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It is calculated by using the false alarm rate and number of features, as shown in (8).
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The Tracy-Widom distribution is used to estimate the false alarm rate of the Akaike Information Criterion and Minimum Description Length methods when no external sources are present.
The expression (9) can be used for evaluating the false alarm probability for different sensing bandwidths in different parts of the spectrum gap.
The Tracy-Widom distribution is used to determine the false alarm rate of information theoretic methods that statistically estimate the number of sources in a multichannel receiver input.
This threshold τ(n o d e) is used to control the false alarm rate and adjusts for the properties of the node such as the mean and depth in the tree.
Using the OR rule, the false alarm probability of the coalition is given as (10).
For illustrative purposes, Table 2 provides the values of p (number of endmembers) estimated by the VD method for the considered hyperspectral scene, using different values of the false alarm probability (P F ).
Using the Tracy-Widom proposition, the false alarm probability of the DED algorithm using MDL criteria can be rewritten as P FA, MDL = F 2 N exp γ MDL + p - 1 2 log N N - μ ν (4.26).
However, the false alarms caused by the edges or strong intensity areas are filtered out using the proposed method, and the false alarm rates are reduced to less than 1 × 10−3 (Fig. 5c).
The kernel optimization criterion used involves the computation of the False Alarm Rate (FAR) and False Detection Rate (FDR) indicators, unified by the Area Under the ROC Curve (AUC).
We use the constant false alarm (CFA) criteria to determine the value of threshold γ t.
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