CAPÍTULO 2. CARACTERÍSTICAS DEL SISTEMA
2.9 Descripción expandida de los casos de uso del sistema
A decision rule [31] or corresponding likelihood ratio determines the maximum error criterion or maximum a posteriori (MAP). A binary decision rule has two possible outcomes, when a new RF-measurement’s RF-Biomarker level falls within the tolerance region, then it is acceptable, rejected otherwise. A tolerance region threshold 𝑒𝑒𝑡𝑡 classifies acceptable Euclidean distance levels of similarity for new RF-Biomarker measurements. A receiver learns to recognize a device specific signature benchmark by observing 𝑛𝑛 independent normal benign RF-Events.
After observation of the events, a self-similarity test occurs that consists of all “𝑛𝑛-vs.𝑛𝑛”
observations, measurement and analysis of fingerprints to establish the true benchmark similarity levels for each local RF-Biomarker of a composite RF-DNA fingerprint.
100%
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The aggregation of three decision-rules (tolerance region, ordinal and continuous) aims to improve posterior probability classifications. Screening, binary, continuous, ordinal and paired diagnostic tests were considered in this article. Each test can be utilized together, independently, or as a single stand-alone test depending on the cost and potential benefit of the test given. A thorough discussion of each threshold decision rule is discussed in [39]. The initial screening of a receiver’s log file may be a logical place to conduct network-disease screening using a diagnostic test that meets policy thresholds. During the decision to treat a network for symptoms of network-disease, an initial screening level criterion 𝑆𝑆𝑐𝑐𝑟𝑟𝑒𝑒𝑒𝑒𝑛𝑛𝐿𝐿𝐿𝐿𝐿𝐿 specifies the minimum level of RF origin similarity acceptance. This value was experimentally determined by setting 𝑆𝑆𝑐𝑐𝑟𝑟𝑒𝑒𝑒𝑒𝑛𝑛𝐿𝐿𝐿𝐿𝐿𝐿 = 𝑝𝑝. The screening tolerance is
𝑆𝑆𝑐𝑐𝑟𝑟𝑒𝑒𝑒𝑒𝑛𝑛𝑇𝑇𝑇𝑇𝐿𝐿 = (𝑛𝑛 ∗ 𝑝𝑝) ∗ 𝑆𝑆𝑐𝑐𝑟𝑟𝑒𝑒𝑒𝑒𝑛𝑛𝐿𝐿𝐿𝐿𝐿𝐿. (4) 3.2.2.1 Tolerance Region
A policy-based tolerance region over a distribution of RF-measurements specifies an acceptable similarity level of at least a proportion 𝑝𝑝 of the population 𝑅𝑅 − 𝑝𝑝𝑝𝑝𝑝𝑝𝑟𝑟𝑒𝑒𝑟𝑟 (RF-Events) with confidence (1 – Ψ) is contained within its upper (𝑈𝑈(𝑋𝑋)) and lower 𝐿𝐿(𝑋𝑋) limits of acceptance [60]. A regional tolerance region can be computed to support binary classifications of composite RF-DNA fingerprint authenticity using a threshold for acceptance or tolerance rejection, a (𝑝𝑝, 1 − α) two-sided binary tolerance interval (𝐿𝐿(𝑋𝑋), 𝑈𝑈(𝑋𝑋)) satisfies the condition
𝑃𝑃𝑇𝑇{𝑃𝑃𝑇𝑇(𝐿𝐿(𝑋𝑋) ≤ 𝑋𝑋 ≤ 𝑈𝑈(𝑋𝑋)|𝑋𝑋) ≥ 𝜌𝜌} = 1 − 𝛼𝛼. (5) Where ′α′ represents the significance level. Construction of localized RF-Biomarker tolerance regions aim to improve posterior classification of a composite binary tolerance interval.
The tolerance region is created using a benchmark Composite RF-DNA fingerprint dataset of size N.
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The tolerance factor is computed based on a user’s specification for reliability of new comparisons made to a specified benchmark value. The specifications include the content of new
′𝑋𝑋 = 𝑏𝑏′ RF-Events (independent random variable) that are to be tested, the overall level of confidence that the RF-Biomarker levels should fall within and the proportion of 𝑋𝑋 samples that should are acceptable to a known benchmark [60].
Each tolerance region is adjusted using the Gauss-Kronrod factor 𝑘𝑘2 [30], which makes the interval slightly different from a conventional confidence interval which is generated about a distribution’s mean. Using the training RF benchmark, a tolerance region is computed for each local RF-Biomarker candidate. Each RF-Biomarker candidate component generates a localized benchmark using a [(𝜌𝜌 = 𝑛𝑛), (Ψ = {90,95})] tolerance interval. Threshold 𝑇𝑇ℎ1 accepts RF-Events where the combined Euclidean distance of RF-measurements of similarity falls within the bounds of (5). An extension is made to tune this decision rule to reduce errors made from composite averaging of all RF-measurements, instead each localized measurement develops its own local tolerance region specification in parallel. In uncertainty, two or more classifiers used in parallel, as shown in Figure 10b may improve posterior estimates when Bayesian aggregation is employed in uncertainty.
