New methodology is proposed for the clustering of noisy and directional data. The dissertation contains three separate research papers. The first provides an

efficient k-means type algorithm for clustering observations in the presence of scattered observations. Scattered observations are defined as unlike any other, so traditional approaches that force them into groups can lead to erroneous conclusions. The second paper develops a computationally efficient k-means algorithm for grouping observations that lie on the surface of a high dimensional sphere. The final paper builds off the first two to develop an

algorithm that clusters directional data in the presence of scatter.