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Overweight and obesity are highly prevalent in the United States, with over two-thirds of the adult population classified as overweight and over one-third as obese. Associated with a number of serious diseases, these conditions have been shown to increase the risk of issues such as hypertension, type 2 diabetes mellitus, and depression, among others. All told, overweight and obesity place a significant burden on the modern healthcare industry, with estimates on the cost as high as $210 billion per year. Many obese individuals attempt to lose weight but, following a loss, a series of neurobehavioral mechanisms activate that commonly result in weight regain. There are no methods to date for determining a priori who will successfully lose weight and maintain the loss, nor have any definitive factors been identified that can be used to predict who will see a long-term reduction in his or her weight-related medication regimen. These problems, along with many others in the clinical field, stand to benefit from the application of signal processing and machine learning methods. To begin addressing these issues, participants in a two-year weight-loss study are split into two groups based on their ability to lose weight while dieting and to maintain at least a portion of that loss. Utilizing accelerometer data collected before each subject's diet, a windowed approach to persistent homology is used to show a clear difference in the intra-group similarities between the movement profiles of the two groups (p = 1.505 x 10^-23). This application of persistent homology presents a novel take on the topological method, allowing for more clinically relevant results by placing limits on the time frame in which two activities can be considered related. By expanding upon and investigating the measured difference, insights can be gained on how movement affects diet efficacy. From the same study, a separate metric for success based on an individual's medication history is developed. Using features extracted from physiological signals collected both before and after the diet, a Naive Bayes model is generated. After reducing the feature set to filter out noise, this model is shown to be able to predict, with an accuracy of nearly 86%, which individuals will require more prescription medications and which will require fewer a year and a half later. This indicates that weight loss can have a lasting impact on health, regardless of future weight regain, and has major implications for the pharmacological industry. Furthering these results, a new machine learning algorithm is developed and presented. Meant for noisy datasets, Laplacian of Correlation Graph Classification shows improvements in accuracy and robustness over standard machine learning algorithms when applied to unreduced feature sets of varying sizes. This method not only removes the risk of excluding potentially useful data through feature selection, but it can also provide clinically relevant insights into the underlying relationships between disparate measurements.