3.2.2.2 Ordinal Valued Threshold
The second decision-rule aims to refine the results obtained in (5) using an ordinal valued threshold. When the total number of characteristic RF-Biomarker features is defined from {1, 2,
…, b}, an ordinal threshold setting accounts for the majority vote ′O𝐿𝐿𝑉𝑉𝑡𝑡𝑉𝑉′ of local feature diagnostics that meet local policy threshold requirements for acceptable tolerance.
𝑂𝑂𝑑𝑑𝑡𝑡= ��𝑏𝑏
2� + 1�. (6)
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The ordinal valued data decision rule can be reduced to a binary result by comparing O𝐿𝐿𝑉𝑉𝑡𝑡𝑉𝑉
to the threshold specified in (6) above as;
O𝐿𝐿𝑉𝑉𝑡𝑡𝑉𝑉 ≥ 𝑂𝑂𝑑𝑑𝑡𝑡, �1, 𝑆𝑆𝑅𝑅𝑚𝑚𝑅𝑅𝑝𝑝𝑎𝑎𝑟𝑟𝑅𝑅𝑡𝑡𝑦𝑦 𝑀𝑀𝑎𝑎𝑀𝑀𝑀𝑀𝑟𝑟𝑅𝑅𝑡𝑡𝑦𝑦 𝑒𝑒𝑅𝑅𝑅𝑅𝑟𝑟𝑡𝑡𝑟𝑟;0, 𝑀𝑀𝑡𝑡ℎ𝑒𝑒𝑟𝑟𝑤𝑤𝑅𝑅𝑟𝑟𝑒𝑒. (7) The threshold specification from (6) implies a majority of features, from measurements must meet or exceed local pathology similarity to the RF signature’s benchmark. For example, let 𝑏𝑏 = 8 local RF-measurements. Let each local RF-measurement that meets acceptable tolerance count as a vote for RF-Event similarity, while each local tolerance failure counts as a vote against RF-Event similarity. When threshold [𝑂𝑂𝑑𝑑𝑡𝑡 = 5] and the count of local similarity acceptance meet or exceeds 𝑂𝑂𝑑𝑑𝑡𝑡, the RF-Event is counted as a benign RF-Event occurrence.
3.2.2.3 Continuous Valued Threshold
A third decision-rule option employs a continuous data threshold ′𝑍𝑍𝑑𝑑𝑡𝑡′ that provides an average risk ′𝑍𝑍̅𝑃𝑃𝑖𝑖𝑠𝑠𝑘𝑘′ of acceptance based on the benchmark similarity rating, using risk zones. A risk zone divides a binary policy defined tolerance region from (5) into three weighted zones of similarity error (lower is better). Where the upper and lower bounds for [𝑧𝑧 = 3] zones becomes;
�𝐿𝐿𝑧𝑧(𝑋𝑋), 𝑈𝑈𝑧𝑧(𝑋𝑋)� = 𝐿𝐿3(𝑋𝑋) < 𝐿𝐿2(𝑋𝑋) < 𝐿𝐿1(𝑋𝑋), 𝑈𝑈1(𝑋𝑋) < 𝑈𝑈2(𝑋𝑋) < 𝑈𝑈3(𝑋𝑋). (8) Where each local RF-Biomarker candidate receives a risk zone match score that ranges from one to four. In isolation, a risk zone match score value that is close to ‘1’ (i.e. Euclidean distance is near or equal to ‘0’) indicates an RF-Biomarker candidate that has a high similarity to the benchmark and presents a low risk of forged credential acceptance.
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When a pulse fails to meet the original benchmark’s binary tolerance interval, it receives a risk score of four to indicate complete tolerance region boundary failure. When average risk zone scores are less than or equal to 𝑍𝑍𝑑𝑑𝑡𝑡, the pulse is accepted, and rejected otherwise. A comparison of the average risk score (𝑍𝑍̅𝑃𝑃𝑖𝑖𝑠𝑠𝑘𝑘) to the threshold 𝑍𝑍𝑑𝑑𝑡𝑡 indicates the level of risk associated with allowing network access using the claimed logical credentials of an RF-Event. A summary of the risk zone comparisons is
𝑍𝑍̅𝑃𝑃𝑖𝑖𝑠𝑠𝑘𝑘 ≤ 𝑍𝑍𝑑𝑑𝑡𝑡, �1, 𝑎𝑎𝑐𝑐𝑐𝑐𝑒𝑒𝑝𝑝𝑡𝑡𝑎𝑎𝑏𝑏𝑝𝑝𝑒𝑒 𝑅𝑅𝑅𝑅𝑟𝑟𝑘𝑘;0, 𝑀𝑀𝑡𝑡ℎ𝑒𝑒𝑟𝑟𝑤𝑤𝑅𝑅𝑟𝑟𝑒𝑒. (9)