We tried to find discriminating features for sperm whale clicks in order to distinguish between clicks from different whales, or to enable unique identification. We examined two different methods to obtain suitable characteristics. First, a model based on the Gabor function was used to describe the dominant frequencies in a click, and then the model parameters were used as classification features. The Gabor function model was selected because it has been used to model dolphin sonar pulses with great precision. Additionally, it has the interesting property that it has an optimal time–frequency resolution. As such, it can indicate optimal usage of the sonar by sperm whales. Second, the clicks were expressed in a wavelet packet table, from which subsequently a local discriminant basis was created. A wavelet packet basis has the advantage that it offers a highly redundant number of coefficients, which allow signals to be represented in many different ways. From the redundant signal description a representation can be selected that emphasizes the differences between classes. This local discriminant basis is more flexible than the Gabor function, which can make it more suitable for classification, but it is also more complex. Class vectors were created with both models and classification was based on the distance of a click to these vectors. We show that the Gabor function could not model the sperm whale clicks very well, due to the variability of the changing click characteristics. Best performance was reached when three subsequent clicks were averaged to smoothen the variability. Around 70% of the clicks classified correctly in both the training and validation sets. The wavelet packet table adapted better to the changing characteristics, and gave better classification. Here, also using a 3-click moving average, around 95% of the training sets classified correctly and 78% of the validation sets. These numbers lowered by only a few per cent when single clicks, instead of a moving average, were classified. This indicates that, while the features may show too much variability to enable unique identification of individual whales on a click by click basis, the wavelet approach may be capable of distinguishing between a small group of whales.
A comparison of model and non-model based time-frequency transforms for sperm whale click classification
