Fast Learning of Grammar Production Probabilities in Radar Electronic Support

Although stochastic context-free grammars (SCFG) appear promising for the recognition and threat assessment of complex radar emitters in radar electronic support (ES) systems, the computational requirements for learning their production rule probabilities can be onerous. The two most popular methods, the inside-outside (IO) algorithm and the Viterbi score (VS) algorithm, are both iterative. IO maximizes the likelihood of a training data set, whereas VS maximizes the likelihood of its best parse trees. Even though VS is known to have lower overall computational costs in practice, both algorithms can be impractical for complex grammatical models. Several techniques have been previously developed to accelerate learning. In this paper, two fast variants of the traditional IO algorithm, known as graphical expectation-maximization (gEM(IO)) and tree-scanning (TS(IO)), are reviewed, along with a third technique called HOLA. In addition, two novel algorithms are proposed that apply the gEM (gEM(VS)) and TS (TS(VS)) principles to the Viterbi technique. An experimental protocol is defined and implemented so that the performance of all five techniques (gEM(IO), TS(IO), gEM(VS), TS(VS), and HOLA) can be compared using simulated training sets of complex radar signals. These techniques are compared from several perspectives-perplexity (the likelihood of a test data set), error rate on estimated states, time and memory complexity per iteration, and convergence time. Estimation of the average case and worst case execution time and storage requirements allow for the assessment of complexity, while computer simulations, performed using radar data sets, allow for the assessment of the other performance measures. The impact on performance of the number of sequences in the training set is observed. Results indicate that gEM(IO) and TS(IO) provide the same level of accuracy, yet the resources requirements depend on the ambiguity of the grammars. As expected, the gEM(VS) and TS(VS) techniques provide significantly lower convergence times and time complexities in practice than gEM(IO) and TS(IO), for a comparable level of accuracy. All of these algorithms may provide a greater level of accuracy than HOLA, yet their computational complexities may be orders of magnitude higher.