Mean Square Error Optimal Estimator Research Articles

Time-frequency feature extraction for classification of episodic memory

This paper investigates the extraction of time-frequency (TF) features for classification of electroencephalography (EEG) signals and episodic memory. We propose a model based on the definition of locally stationary processes (LSPs), estimate the model parameters, and derive a mean square error (MSE) optimal Wigner-Ville spectrum (WVS) estimator for the signals. The estimator is compared with state-of-the-art TF representations: the spectrogram, the Welch method, the classically estimated WVS, and the Morlet wavelet scalogram. First, we evaluate the MSE of each spectrum estimate with respect to the true WVS for simulated data, where it is shown that the LSP-inference MSE optimal estimator clearly outperforms other methods. Then, we use the different TF representations to extract the features which feed a neural network classifier and compare the classification accuracies for simulated datasets. Finally, we provide an example of real data application on EEG signals measured during a visual memory encoding task, where the classification accuracy is evaluated as in the simulation study. The results show consistent improvement in classification accuracy by using the features extracted from the proposed LSP-inference MSE optimal estimator, compared to the use of state-of-the-art methods, both for simulated datasets and for the real data example.

Optimal stochastic discrete time–frequency analysis in the ambiguity and time-lag domain

In stochastic time–frequency analysis, the covariance function is often estimated from only one observed realization with the use of a kernel function. For processes in continuous time, this can equivalently be done in the ambiguity domain, with the advantage that the mean square error optimal ambiguity kernel can be computed. For processes in discrete time, several ambiguity domain definitions have been proposed. It has previously been reported that in the Jeong–Williams ambiguity domain, in contrast to the Nutall and the Claasen–Mecklenbräuker ambiguity domain, any smoothing covariance function estimator can be represented as an ambiguity kernel function. In this paper, we show that the Jeong–Williams ambiguity domain cannot be used to compute the mean square error (MSE) optimal covariance function estimate for processes in discrete time. We also prove that the MSE optimal estimator can be computed without the use of the ambiguity domain, as the solution to a system of linear equations. Some properties of the optimal estimator are derived.