Monophonic and Polyphonic Wheezing Classification Based on Constrained Low-Rank Non-Negative Matrix Factorization
Abstract
:1. Introduction
2. Theoretical Background
2.1. Non-Negative Matrix Factorization
2.2. Spectral Sparseness
2.3. Temporal/Spectral Smoothness
3. Proposed Method
3.1. Time-Frequency Signal Representation
3.2. Stage I: Constrained Low-Rank Non-Negative Matrix Factorization
- Low-rank: The number of wheezing components should be much less than the number of normal respiratory components, that is . This assumption allows that the number of frequency components can be reduced in the least number of bases possible for their posterior analysis, while normal respiratory sounds are modeled using a higher range of components. Experimental results showed that the best classification performance was obtained when and . In particular, when , the proposed CL-RNMF approach tends to converge very quickly at the expense of losing relevant wheezing content. On the other hand, when , the spectral wheezing patterns tend to be split into different components of the matrix .
- Constraints: These characterize wheezing sounds and normal respiratory sounds using opposite restrictions between both sounds. The use of constraints allows isolating the spectral wheezing patterns from the spectral patterns of normal respiratory sounds. Therefore, in order to find a better NMF decomposition that shows spectro-temporal features of the wheezing and normal respiratory sounds as can be observed in the real world, we propose to incorporate sparseness and smoothness into the NMF decomposition process. As shown in Figure 1 and Figure 2, wheezing sounds can be considered sparse in frequency because MP wheezing or PP wheezing is characterized by one or more than one narrowband spectral peak. Moreover, wheezing sounds can be considered smooth or continuous events in time, that is slow variation of the magnitude spectrogram along time. On the other hand, normal respiratory sounds can be considered smooth in frequency, that is they can be modeled assuming wideband spectral patterns. Therefore, should contain wheezing spectral patterns composed of one or more than one narrowband spectral peak, depending on the spectral complexity of each wheezing, and should be composed of a set of wideband spectral patterns that model the behavior of normal respiratory sounds.
Algorithm 1: CL-RNMF. |
Require: , , , , , , and M.ss |
1: Compute the normalized magnitude spectrogram using Equation (11).ss |
2: Initialize , , , and with random non-negative values.ss |
3: Update the estimated wheezing basis matrix using Equation (14).ss |
4: Update the estimated respiratory basis matrix using Equation (15).ss |
5: Update the estimated wheezing activations matrix using Equation (16).ss |
6: Update the estimated respiratory activations matrix using Equation (17).ss |
7: Repeat Steps 3–6 until the algorithm converges (or until the maximum number of iterations M is reached).ss |
8: Compute the spectral energy distribution from using Equation (18).ss |
return |
3.3. Stage II: Harmonic Structure Analysis
- The objective of the first step is to locate, in terms of frequency, all the narrowband spectral peaks detected in the previous Stage I. For this, we propose to locate the most prominent frequency in each spectral peak . Each value was calculated using the findpeaks function provided by the MATLAB software [74] due to the satisfactory results obtained in several preliminary analyses performed. Figure 7 shows the location , in terms of frequency, of each spectral peak for the MP example previously shown in Figure 1B.
- The objective of the second step is to check if the different spectral peaks are harmonically related or not. We assume that the first spectral peak () represents the basal peak. Therefore, the wheezing is classified as MP if the rest of spectral peaks () are located in the harmonic frequencies (integer multiple) of the basal peak. Otherwise, the wheezing is classified as PP. From the width of the main lobe of the basal peak () and the value of its most prominent frequency , the spectral intervals where the possible harmonic frequencies should be located are calculated as follows,
Algorithm 2: Harmonic structure analysis. |
Require: . |
1: From , detect the number of narrowband spectral peaks. |
if then |
return Wheezing category = MP |
else |
2: Locate the frequency in each spectral peak .ssssss |
3: Compute the spectral intervals using Equation (20). |
if then |
return Wheezing category = MP |
else |
return Wheezing category = PP |
end if |
end if |
4. Experimental Results and Discussion
4.1. Data Collection
4.2. Experimental Setup
4.3. Evaluation Metrics
4.4. State-of-the-Art Method for Comparison
4.5. Accuracy Results
- the improvement, in terms of , of the proposed method is about 8.25% UPER (SVM), 12% UPER (KNN), and 10.5% UPER (ELM).
- the improvement, in terms of , of the proposed method is about 4% UPER (SVM), 7.1% UPER (KNN), and 5.5% UPER (ELM).
