On the Mahalanobis Distance Classification Criterion for a Ventricular Septal Defect Diagnosis System

In this paper, the Mahalanobis distance classification criterion combined with principal component analysis (PCA)-based heart sound features generation is proposed for diagnosing three-type ventricular septal defects (VSDs): small VSDs (SVSDs), moderate VSDs (MVSDs), and large VSDs (LVSDs). The three stages corresponding to the diagnostic system implementation are summarized as follows. In the first stage, the heart sound is collected via a stethoscope and filtered using the wavelet decomposition. In the second stage, the time-domain features <inline-formula> <tex-math notation="LaTeX">$[{t}_{{12}}, {t}_{{11}}]$ </tex-math></inline-formula> are first extracted from a time-domain envelope <inline-formula> <tex-math notation="LaTeX">${E}_{{T}}$ </tex-math></inline-formula> for the filtered heart sound (<inline-formula> <tex-math notation="LaTeX">${S}_{{T}}$ </tex-math></inline-formula>), and the frequency-domain features <inline-formula> <tex-math notation="LaTeX">$[{f}_{{g}}, {f}_{{w}}]$ </tex-math></inline-formula> are subsequently extracted from a frequency-domain envelope <inline-formula> <tex-math notation="LaTeX">${E}_{{F}}$ </tex-math></inline-formula> for one-period <inline-formula> <tex-math notation="LaTeX">${S}_{{T}}$ </tex-math></inline-formula>, which is automatically segmented from heart sounds via the short time modified Hilbert transform. And then, the PCA-based diagnostic features <inline-formula> <tex-math notation="LaTeX">${\gamma }_{_{{1}}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${\gamma }_{_{{2}}}$ </tex-math></inline-formula> for the features (<inline-formula> <tex-math notation="LaTeX">${\mathrm {TFF}}=[{t}_{{12}}, {t}_{{11}}, {f}_{{g}}, {f}_{{w}}]$ </tex-math></inline-formula>) extracted from SVSD, MVSD, LVSD, and normal sounds (NM) are generated and expressed as the mean and standard deviation [−2.41 ± 0.49, 2.16 ± 0.45], [−1.87 ± 0.35, 0.22 ± 0.33], [−1.63 ± 0.56,−2.11 ± 0.68], and [1.11 ± 0.43, 0.09 ± 0.43], respectively. In the third stage, The Gaussian mixture models for the features <inline-formula> <tex-math notation="LaTeX">$[{\gamma }_{_{{1}}}, {\gamma }_{_{{2}}}]$ </tex-math></inline-formula> are first built, and then the Mahalanobis distance classification criterion-based diagnostic method is defined for diagnosing the VSD and NM. Moreover, to validate the usefulness of the proposed diagnostic system, mitral regurgitation and aortic stenosis sounds are used as examples for detection analysis. As comparative accuracies with other well-known classifiers, the higher classification accuracies achieved are 95.5%, 92.1%, 96.2%, and 99.0% for diagnosing SVSD, MVSD, LVSD, and NM, respectively.

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