Intra-subject enveloped multilayer fuzzy sample compression for speech diagnosis of Parkinson's disease

Abstract

Machine learning-based Parkinson’s disease (PD) speech diagnosis is a current research hotspot. However, existing methods use each corpus sample as the base unit for modeling. Since different corpus samples within the same subject have different sensitive speech features, it is difficult to obtain unified and stable sensitive speech features (diagnostic markers) that reflect the pathology of the whole subject. Therefore, this study aims at compressing the corpus samples within the subject to facilitate the search for diagnostic markers with high diagnostic accuracy. A two-step sample compression module (TSCM) can solve the problem above. It includes two major parts: sample pruning module (SPM) and sample fuzzy clustering mechanism (SFCMD). Based on stacking multiple TSCMs, a multilayer sample compression module (MSCM) is formed to obtain multilayer compression samples. After that, simultaneous sample/feature selection mechanism (SS/FSM) is designed for feature selection. Based on the multilayer compression samples processed by MSCM and SS/FSM, a novel ensemble learning algorithm (EMSFE) is designed with sparse fusion ensemble learning mechanism (SFELM). The proposed EMSFE is validated by visualization of extracted features and performance comparison with related algorithms. The experimental results show that the proposed algorithm can effectively extract the stable diagnostic markers by compressing the corpus samples within the subject. Furthermore, based on LOSO cross validation, the proposed algorithm with extreme learning machine (ELM) classifier can achieve the accuracy of 92.5%, 93.75% and 91.67% on three datasets, respectively. The proposed EMSFE can extract unified and stable sensitive features that accurately reflect the overall pathology of the subject, which can better meet the requirements of clinical applications.

The code and datasets can be found in: https://github.com/wywwwww/EMSFE-supplementary-material.git

Graphical Abstract

Main flowchart of the proposed algorithm

Appendix

The objective function of SFCMD is expressed as follows:

$$\begin{array}{l} J_{SFCMD} ({\varvec{U}},{\varvec{X}},{\varvec{V}}) = J_{FCM} ({\varvec{U}},{\varvec{V}}) + J_{MIDMD} ({\varvec{X}},{\varvec{V}}) \hfill \\ = \mathop {\min }\limits_{{{\varvec{U}},{\varvec{V}}}} \sum\limits_{{i{ = }1}}^{C} {\sum\limits_{{k{ = }1}}^{{N^{\prime} }} {\left( {u_{ik} } \right)^{m} \left\| {{\varvec{x}}_{k} - {\varvec{v}}_{i} } \right\|^{2} } } + \lambda \left( {\sum\limits_{{i{ = }1}}^{C} {u_{ik} - 1} } \right) + \frac{1}{{N^{\prime 2} }}\sum\limits_{{k{ = }1}}^{{N^{\prime} }} {\sum\limits_{{k^{\prime} { = }1}}^{{N^{\prime} }} {\kappa \left( {{\varvec{x}}_{k} ,{\varvec{x}}_{{k^{\prime} }} } \right)} } - \frac{2}{{N^{\prime} C}}\sum\limits_{{k{ = }1}}^{{N^{\prime} }} {\sum\limits_{{i{ = }1}}^{C} {\kappa \left( {{\varvec{x}}_{k} ,{\varvec{v}}_{i} } \right)} } + \frac{1}{{C^{2} }}\sum\limits_{{i{ = }1}}^{C} {\sum\limits_{{i^{\prime} { = }1}}^{C} {\kappa \left( {{\varvec{v}}_{i} ,{\varvec{v}}_{{i^{\prime} }} } \right)} } \hfill \\ \end{array}$$

In the SFCMD model there are two variables ${\varvec{U}}$ and ${\varvec{V}}$ that need to be optimized, so an effective alternating variable optimization strategy can be considered to optimize the solution, i.e., to solve for one variable while fixing the other variable constant. Therefore, in solving the objective function, ${\varvec{V}}$ and ${\varvec{U}}$ can be fixed in turn and solved using the gradient descent method for the other variable, and the optimization details are specified as follows.

• 1) Fixing ${\varvec{V}}$ to solve ${\varvec{U}}$.