- the improvement, in terms of , of the proposed method is about 12.5% UPER (SVM), 17% UPER (KNN), and 15.5% UPER (ELM).
- the improvement, in terms of , of the proposed method is about 5% UPER (SVM), 10% UPER (KNN), and 8% UPER (ELM).
- the improvement, in terms of , of the proposed method is about 20% UPER (SVM), 24% UPER (KNN), and 23% UPER (ELM).
- (i)
- Due to the time-frequency overlapping problem, normal respiratory sounds often mask wheezing sounds, hiding relevant medical information [5]. While the proposed method (based on CL-RNMF) allows removing as much as possible the acoustic interference from normal respiratory sounds, the method UPER is based on a feature PER obtained from the sub-band energy of the wavelet coefficients, so the presence of normal respiratory sounds interferes in the selection of the optimal sub-bands that really belong to the wheezing components.
- (ii)
- The method UPER has more difficulty in discriminating between PP and MP wheezing composed by a basal peak and its harmonics since it achieves the worst performance in terms of . The reason is because UPER is based on energy and ignoring the spectral location of the components that model the harmonic behavior of MP wheezing. Results in Table 2 suggest that MP/PP classification based on the spectral location of the harmonic structure as occurs in the proposed method is more reliable than the use of the energy of the wheezing spectral components, as occurs in UPER.
5. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Terms of the Multiplicative Update Rules
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Terms | Definitions |
---|---|
(True PP) | PP wheezing segments correctly classified |
(True MP) | MP wheezing segments correctly classified |
(False PP) | PP wheezing segments misclassified as MP |
(False MP) | MP wheezing segments misclassified as PP |
(True MP Type 1) | MP Type 1 wheezing segments correctly classified |
(True MP Type 2) | MP Type 2 wheezing segments correctly classified |
(False MP Type 1) | MP Type 1 wheezing segments misclassified as PP |
(False MP Type 2) | MP Type 2 wheezing segments misclassified as PP |
Algorithm | |||||
---|---|---|---|---|---|
Proposed Method | 92% | 91.5% | 92.5% | 91% | 94% |
UPER (SVM) [7] | 83.75% | 87.5% | 80% | 86% | 74% |
UPER (KNN) [7] | 80% | 84.4% | 75.5% | 81% | 70% |
UPER (ELM) [7] | 81.5% | 86% | 77% | 83% | 71% |
Scheme | Training Set | Validate Set | SVM | KNN | ELM |
---|---|---|---|---|---|
LOO | 399 (99.75%) | 1 (0.25%) | 83.75% | 80% | 81.5% |
LPO () | 320 (80%) | 80 (20%) | 81.5% | 79.25% | 80% |
LPO () | 240 (60%) | 160 (40%) | 80.5% | 77.75% | 79.5% |
LPO () | 160 (40%) | 240 (60%) | 78.25% | 74.75% | 77.25% |
LPO () | 80 (20%) | 320 (80%) | 76.25% | 71.75% | 75.25% |
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De La Torre Cruz, J.; Cañadas Quesada, F.J.; Ruiz Reyes, N.; García Galán, S.; Carabias Orti, J.J.; Peréz Chica, G. Monophonic and Polyphonic Wheezing Classification Based on Constrained Low-Rank Non-Negative Matrix Factorization. Sensors 2021, 21, 1661. https://doi.org/10.3390/s21051661
De La Torre Cruz J, Cañadas Quesada FJ, Ruiz Reyes N, García Galán S, Carabias Orti JJ, Peréz Chica G. Monophonic and Polyphonic Wheezing Classification Based on Constrained Low-Rank Non-Negative Matrix Factorization. Sensors. 2021; 21(5):1661. https://doi.org/10.3390/s21051661
Chicago/Turabian StyleDe La Torre Cruz, Juan, Francisco Jesús Cañadas Quesada, Nicolás Ruiz Reyes, Sebastián García Galán, Julio José Carabias Orti, and Gerardo Peréz Chica. 2021. "Monophonic and Polyphonic Wheezing Classification Based on Constrained Low-Rank Non-Negative Matrix Factorization" Sensors 21, no. 5: 1661. https://doi.org/10.3390/s21051661
APA StyleDe La Torre Cruz, J., Cañadas Quesada, F. J., Ruiz Reyes, N., García Galán, S., Carabias Orti, J. J., & Peréz Chica, G. (2021). Monophonic and Polyphonic Wheezing Classification Based on Constrained Low-Rank Non-Negative Matrix Factorization. Sensors, 21(5), 1661. https://doi.org/10.3390/s21051661