Читать книгу Informatics and Machine Learning. From Martingales to Metaheuristics онлайн

37 страница из 101

The HMM “sensor” capabilities can be significantly improved via switching from profile‐Markov Model (pMM) sensors to pMM/SVM‐based sensors, as indicated in [1, 3] and ssss1, where the improved performance and generalization capability of this approach is demonstrated.

In standard band‐limited (and not time‐limited) signal analysis with periodic waveforms, sampling is done at the Nyquist rate to have a fully reproducible signal. If the sample information is needed elsewhere, it is then compressed (possibly lossy) and transmitted (a “smart encoder”). The received data is then decompressed and reconstructed (by simply summing wave components, e.g. a “simple” decoder). If the signal is sparse or compressible, then compressive sensing [190] can be used, where sampling and compression are combined into one efficient step to obtain compressive measurements (the simple encoding in [190] since a set of random projections are employed), which are then transmitted (general details on noise in this context are described in [191, 192]). On the receiving end, the decompression and reconstruction steps are, likewise, combined using an asymmetric “smart” decoding step. This progression toward asymmetric compressive signal processing can be taken a step further if we consider signal sequences to be equivalent if they have the same stationary statistics. What is obtained is a method similar to compressive sensing, but involving stationary‐statistics generative‐projection sensing, where the signal processing is non‐lossy at the level of stationary statistics equivalence. In the SCW signal analysis the signal source is generative in that it is describable via use of a HMM, and the HMM’s Viterbi‐derived generative projections are used to describe the sparse components contributing to the signal source. In SCW encoding the modulation of stationary statistics can be man‐made or natural, with the latter in many experimental situations involving a flow phenomenology that has stationary statistics. If the signal is man‐made, usually the underlying stochastic process is still a natural source, where it is the changes in the stationary statistics that is under the control of the man‐made encoding scheme. Transmission and reception are then followed by generative projection via Viterbi‐HMM template matching or via Viterbi‐HMM feature extraction followed by separate classification (using SVM). So in the SCW approach the encoding is even simpler (possibly non‐existent, other than directly passing quantized signal) and is applicable to any noise source with stationary statistics (e.g. a stationary signal with reproducible statistics, the case for many experimental observations). The decoding must be even “smarter,” on the other hand, in that generalized Viterbi algorithms are used, and possibly other ML methods as well, SVMs in particular. An example of the stationary statistics sensing with a ML‐based decoder is described in application to CCC studies in ssss1.