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The computation of moments of probabilistic finite-state automata (PFA) is researched in this article. First, the computation of moments of the length of the paths is introduced for general PFA, and then, the computation of moments of the number of times that a symbol appears in the strings generated by the PFA is described. These computations require a matrix inversion. Acyclic PFA, such as word graphs, are quite common in many practical applications. Algorithms for the efficient computation of the moments for acyclic PFA are also presented in this paper. [ABSTRACT FROM AUTHOR]

Line-level keyword spotting (KWS) is presented on the basis of frame-level word posterior probabilities. These posteriors are obtained using word graphs derived from the recognition process of a full-fledged handwritten text recognizer based on hidden Markov models and N -gram language models. This approach has several advantages. First, since it uses a holistic, segmentation-free technology, it does not require any kind of word or character segmentation. Second, the use of language models allows the context of each spotted word to be taken into account, thereby considerably increasing KWS accuracy. And third, the proposed KWS scores are based on true posterior probabilities, taking into account all (or most) possible word segmentations of the input image. These scores are properly bounded and normalized. This mathematically clean formulation lends itself to smooth, threshold-based keyword queries which, in turn, permit comfortable trade-offs between search precision and recall. Experiments are carried out on several historic collections of handwritten text images, as well as a well-known data set of modern English handwritten text. According to the empirical results, the proposed approach achieves KWS results comparable to those obtained with the recently-introduced “BLSTM neural networks KWS” approach and clearly outperform the popular, state-of-the-art “Filler HMM” KWS method. Overall, the results clearly support all the above-claimed advantages of the proposed approach. [ABSTRACT FROM AUTHOR]