc did here was to take categorical information as a quantitative value. So if wc have, for instance, a vector of class 1 and one of c lass 9 falling into the same neuron, the weights of the output layer will be adapted to a value between 1 and 9, which docs not make much sense. Thus, it is necessary to choose another representation with one layer for each biological activity. The architecture of such a counter-propagation network is shown in Figure 10.1 -11. Each of the nine layers in the output block corresponds to a different MOA. 

However, these results illustrate that the use of a counter-propagation network can lead to new insights when several biological activities arc given. Furthermore, a CPG network can also be applied for studying selectivity between different biological activities. 

Conical emission, 85, 89, 93 Constructive interference, 66 Continuous wavelet transforms, 145 Contrast ratio, 142-144, 191 Conversion efficiency, 96 Corona discharges, 110 Counter-propagating laser pulses, 171 CPA, 187 Critical power, 83 Cross section, 125... 

Fig. 18.15 Advanced methods for single particle analysis in LC ARROW chips, (a) Nanopore added to reservoir for single particle entry into LC ARROW (b) Optical dual beam particle trap based on balancing the scattering force due to counter propagating beams...

If more than one property is relevant, then we have an A-matrix and a corresponding y-matrix. If the properties are highly correlated, a combined treatment of all properties is advisable, otherwise each property can be handled separately as described above. Mostly used for a joined evaluation of X and Y is PLS (then sometimes called PLS2) a nonlinear method is a Kohonen counter propagation network. 

Cosio et al. (2006) used an electronic tongue system based on flow injection analysis (FIA) with two amperometric detectors, together with the use of an electronic nose, in order to classify olive oil samples on the basis of their geographical origin. Counter-propagation maps were used as classification tools. 

In the previous section, we described the situation that a single WP created by a pump pulse splits into two counter-propagating WPs due to potential anharmonic-ity. Similar interfering WPs can be generated by time-delayed double pump pulses. 

Figure 7.2 The enlarged view of the wave packet motion given in Figure 7.1 around the quarter revival (T /4) region. The motion of the two counter-propagating packets is indicated with dotted lines.

If molecules are cooled to a very low temperature, their translational motion may be restricted by an application of an optical lattice. An optical lattice is an interference of counter-propagating laser beams, producing a standing wave of electric field. Molecules in the ground state placed in an optical lattice will be pushed toward regions of the field strength maxima. An optical lattice can... 

This instrument is used to measure the flow of clean liquids and involves the determination of the time required for an acutely angled, high frequency pressure wave to reach the opposite wall of a pipe. The elapsed time depends upon the velocity of the liquid u(, whether the pressure wave is moving with, or against the flow and upon the speed of sound in the liquid us. The most common time-of-flight meter is the counter-propagating type in which two transducers are placed on opposite sides of the liquid stream as shown in Fig. 6.3. 

Fig. 6.3. Counter-propagating time-of-flight ultrasonic flowmeter...

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