Fractal-based supervised approach for dimensionality reduction of hyperspectral images

Dimensionality reduction is one of the most challenging and crucial issues apart from data mining, security, and scalability, which have retained much traction due to the ever-growing need to analyze the large volumes of data generated daily. Fractal Dimension (FD) has been successfully used to characterize data sets and has found relevant applications in dimension reduction. This paper presents an application of the FD Reduction (FDR) Algorithm on geospatial hyperspectral data, examining its usefulness for data sets with a relatively high embedding dimension. We examine the algorithm at two levels. First is the conventional FDR approach (unsupervised) at the image level. Alternatively, we propose a pixel-level supervised approach for band reduction based on time-series complexity analysis. Techniques for determining an optimal intrinsic dimension for the dataset using these two techniques are examined. We also develop a parallel GPU-based implementation for the unsupervised image-level FDR algorithm, reducing the run-time by nearly 10 times. Furthermore, both approaches use a support vector machine classifier to compare the classification performance of the original and reduced image obtained.