Threshold Selection for Unsupervised Detection, with an Application to Microphone Arrays

Detection is usually done by comparing some criterion to a threshold. It is often desirable to keep a performance metric such as False Alarm Rate constant across conditions. Using training data to select the threshold may lead to suboptimal results on test data recorded in different conditions. This paper investigates unsupervised approaches, where no training data is used. A probabilistic model is fitted on the test data using the EM algorithm, and the threshold value is selected based on the model. The proposed approach (1)~does not use training data, (2)~uses the test data itself to compensate simplifications inherent to the model, (3)~permits the use of more complex models in a straightforward manner. On a microphone array speech detection task, the proposed unsupervised approach achieves similar or better results than the ``training'' approach. The methodology is general and may be applied to other contexts than microphone arrays, and other performance metrics than FAR.