Hyperspectral images consist of large number of bands which require sophisticated analysis to extract. One approach to reduce computational cost, information representation, and accelerate knowledge discovery is to eliminate bands that do not add value to the classification and analysis method which is being applied. In particular, algorithms that perform band elimination should be designed to take advantage of the structure of the classification method used. This letter introduces an embedded-feature-selection (EFS) algorithm that is tailored to operate with support vector machines (SVMs) to perform band selection and classification simultaneously. We have successfully applied this algorithm to determine a reasonable subset of bands without any user-defined stopping criteria on some sample AVIRIS images; a problem occurs in benchmarking recursive-feature-elimination methods for the SVMs.

We propose a new edge detection method that is effective on multivariate irregular data in any domain. The method is based on a local polynomial annihilation technique and can be characterized by its convergence to zero for any value away from discontinuities. The method is numerically cost efficient and entirely independent of any specific shape or complexity of boundaries. Application of the minmod function to the edge detection method of various orders ensures a high rate of convergence away from the discontinuities while reducing the inherent oscillationsnear the discontinuities. It further enables distinction of jump discontinuities from steep gradients, even in instances where only sparse nonuniform data is available. These results are successfully demonstrated in both one and two dimensions.

The development of electron and scanning probe microscopies in the second half of the twentieth century has produced spectacular images of the internal structure and composition of matter with nanometer, molecular, and atomic resolution. Largely, this progress was enabled by computer-assisted methods of microscope operation, data acquisition, and analysis. Advances in imaging technology in the beginning of the twenty-first century have opened the proverbial floodgates on the availability of high-veracity information on structure and functionality. From the hardware perspective, high-resolution imaging methods now routinely resolve atomic positions with approximately picometer precision, allowing for quantitative measurements of individual bond lengths and angles. Similarly, functional imaging often leads to multidimensional data sets containing partial or full information on properties of interest, acquired as a function of multiple parameters (time, temperature, or other external stimuli). Here, we review several recent applications of the big and deep data analysis methods to visualize, compress, and translate this multidimensional structural and functional data into physically and chemically relevant information.