Data patterns

Software is rarely completely free of coding errors. While manifest errors are eliminated during the debugging stage, the remaining ones crop up only when specific data patterns or sequences of instructions are encountered. 

With respect to cluster seeking performance, RBFNs are influenced heavily by the occurrences of input data patterns because clustering effectively is averaged over individual pattern occurrences. It has been shown that this decreases the utility for interpretation (Kavuri and Venkatasubra-manian, 1993). Current approaches also require a priori specification of the number of clusters, a drawback from an adaptation standpoint. 

Here xik is an estimated value of a variable at a given point in time. Given that the estimate is calculated based on a model of variability, i.e., PCA, then Qi can reflect error relative to principal components for known data. A given pattern of data, x, can be classified based on a threshold value of Qi determined from analyzing the variability of the known data patterns. In this way, the -statistic will detect changes that violate the model used to estimate x. The 0-statistic threshold for methods based on linear projection such as PCA and PLS for Gaussian distributed data can be determined from the eigenvalues of the components not included in the model (Jack-son, 1992). 

As shown, the data patterns 1 and 2 are classified as Normal with high certainty, as they lie within the boundaries of the normal class. However, 3 and 4 are classified as normal with medium certainty, as they lie outside the normal region, but their similarities are closest to the normal cluster. Similarly, the data pattern represented by 5 is classified as fault2 with medium certainty and the data patterns represented by 6, 7, and 8 are classified as fault2, and so on. If the data are collected every 20 seconds as in the case study, the dynamic interpretation is tabulated as shown in Table V, with the labels in italics representing the correct class and appropriate certainty. An x means there was not an interpretation with this certainty. 

A quite different way to reduce overfitting is to use random noise. A random signal is added to each data point as it is presented to the network, so that a data pattern ... 

Provide simple data patterns that allow visual evaluation... 

The 740 specimens received for routine drug analysis were divided into groups according to the level of THC-CRC detected. Figure 6 shows the data pattern. Values of 10 yg/1 or less were classed as negative. 

The score matrix gives a simplified picture of the objects (probe-target interactions), represented by only a few, uncorrelated new variables (the PCs). Score plots, i.e. plots of the score vectors against each other, are a summary of the relationships between the objects and reveal the essential data patterns of the objects. Thus, objects which behave similarly have similar scores and are close in the score plot. In our context, score plots can be used to identify clusters of objects according to the different kind of targets (macromolecules) and probes (ligand chemical groups) involved. 

The main task of data acquisition systems for time resolved measurement is to record this three-dimensional data patterns. The amount of information which has to be recorded can become quite high. 

Azuaje F. Clustering-based approaches to discovering and visualising microarray data patterns. Brief Bioinform. 2003 4 31-42. Quackenbush J. Computational analysis of microarray data. Nat. Rev. Genet. 2001 2 418-427. 

An adaptation of the simple feed-forward network that has been used successfully to model time dependencies is the so-called recurrent neural network. Here, an additional layer (referred to as the context layer) is added. In effect, this means that there is an additional connection from the hidden layer neuron to itself. Each time a data pattern is presented to the network, the neuron computes its output function just as it does in a simple MLP. However, its input now contains a term that reflects the state of the network before the data pattern was seen. Therefore, for subsequent data patterns, the hidden and output nodes will depend on everything the network has seen so far. For recurrent neural networks, therefore, the network behaviour is based on its history. 

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