# SCMs: Systematic Conglomerated Models for Audio Cough Signal Classification
## 1 Introduction
A Variable Markov Model and recurrence dynamics were used for cough sound detection by [PERSON] et al. (2018). Cough sound analysis for pneumonia and asthma classification in a pediatric population were conducted by [PERSON] et al. (2018). The acoustic features were analyzed for the speech-sound-based classification of asthmatic and health subjects by [PERSON] et al. (2018). A proof-of-concept study was conducted for the development of machine learning for asthmatic and healthy voluntary cough sounds by [PERSON] et al. (2018). In this work, three systematic conglomerated models (SCMs) are proposed for audio cough signal classification. Initially, the pre-processing aspect is given some importance in our work, as follows. To pre-process and preserve the audio cough signal, a filter is applied so that the unnecessary and redundant detail coefficients are removed. To mitigate the noise with both non-white and uncertain sources, a time-frequency domain filter back dependent on the Wavelet Transform is used. Depending on a collection of recursive functions, the versatile form of a time series signal technique utilized is the Discrete Wavelet Transform (DWT) ([PERSON] et al., 2018). Wavelet functions aid greatly in the formation of the Wavelet Transform (WT). To mitigate the noise in the signal, Wavelet Transforms are used widely. A low-pass digital filter is utilized initially for the audio cough signal to pass through it efficiently. Most of the redundant frequency components of the signals are eliminated completely. A signal can be decomposed into various frequency sub-bands by DWT, which is expressed in the following equation:  
\[\psi(t)=\frac{1}{\sqrt{s^{*}}}\psi\bigg{(}\frac{t-p}{s^{*}}\bigg{)} \tag{1}\]where \(s^{*}\) denotes the scale and \(p\) denotes the translation parameter. At various frequencies, the correlation is expressed as follows:  
\[W_{s^{*}}(p,s^{*})=\frac{1}{s^{*}}\int\limits_{-\infty}^{\infty}x(t)\phi^{*} \bigg{(}\frac{t-p}{s^{*}}\bigg{)}dt \tag{2}\]  
To define the signal frequency, the DWT coefficients are used, and this is represented as follows:  
\[\bigg{(}s^{*}_{j},p_{k}\bigg{)}=\bigg{(}2^{j},k2^{j}:j,k\in Z\bigg{)} \tag{3}\]  
Once the cough audio signals are pre-processed, the proposed models are implemented. The main innovation of this proposal is to select and choose the various available models in the literature and create a novel conglomerated or hybrid model and test its performance on the audio cough signal datasets. The following techniques are used:  
1. The first technique utilizes the concept of robust models with Gabor dictionary analysis and machine learning techniques with special focus on support vector regression (SVR) and ensemble models;
2. The second technique utilizes the concept of stacked conditional autoencoders (SAEs);
3. The third technique utilizes the concept of using some efficient feature extraction schemes like TQWT, sparse TQWT, MIC and DCC and some feature selection techniques like BTSA, aggregation functions, FA, EFA classified with machine learning classifiers, KELM, arc-cosine ELM, RSO-based KELM, etc.