Discriminant functional cascades in time series analysis using covariance matrix eigenvector basis

Many natural phenomena expose covariance matrices the most of eigenvalues of which are less than average. The contribution of these eigenvalues to total energy is therefore less than 10-4 - 10-3. Such are the eigenvalues of Earth electromagnetic field time series. [1].

The eigenvectors with small eigenvalues are supposed to be more sensitive than with the big ones while been used to discrover the attributes of time series. Change of components which correspond to these eigenvectors may occur when time series capacity is changed slightly.

The obstacles for usage of these vectors are moreover algorithmical in nature. The selection of principal components in the time series produce a component set which is to be sift to get a subset of events which may serve as significant attributes.

The authors propose to use an algorithm called «cascaded discriminant functional». The algorithm consists of two stages. At first, recursive decimation procedure is used to get so called «cascades» (sets of lowering capacity) of eigenvectors, then discriminant functionals are computed for each cascade.