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Methodological framework for estimating the correlation dimension in HRV signals.

Bolea J, Laguna P, Remartínez JM, Rovira E, Navarro A, Bailón R - Comput Math Methods Med (2014)

Bottom Line: Each approach for slope estimation leads to a correlation dimension estimate, called D₂, D(2(⊥)), and D(2(max)).D₂ and D(2(max)) estimate the theoretical value of correlation dimension for the Lorenz attractor with relative error of 4%, and D(2(⊥)) with 1%.D₂ keeps the 81% of accuracy previously described in the literature while D(2(⊥)) and D(2(max)) approaches reach 91% of accuracy in the same database.

View Article: PubMed Central - PubMed

Affiliation: Communications Technology Group (GTC), Aragón Institute for Engineering Research (I3A), IIS Aragón, University of Zaragoza, 50018 Zaragoza, Spain ; CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 50018 Zaragoza, Spain.

ABSTRACT
This paper presents a methodological framework for robust estimation of the correlation dimension in HRV signals. It includes (i) a fast algorithm for on-line computation of correlation sums; (ii) log-log curves fitting to a sigmoidal function for robust maximum slope estimation discarding the estimation according to fitting requirements; (iii) three different approaches for linear region slope estimation based on latter point; and (iv) exponential fitting for robust estimation of saturation level of slope series with increasing embedded dimension to finally obtain the correlation dimension estimate. Each approach for slope estimation leads to a correlation dimension estimate, called D₂, D(2(⊥)), and D(2(max)). D₂ and D(2(max)) estimate the theoretical value of correlation dimension for the Lorenz attractor with relative error of 4%, and D(2(⊥)) with 1%. The three approaches are applied to HRV signals of pregnant women before spinal anesthesia for cesarean delivery in order to identify patients at risk for hypotension. D₂ keeps the 81% of accuracy previously described in the literature while D(2(⊥)) and D(2(max)) approaches reach 91% of accuracy in the same database.

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Maximum slope points are marked with crosses over fitted sigmoid curves. Points calculated using gradient descent criteria from two starting points are shown in dots and circles. rj is the point which corresponds to the maximum slope in the lowest embedded dimension. The inset illustrates the correlation dimension estimation of the three sets of points.
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fig3: Maximum slope points are marked with crosses over fitted sigmoid curves. Points calculated using gradient descent criteria from two starting points are shown in dots and circles. rj is the point which corresponds to the maximum slope in the lowest embedded dimension. The inset illustrates the correlation dimension estimation of the three sets of points.

Mentions: The proposed strategy is based on selecting one point of the linear range in the SCF log-log curve of the lowest embedded dimension m and moving forward to the next embedded dimension m + 1, selecting the point of the corresponding SCF log-log curve with minimum distance to the former curve (i.e. where the perpendicular to the mth log-log curve intersects the (m + 1)th log-log curve, as in the gradient descent technique); see Figure 3. The procedure is repeated up to the maximum embedded dimension analyzed. Then, several sets of slopes are computed (one for each point in the linear region around the maximum slope of the SCF log-log curve of the lowest embedded dimension) providing a set of correlation dimension estimates per embedded dimension (). The dependence on r in the notation indicates that each set of correlation dimension estimates is linked to an r value, corresponding to the first value of each set.


Methodological framework for estimating the correlation dimension in HRV signals.

Bolea J, Laguna P, Remartínez JM, Rovira E, Navarro A, Bailón R - Comput Math Methods Med (2014)

Maximum slope points are marked with crosses over fitted sigmoid curves. Points calculated using gradient descent criteria from two starting points are shown in dots and circles. rj is the point which corresponds to the maximum slope in the lowest embedded dimension. The inset illustrates the correlation dimension estimation of the three sets of points.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3926396&req=5

fig3: Maximum slope points are marked with crosses over fitted sigmoid curves. Points calculated using gradient descent criteria from two starting points are shown in dots and circles. rj is the point which corresponds to the maximum slope in the lowest embedded dimension. The inset illustrates the correlation dimension estimation of the three sets of points.
Mentions: The proposed strategy is based on selecting one point of the linear range in the SCF log-log curve of the lowest embedded dimension m and moving forward to the next embedded dimension m + 1, selecting the point of the corresponding SCF log-log curve with minimum distance to the former curve (i.e. where the perpendicular to the mth log-log curve intersects the (m + 1)th log-log curve, as in the gradient descent technique); see Figure 3. The procedure is repeated up to the maximum embedded dimension analyzed. Then, several sets of slopes are computed (one for each point in the linear region around the maximum slope of the SCF log-log curve of the lowest embedded dimension) providing a set of correlation dimension estimates per embedded dimension (). The dependence on r in the notation indicates that each set of correlation dimension estimates is linked to an r value, corresponding to the first value of each set.

Bottom Line: Each approach for slope estimation leads to a correlation dimension estimate, called D₂, D(2(⊥)), and D(2(max)).D₂ and D(2(max)) estimate the theoretical value of correlation dimension for the Lorenz attractor with relative error of 4%, and D(2(⊥)) with 1%.D₂ keeps the 81% of accuracy previously described in the literature while D(2(⊥)) and D(2(max)) approaches reach 91% of accuracy in the same database.

View Article: PubMed Central - PubMed

Affiliation: Communications Technology Group (GTC), Aragón Institute for Engineering Research (I3A), IIS Aragón, University of Zaragoza, 50018 Zaragoza, Spain ; CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 50018 Zaragoza, Spain.

ABSTRACT
This paper presents a methodological framework for robust estimation of the correlation dimension in HRV signals. It includes (i) a fast algorithm for on-line computation of correlation sums; (ii) log-log curves fitting to a sigmoidal function for robust maximum slope estimation discarding the estimation according to fitting requirements; (iii) three different approaches for linear region slope estimation based on latter point; and (iv) exponential fitting for robust estimation of saturation level of slope series with increasing embedded dimension to finally obtain the correlation dimension estimate. Each approach for slope estimation leads to a correlation dimension estimate, called D₂, D(2(⊥)), and D(2(max)). D₂ and D(2(max)) estimate the theoretical value of correlation dimension for the Lorenz attractor with relative error of 4%, and D(2(⊥)) with 1%. The three approaches are applied to HRV signals of pregnant women before spinal anesthesia for cesarean delivery in order to identify patients at risk for hypotension. D₂ keeps the 81% of accuracy previously described in the literature while D(2(⊥)) and D(2(max)) approaches reach 91% of accuracy in the same database.

Show MeSH
Related in: MedlinePlus