Chaos Theory-Based Data-Mining Technique for Image Endmember Extraction: Laypunov Index and Correlation Dimension (L and D)

Abstract

It is often hard to collect a large size of high-quality field samples as ground reference points (GRPs) to support image analysis. Endmember extraction (EE) is an important technique to obtain spectrally identifiable image pixels to provide a supplementary solution to field sampling. However, most current EE methods are based on simplex models and thus rarely consider capricious occurrences in the data. The new approach developed in this paper synthesizes two quantitative measures of chaotic tendencies, Lyapunov index (L) and correlation dimension (D) into an integrated statistic, L and D for EE. L and D reconstructs a spectral dataset into phases, over which the chaotic or complex characteristics hidden in the dataset could be rearranged into predictable sequences. Therefore, better endmembers could be selected from the spectral or hyperspectral dataset. The usability and applicability of L and D are tested against the USGS standard spectral library first and then with a Hyperion image classification in Wulate Zhongqi (central county) of Inner Mongolia in China. L and D, along with four other methods, PPI+n-DV+GRPs, SMACC, VCA, and PPI+VCA, is applied to extract endmembers, which are used as the surrogates of GRPs for creating the training and testing samples and classifying the Hyperion image with two classifiers, spectral angle mapper (SAM) and support vector machine (SVM). The classification results based on GRPs derived from L and D have the overall accuracy and kappa statistics, 81.93% and 0.7905 (by SAM) or 84.11% and 0.814% (by SVM), whereas the other four methods have lower accuracies.