The following thesis proposes solutions to problems in two main areas of focus, computer vision and machine learning. Chapter 2 utilizes traditional computer vision methods implemented in a novel manner to successfully identify overlays contained in broadcast footage. The remaining chapters explore machine learning algorithms and apply them in various manners to big data, multi-channel image data, and ECG data. L1 and L2 principal component analysis (PCA) algorithms are implemented and tested against each other in Python, providing a metric for future implementations. Selected algorithms from this set are then applied in conjunction with other methods to solve three distinct problems. The first problem is that of big data error detection, where PCA is effectively paired with statistical signal processing methods to create a weighted controlled algorithm. Problem 2 is an implementation of image fusion built to detect and remove noise from multispectral satellite imagery, that performs at a high level. The final problem examines ECG medical data classification. PCA is integrated into a neural network solution that achieves a small performance degradation while requiring less then 20% of the full data size.