Data analysis feature mapping

Using this notation, X corresponds to any time series of data with xt being a sampled value, and Z represents the processed forms of the data (i.e., a pattern). The z, are the pattern features, wy is the appropriate label or interpretation, is the feature extraction or data analysis transformation, and l is the mapping or interpretation that must be developed. 

The objective of data analysis (or feature extraction) is to transform numeric inputs in such a way as to reject irrelevant information that can confuse the information of interest and to accentuate information that supports the feature mapping. This usually is accomplished by some form of numeric-numeric transformation in which the numeric input data are transformed into a set of numeric features. The numeric-numeric transformation makes use of a process model to map between the input and the output. 

Data Interpretation extends data analysis techniques to label assignment and considers both integrated approaches to feature extraction and feature mapping and approaches with explicit and separable extraction and mapping steps. The approaches in this section focus on those that form numeric-symbolic interpreters to map from numeric data to specific labels of interest. 

As discussed and illustrated in the introduction, data analysis can be conveniently viewed in terms of two categories of numeric-numeric manipulation, input and input-output, both of which transform numeric data into more valuable forms of numeric data. Input manipulations map from input data without knowledge of the output variables, generally to transform the input data to a more convenient representation that has unnecessary information removed while retaining the essential information. As presented in Section IV, input-output manipulations relate input variables to numeric output variables for the purpose of predictive modeling and may include an implicit or explicit input transformation step for reducing input dimensionality. When applied to data interpretation, the primary emphasis of input and input-output manipulation is on feature extraction, driving extracted features from the process data toward useful numeric information on plant behaviors. 

Figure 17.19. Carbon (1 s) NEXAFS spectra of clusters obtained from principal component analysis. Cluster maps are shown in Figure 17.18. Further reduction in the number of clusters will reduce redundancy, but can mask minor features such as those in cluster 19 (J. Lehmann, unpublished data 2006, measured as described in Lehmann et al., 2007).

Self-organizing maps in conjunction with principal component analysis constitute a powerful approach for display and classification of multivariate data. However, this does not mean that feature selection should not be used to strengthen the classification of the data. Deletion of irrelevant features can improve the reliability of the classification because noisy variables increase the chances of false classification and decrease classification success rates on new data. Furthermore, feature selection can lead to an understanding of the essential features that play an important role in governing the behavior of the system or process under investigation. It can identify those measurements that are informative and those measurements that are uninformative. However, any approach used for feature selection should take into account the existence of redundancies in the data and be multivariate in nature to ensure identification of all relevant features. 

Sklorz, S. A Method for Data Analysis Based on Self Organizing Feature Maps. In Proceedings of the Internal. Symposium on Soft Computing for Industry (ISSCr96), Montpellier, Prance (May 1996)... 

Certain structural features arise from a cursory analysis of any of the data sets. Each of the 3 above data sets yields maps similar to those in Figures 2 and 3 that clearly show an area of optimal chain rotation. (Because of the overlapped reflections, there is a false minimum at about 140°, 140° that aligns the chains along the shorter x axis. Chains rotated to the position of the false minima have short interatomic distances.) With similar clarity, the gg 06 position is eliminated by all of the above data sets, as exemplified in Table X, below. 

---