Support vector machine classification trees based on fuzzy entropy of classification

• Parameter free SVM classification tree.
• Fuzzy entropy analytical gradient and Hessian.
• Overlapping classes without slack variables or cost C parameters.

The support vector machine (SVM) is a powerful classifier that has recently been implemented in a classification tree (SVMTreeG). This classifier partitioned the data by finding gaps in the data space. For large and complex datasets, there may be no gaps in the data space confounding this type of classifier. A novel algorithm was devised that uses fuzzy entropy to find optimal partitions for situations when clusters of data are overlapped in the data space. Also, a kernel version of the fuzzy entropy algorithm was devised. A fast support vector machine implementation is used that has no cost C or slack variables to optimize. Statistical comparisons using bootstrapped Latin partitions among the tree classifiers were made using a synthetic XOR data set and validated with ten prediction sets comprised of 50,000 objects and a data set of NMR spectra obtained from 12 tea sample extracts.

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