Multivariate Sensing

The number and types of sensors that are available for most sensing situations are very large the computational capacity is abundant and cheap. Miniaturization is a strong trend in the chemical sensor field. The stage is then set for extraction of information from data by means of computational multivariate analysis. 

The two terms have different meaning. By data we mean raw output from the sensor, usually in the form of an electrical signal. In a well-behaved individual sensor, the relationship between the output signal and the concentration of a specific analyte is defined and reproducible. This is what we have learned so far from the discussion of the principles of the individual sensors in the preceding chapters. 

A word of caution is necessary at the onset. The correct information cannot be obtained if the raw data from the sensors are false. Likewise, an incorrect application of a chemometric technique can lead to misinformation. Thus, the two parts of the information acquisition process are complementary, but can never substitute for each other. 

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When we plot the sample concentrations in this way, we begin to see that each sample with a unique combination of component concentrations occupies a unique point in this concentration space. (Since this is the concentration space of a training set, it sometimes called the calibration space.) If we want to construct a training set that spans this concentration space, we can see that we must do it in the multivariate sense by including samples that, taken as a set, will occupy all the relevant portions of the concentration space. 

In this example, data interpretations are based on g-statistic limits. These are computed by assuming the data are normally distributed in the multivariate sense. The diagnostic limits are used to establish when a statistically significant shift has occurred. Charts based on these statistics and used in this manner are analogous to conventional SPC charts. 

The test or Hotelling s test, (named after Harold Hotelling, who developed a test to generalise Student s Z-test [46]). This test is used to verify, in a multivariate sense, whether a sample belongs to a distribution... 

A test profile may be distinctly unusual in the multivariate sense even though each individual result is within its proper reference interval (e.g., point B in Figure 16-6). 

On the other hand, the predictive ability of a calibration model is very difficult to assess empirically. Even the computational methods that we use are questionable Do squared errors correspond to the loss function that the user really wants And the statistical requirements are important How many test samples should be needed to test the predictive ability to what detail, and how should these test samples be distributed statistically in the multivariate sense These are difficult questions for statisticians and chemists alike. On this basis, how can we assess PLSR as an NIR calibration method ... 

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