Optimizing time-frequency kernels for classification

In many pattern recognition applications, features are traditionally extracted from standard time-frequency representations (TFRs). This assumes that the implicit smoothing of, say, a spectrogram is appropriate for the classification task. Making such assumptions may degrade classification performance. In general, ana time-frequency classification technique that uses a singular quadratic TFR (e.g., the spectrogram) as a source of features will never surpass the performance of the same technique using a regular quadratic TFR (e,g., Rihaczek or Wigner-Ville). Any TFR that is not regular is said to be singular. Use of a singular quadratic TFR implicitly discards information without explicitly determining if it is germane to the classification task. We propose smoothing regular quadratic TFRs to retain only that information that is essential for classification. We call the resulting quadratic TFRs class-dependent TFRs. This approach makes no a priori assumptions about the amount and type of time-frequency smoothing required for classification. The performance of our approach is demonstrated on simulated and real data. The simulated study indicates that the performance can approach the Bayes optimal classifier. The real-world pilot studies involved helicopter fault diagnosis and radar transmitter identification.