27,625 research outputs found
Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions
The scaled complex Wishart distribution is a widely used model for multilook
full polarimetric SAR data whose adequacy has been attested in the literature.
Classification, segmentation, and image analysis techniques which depend on
this model have been devised, and many of them employ some type of
dissimilarity measure. In this paper we derive analytic expressions for four
stochastic distances between relaxed scaled complex Wishart distributions in
their most general form and in important particular cases. Using these
distances, inequalities are obtained which lead to new ways of deriving the
Bartlett and revised Wishart distances. The expressiveness of the four analytic
distances is assessed with respect to the variation of parameters. Such
distances are then used for deriving new tests statistics, which are proved to
have asymptotic chi-square distribution. Adopting the test size as a comparison
criterion, a sensitivity study is performed by means of Monte Carlo experiments
suggesting that the Bhattacharyya statistic outperforms all the others. The
power of the tests is also assessed. Applications to actual data illustrate the
discrimination and homogeneity identification capabilities of these distances.Comment: Accepted for publication in the IEEE Transactions on Geoscience and
Remote Sensing journa
The spectral analysis of nonstationary categorical time series using local spectral envelope
Most classical methods for the spectral analysis are based on the assumption that the time
series is stationary. However, many time series in practical problems shows nonstationary
behaviors. The data from some fields are huge and have variance and spectrum which changes
over time. Sometimes,we are interested in the cyclic behavior of the categorical-valued time
series such as EEG sleep state data or DNA sequence, the general method is to scale the
data, that is, assign numerical values to the categories and then use the periodogram to find
the cyclic behavior. But there exists numerous possible scaling. If we arbitrarily assign the
numerical values to the categories and proceed with a spectral analysis, then the results will
depend on the particular assignment. We would like to find the all possible scaling that
bring out all of the interesting features in the data. To overcome these problems, there have
been many approaches in the spectral analysis.
Our goal is to develop a statistical methodology for analyzing nonstationary categorical
time series in the frequency domain. In this dissertation, the spectral envelope methodology
is introduced for spectral analysis of categorical time series. This provides the general
framework for the spectral analysis of the categorical time series and summarizes information
from the spectrum matrix. To apply this method to nonstationary process, I used the
TBAS(Tree-Based Adaptive Segmentation) and local spectral envelope based on the piecewise
stationary process. In this dissertation,the TBAS(Tree-Based Adpative Segmentation)
using distance function based on the Kullback-Leibler divergence was proposed to find the
best segmentation
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