This study presents and evaluates several methods for automated species-level classification of echolocation clicks from three beaked whale species recorded in the northern Gulf of Mexico. The species included are Cuvier's and Gervais' beaked whales, as well as an unknown species denoted Beaked Whale Gulf. An optimal feature set for discriminating the three click types while also separating detected clicks from unidentified delphinids was determined using supervised step-wise discriminant analysis. Linear and quadratic discriminant analyses both achieved error rates below 1% with three features, determined by tenfold cross validation. The waveform fractal dimension was found to be a highly ranked feature among standard spectral and temporal parameters. The top-ranking features were Higuchi's fractal dimension, spectral centroid, Katz's fractal dimension, and -10 dB duration. Six clustering routines, including four popular network-based algorithms, were also evaluated as unsupervised classification methods using the selected feature set. False positive rates of 0.001 and 0.024 were achieved by Chinese Whispers and spectral clustering, respectively, across 200 randomized trials. However, Chinese Whispers clustering yielded larger false negative rates. Spectral clustering was further tested on clicks from encounters of beaked, sperm, and pilot whales in the Tongue of the Ocean, Bahamas.