  By fixed ${\varvec{V}}$, the problem is solved with respect to ${\varvec{U}}$. After removing the terms unrelated to ${\varvec{U}}$, the objective function is transformed into (13).

  $${J}_{1}\left({\varvec{U}},{\varvec{V}}\right)=\underset{{\varvec{U}},{\varvec{V}}}{\mathrm{min}}\sum_{i=1}^{C}\sum_{k=1}^{{N}^{\mathrm{^{\prime}}}}{\left({u}_{ik}\right)}^{m}{\Vert {{\varvec{x}}}_{k}-{{\varvec{v}}}_{i}\Vert }^{2}+\lambda \left(\sum_{i=1}^{C}{u}_{ik}-1\right)$$

  (13)

  Solve for the minimalist solution of (13).

  $$\frac{{\partial J}_{1}\left({\varvec{U}},{\varvec{V}}\right)}{\partial {u}_{ik}}=m{\left({u}_{ik}\right)}^{m-1}{\Vert {{\varvec{x}}}_{k}-{{\varvec{v}}}_{i}\Vert }^{2}+\lambda =0$$

  (14)

  By calculation, the partition matrix is obtained as follows.

  $${u}_{ik}=\frac{{\Vert {{\varvec{x}}}_{k}-{{\varvec{v}}}_{i}\Vert }^{-\frac{2}{m-1}}}{\sum_{w=1}^{C}{\Vert {{\varvec{x}}}_{k}-{{\varvec{v}}}_{i}\Vert }^{-\frac{2}{m-1}}}$$

  (15)

• 2) Fixing ${\varvec{U}}$ to solve ${\varvec{V}}$.

  By fixed ${\varvec{U}}$, the problem is solved with respect to ${\varvec{V}}$. After removing the terms unrelated to ${\varvec{V}}$, the objective function is transformed into (16).

  $$\begin{array}{l} J_{2} ({\varvec{U}},{\varvec{V}}) = \mathop {\min }\limits_{{{\varvec{U}},{\varvec{V}}}} \sum\limits_{{i{ = }1}}^{C} {\sum\limits_{{k{ = }1}}^{{N^{\prime} }} {\left( {u_{ik} } \right)^{m} \left\| {{\varvec{x}}_{k} - {\varvec{v}}_{i} } \right\|^{2} } } \hfill \\ + \frac{1}{{{N^{\prime}}^{2} }}\sum\limits_{{k{ = }1}}^{{N^{\prime} }} {\sum\limits_{{k^{\prime} { = }1}}^{{N^{\prime} }} {\kappa \left( {{\varvec{x}}_{k} ,{\varvec{x}}_{{k^{\prime} }} } \right)} } - \frac{2}{{N^{\prime} C}}\sum\limits_{{k{ = }1}}^{{N^{\prime} }} {\sum\limits_{{i{ = }1}}^{C} {\kappa \left( {{\varvec{x}}_{k} ,{\varvec{v}}_{i} } \right)} } + \frac{1}{{C^{2} }}\sum\limits_{{i{ = }1}}^{C} {\sum\limits_{{i^{\prime} { = }1}}^{C} {\kappa \left( {{\varvec{v}}_{i} ,{\varvec{v}}_{{i^{\prime} }} } \right)} } \hfill \\ \end{array}$$

  (16)

  Based on the kernel function $\kappa \left({{\varvec{x}}}_{k},{{\varvec{v}}}_{i}\right)={{{\varvec{x}}}_{k}}^{T}{{\varvec{v}}}_{i}$ to solve the minimum solution of (16).

  $$\frac{{\partial J_{2} \left( {{\varvec{U}},{\varvec{V}}} \right)}}{{\partial {\varvec{v}}_{i} }} = - 2\sum\limits_{{k{ = }1}}^{{N^{\prime} }} {\left( {u_{ik} } \right)^{m} } \left( {{\varvec{x}}_{k} - {\varvec{v}}_{i} } \right) - \frac{2}{{N^{\prime} C}}\sum\limits_{{k{ = }1}}^{{N^{\prime} }} {{\varvec{x}}_{k} } + \frac{2}{{C^{2} }}\sum\limits_{{i{ = }1}}^{C} {{\varvec{v}}_{i} } = 0$$

  (17)

  The envelope compressed by SFCMD is obtained from (18).

  $${\varvec{V}} = {\varvec{A}}^{ - 1} \left[ {\begin{array}{*{20}c} {b_{1} } \\ {b_{2} } \\ \vdots \\ {b_{C} } \\ \end{array} } \right]$$

  (18)

  Among them:

  $${\varvec{A}} = diag\left( {a_{1} ,a_{2} ,...,a_{C} } \right) + \frac{1}{{C^{2} }} * {\varvec{I}}$$
  $$a_{i} = \sum\limits_{k = 1}^{{N^{\prime} }} {\left( {u_{ik} } \right)^{m} ,b_{i} = \sum\limits_{k = 1}^{{N^{\prime} }} {\left[ {\left( {u_{ik} } \right)^{m} + \frac{1}{{N^{\prime} C}}} \right]} } * {\varvec{x}}_{k} ,i = 1,2,...,C$$