Big data and deep data in scanning and electron microscopies: deriving functionality from multidimensional data sets

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.