Recent advances in machine learning research promise to bring us closer to the original goals of artificial intelligence. Spurred by recent innovations in low-cost, specialized hardware and incremental refinements in machine learning algorithms, machine learning is revolutionizing entire industries. Perhaps the biggest beneficiary of this progress has been the field of computer vision. Within the domains of computational geometry and computer vision are two problems: Finding large, interesting holes in high dimensional data, and locating and automatically classifying facial features from images. State of the art methods for facial feature classification are compared and new methods for finding empty hyper-rectangles are introduced. The problem of finding holes is then linked to the problem of extracting features from images and deep learning methods such as convolutional neural networks. The performance of the hole-finding algorithm is measured using multiple standard machine learning benchmarks as well as a 39 dimensional dataset, thus demonstrating the utility of the method for a wide range of data
