Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Computer Manual in MATLAB to Accompany Pattern Classification, Second Edition
Computer Manual in MATLAB to Accompany Pattern Classification, Second Edition
A spatio-temporal extension to Isomap nonlinear dimension reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
A comparison of one-class classifiers for novelty detection in forensic case data
IDEAL'07 Proceedings of the 8th international conference on Intelligent data engineering and automated learning
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Chemical data related to illicit cocaine seizures is analyzed using linear and nonlinear dimensionality reduction methods. The goal is to find relevant features that could guide the data analysis process in chemical drug profiling, a recent field in the crime mapping community. The data has been collected using gas chromatography analysis. Several methods are tested: PCA, kernel PCA, isomap, spatio-temporal isomap and locally linear embedding. ST-isomap is used to detect a potential time-dependent nonlinear manifold, the data being sequential. Results show that the presence of a simple nonlinear manifold in the data is very likely and that this manifold cannot be detected by a linear PCA. The presence of temporal regularities is also observed with ST-isomap. Kernel PCA and isomap perform better than the other methods, and kernel PCA is more robust than isomap when introducing random perturbations in the dataset.