Time-Frequency Pepresentations (TFPs) are efficient tools for nonstationary signal classification. However, the choice of the TFP and of the distance measure employed is critical when no prior information other than a learning set of limited size is available. In this letter, we propose to jointly optimize the TFP and distance mea- sure by minimizing the (estimated) probability of classifi- cation error. The resulting optimized classification method is applied to multicomponent chirp signals and real speech records (speaker recognition). Extensive simulations show the substantial improvement of classification performance obtained with our optimization method.

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, any 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.

In this paper, we propose a method for selecting time-frequency distributions appropriate for given learning tasks. It is based on a criterion that has recently emerged from the machine learning literature: the kernel-target alignment. This criterion makes possible to find the optimal representation for a given classification problem without designing the classifier itself. Some possible applications of our framework are discussed. The first one provides a computationally attractive way of adjusting the free parameters of a distribution to improve classification performance. The second one is related to the selection, from a set of candidates, of the distribution that best facilitates a classification task. The last one addresses the problem of optimally combining several distributions.

In this article a problem of industrial quality control is investigated. Electric motors have to be tested for proper working by analyzing their emitted noise signal in regular running. The noise signal being (approximately) periodic, it can be seen as a sequence of single signal segments p i (t); i = 1; : : : ; N ; t = 1; : : : ; L i with approximately equal length L i . These segments are represented in the time-frequency space by their timefrequency representations (TFR) C i (t; ; \Phi). For each of the two considered fault classes "beating" and "gear noise" a fault parameter is defined based on the sequence of periods. This parameter implements a coarse knowledge of the corresponding physical fault. Since the representation of the signal segments depends explicitely on the kernel function \Phi of the TFR, the ability of the fault parameter to discriminate between good and defective motors can be optimized by varying \Phi. The resulting optimum kernel functions enables a reliable c...

this article we consider the problem of classification of finite time series of length L: f(t); t = 1; : : : ; L, for the case of two classes. The usual way of dealing with this problem is the following: First a number of features

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