Cluster significance tests

There are two goals for significance testing. The first is to estimate ttie number of clusters in the data and the second is to identify the amount of overlap between ttie various clusters. Unfortunately, no completely satisfactory statistical test exists. One is faced with a difficult decision, either to ignore the problem or to make do with available testing methods. The simplest, most straight-forward test is chosen for this study, the sum of squares ratio test. Even though the test method may be flawed, it is necessary to underscore the importance and usefulness of statistical measures of cluster separation. 

Signal-to-noise ratio, 30 Significance tests, 6 Similarity measures, 94 Simpson s integration, 64 Sin e linkage, clustering, 106 Spline interpolation, 50 Standard deviation, 2 pooled estimate, 9 relative, 5 Standard error, 5 Standardization, 10 Standardized regression coefficients, 168... 

We computed an analysis of variance over Table 1, followed by tests of specific effects. Two results were statistically significant. Random selection of compounds was better than cluster or space-filling selection. BCUT descriptors were better for analysis than either of the principal component descriptor sets. 

The reason for this effect has to be attributed to a better and adequate ratio between sample size and array dimensionality. For a significant clustering of the patterns, with an array of six sensors a sample size of at least 18 is required [149, 184]. As a consequence, the discrimination based on only 12 measurements has poor statistical relevance. Most of the applications with sensor arrays found in the literature do not consider this fact frequently discriminations with 12-32 sensors in an array and with a sample size of three to four are described. All of them are of limited feasibility with concurrent poor validation, especially in terms of reproducibility and predictive ability. In other words, if there are not enough calibration measurements one can separate data in a predetermined way, but will fail to verify the result using independent test samples. 

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