Monophonic and Polyphonic Wheezing Classification Based on Constrained Low-Rank Non-Negative Matrix Factorization

Abstract

The appearance of wheezing sounds is widely considered by physicians as a key indicator to detect early pulmonary disorders or even the severity associated with respiratory diseases, as occurs in the case of asthma and chronic obstructive pulmonary disease. From a physician's point of view, monophonic and polyphonic wheezing classification is still a challenging topic in biomedical signal processing since both types of wheezes are sinusoidal in nature. Unlike most of the classification algorithms in which interference caused by normal respiratory sounds is not addressed in depth, our first contribution proposes a novel Constrained Low-Rank Non-negative Matrix Factorization (CL-RNMF) approach, never applied to classification of wheezing as far as the authors' knowledge, which incorporates several constraints (sparseness and smoothness) and a low-rank configuration to extract the wheezing spectral content, minimizing the acoustic interference from normal respiratory sounds. The second contribution automatically analyzes the harmonic structure of the energy distribution associated with the estimated wheezing spectrogram to classify the type of wheezing. Experimental results report that: (i) the proposed method outperforms the most recent and relevant state-of-the-art wheezing classification method by approximately 8% in accuracy; (ii) unlike state-of-the-art methods based on classifiers, the proposed method uses an unsupervised approach that does not require any training.

Keywords: asthma; chronic obstructive pulmonary disease; constraint; low-rank; monophonic; non-negative matrix factorization; polyphonic; spectral pattern; spectrogram; wheezing.

Figure 1

Time-frequency representation of two examples of Monophonic (MP) wheezing: (A) with a single basal peak; (B) with the harmonics of a single basal peak. Note that the frequency components are harmonically related in (B).

Figure 2

Time-frequency representation of two examples of Polyphonic (PP) wheezing: (A) with two non-harmonically related peaks; (B) with five non-harmonically related peaks. Note that the frequency components are not harmonically related in the case of PP wheezing.

Figure 3

Flowchart of the proposed method.

Figure 4

Example of the estimated matrices ${\mathbf{B}}_W$ and ${\mathbf{B}}_R$ obtained from the proposed CL-RNMF approach, analyzing the MP wheezing spectrogram previously shown in Figure 1B. (A) Although the matrix ${\mathbf{B}}_W$ is composed of four spectral bases, the spectral wheezing patterns are compacted into the fourth basis ${\mathbf{B}}_W\left(4\right)$. This spectral basis ${\mathbf{B}}_W\left(4\right)$ is composed of three narrowband spectral peaks. (B) The matrix ${\mathbf{B}}_R$ is composed of thirty-two wideband spectral bases.

Figure 5

The estimated basis matrices ${\mathbf{B}}_W$ obtained from CL-RNMF in the examples shown in Section 1. (A) ${\mathbf{B}}_W$ for the MP wheezing shown in Figure 1A. (B) ${\mathbf{B}}_W$ for the MP wheezing shown in Figure 1B. (C) ${\mathbf{B}}_W$ for the PP wheezing shown in Figure 2A. (D) ${\mathbf{B}}_W$ for the PP wheezing shown in Figure 2B. The wheezing spectral patterns were compacted into a single basis, ${\mathbf{B}}_W\left(2\right)$ (in Case (A)), ${\mathbf{B}}_W\left(4\right)$ (in Case (B)), and ${\mathbf{B}}_W\left(2\right)$ (in Case (C)). However, the energy of the narrowband spectral peaks was divided into two bases ${\mathbf{B}}_W\left(1\right)$ and ${\mathbf{B}}_W\left(2\right)$, as can be seen in Case (D).

Figure 6

The spectral energy distribution $\xi \left(f\right)$ provided by CL-RNMF from the estimated basis matrix ${\mathbf{B}}_W$ shown in Figure 5: (A) Figure 5A. (B) Figure 5B. (C) Figure 5C. (D) Figure 5D.

Figure 7

Example of the proposed two-step procedure to classify between MP and PP wheezing when $\eta >1$ from the example of MP wheezing shown in Figure 1B. Note that the arrows indicate the narrowband spectral peaks that compose the wheezing. In this case, the wheezing is classified as MP because all spectral peaks are harmonically related.

Figure 8

Example of the proposed two-step procedure to classify between MP and PP wheezing when $\eta >1$, considering the two examples of PP wheezing shown in Figure 2. (A) Two-step procedure applied to the PP wheezing shown in Figure 2A. (B) Two-step procedure applied to the PP wheezing shown in Figure 2B. Note that the arrows indicate the narrowband spectral peaks that compose the wheezing. In this case, both wheezing are classified as PP because not all spectral peaks are harmonically related.

Figure 9

Scheme of the types of wheezing contained in the database.

Figure 10

LOO cross-validation scheme for the database described in this paper.