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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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(a) Set of points where slope is estimated from the fitted sigmoid curves in the approach proposed in Section 2.3. (b) Set of  estimates for different starting points versus embedded dimensions are fitted by the exponential equation (15). (c) Correlation dimension estimate for each set corresponding to different starting points. Data extracted from Lorenz attractor of 5000-sample length.
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fig5: (a) Set of points where slope is estimated from the fitted sigmoid curves in the approach proposed in Section 2.3. (b) Set of estimates for different starting points versus embedded dimensions are fitted by the exponential equation (15). (c) Correlation dimension estimate for each set corresponding to different starting points. Data extracted from Lorenz attractor of 5000-sample length.

Mentions: The Lorenz attractor series was used to validate the new proposed methodologies. Figure 5(a) displays the SCF log-log curves for embedded dimensions m from 1 to 10. The sets of points where the slope is evaluated according to (15) are displayed for different starting points. For each starting point, the corresponding set of points is selected following a gradient descent technique. Figure 5(b) shows the slope estimate () versus m for each starting point. Figure 5(c) displays the correlation dimension estimate () versus log⁡(r) for each starting point. The maximum () constitutes the novel D2 estimate ().


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)

(a) Set of points where slope is estimated from the fitted sigmoid curves in the approach proposed in Section 2.3. (b) Set of  estimates for different starting points versus embedded dimensions are fitted by the exponential equation (15). (c) Correlation dimension estimate for each set corresponding to different starting points. Data extracted from Lorenz attractor of 5000-sample length.
© Copyright Policy
Related In: Results  -  Collection

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

fig5: (a) Set of points where slope is estimated from the fitted sigmoid curves in the approach proposed in Section 2.3. (b) Set of estimates for different starting points versus embedded dimensions are fitted by the exponential equation (15). (c) Correlation dimension estimate for each set corresponding to different starting points. Data extracted from Lorenz attractor of 5000-sample length.
Mentions: The Lorenz attractor series was used to validate the new proposed methodologies. Figure 5(a) displays the SCF log-log curves for embedded dimensions m from 1 to 10. The sets of points where the slope is evaluated according to (15) are displayed for different starting points. For each starting point, the corresponding set of points is selected following a gradient descent technique. Figure 5(b) shows the slope estimate () versus m for each starting point. Figure 5(c) displays the correlation dimension estimate () versus log⁡(r) for each starting point. The maximum () constitutes the novel D2 estimate ().

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