-The goal of this research is the robust detection of Parkinson's disease by acoustic analysis of sustained voice recordings. Application of signal decomposition into intrinsic mode functions (IMFs) is investigated as a novel type of audio features and a custom solution for decision-level fusion, employing statistical functionals to compress decisions from all IMFs. Proposed audio features are perceptual linear predictive cepstral coefficients (PLPCCs) estimated on the extracted components from one or several equally-spaced windows of audio signal. Decompositions used are empirical mode decomposition (EMD) and variational mode decomposition (VMD). Random forest (RF) is used as a base detector as well as meta learner for decision-level fusion. Cost of log-likelihood ratio and equal error rate (EER) were used to measure goodness-of-detection. Baseline solution using PLPCCs from all frames was compared to several types of decision-level fusion (EMD, VMD, and EMD+VMD) using 1-3 windows of various sizes (10-100 ms). Decomposition-based PLPCCs and EMD+VMD fusion from three 30 ms sized windows resulted in detection performance with an average EER of 6.5% and clearly outperformed the baseline solution of decompositionless PLPCCs, having EER of 32.9%. Variable importance from meta RF found both decompositions as useful and variancerelated statistics of base RF decisions as the most important.
I. INTRODUCTION
Parkinson’s disease (PD) is the second most common neurodegenerative disease after Alzheimer’s [1] and it is expected that the prevalence of PD is going to increase due to population ageing. If it is detected early, the progression of PD may be more researched using neuroprotective strategies, which could result in increased life span and improved living conditions.
Amongst many various symptoms, PD induces speech
disorders, which can be observed as early as 5 years before the
diagnosis [
approach for PD detection. Detailed review of the related work
can be found in [
Most of the studies use audio features obtained from the
entire record (global attributes) directly or calculated from
shortterm frames (local attributes). Frame-based features usually are
compressed with the statistical functionals or the Gaussian
mixture model [
Small size of previously used databases and data samples
(less than 60 PD subjects) is a major deficiency resulting in
unreliable estimates of reported performance. Incorrect
assessment of accuracy is another common deficiency – studies
often lack conformity to leave-one-subject-out [
This work explores application of two techniques for voice signal decomposition into intrinsic mode functions, namely, empirical mode decomposition (EMD) and variational mode decomposition (VMD), introduces a novel decision-level fusion approach using EMD and VMD base detectors and addresses the aforementioned deficiencies by using relatively large database and leave-one-subject-out validation for a task of PD detection.
The organization of this paper is as follows: voice recordings database is described in section 2, feature extraction in section 3, detection methodology is presented by section 4, results of experiments are in section 5, while conclusions are drawn in section 6.
Audio features of choice were PLPCC, which were extracted either from all frames of recording and compressed using statistical functionals (baseline solution) or from a few frames after applying decomposition and extracting IMFs (researched solution). Two approaches for decomposition were considered – empirical mode decomposition (EMD) and variational mode decomposition (VMD). Therefore, the researched solution proposes EMD-PLPCC and VMD-PLPCC as audio descriptors.
Empirical mode decomposition is a recent method for
nonstationary signal analysis which has found extensive application
in
many
areas of science and
engineering [
The number of maxima, which are strictly positive, and the number of minima, which are strictly negative, for each IMF, are either equal, or differ at most by one. The mean value of the envelope, as defined by the maxima and the minima, for each IMF, is zero.
The technique for decomposition of the data into IMFs is known as sifting, a brief description of which follows: For a given discrete time signal [ ], all the local minima and maxima of [ ] are identified.
The upper envelope is calculated by using a cubic spline to connect all the local maxima. Similarly, the lower envelope is calculated from the local minima. The upper and lower envelopes should cover all the data in [ ] between them.
The mean
= + /2 of the upper and lower envelopes is calculated, and [ ] is updated by subtracting the mean from it [ ] ← [ ] − .
The previous three steps are executed till [ ] is reduced to an IMF 1[ ], which conforms to the properties of IMFs described previously. The first IMF contains the highest oscillation frequencies found in the original data [ ].
The first IMF 1[ ] is subtracted from [ ] to get the residue 1[ ]. residue
The residue 1[ ] is now taken as the starting point instead of [ ], and the previously mentioned steps are repeated to find all the IMFs 1[ ] so that the final either becomes a constant, a monotonic function, or a function with a single maximum and minimum from which no further IMF can be extracted. =1 [ ] = ∑ [ ] + [ ]
Therefore, at the end of the decomposition, we can represent [ ] as the sum of K IMFs and a residue : The EMD algorithm variant used is ensemble empirical mode decomposition with adaptive noise (CEEMDAN) [7], which (1) automatically selects the number of intrinsic mode functions (IMFs). According to the selected number of IMFs for EMD, the same number of IMFs was used in the VMD algorithm.
Variational mode decomposition [
The
original formulation
of the
optimization problem is continuous in time domain. The
constrained formulation is given in [
The idea of a perceptual front end for determining linear prediction cepstral coefficients (PLPCCs) has been applied in different ways to improve speech detection and coding, as well as noise reduction, reverberation suppression, and cancellation.
Linear prediction of a signal is done
echo
via
autoregressive moving average (ARMA) modeling of the time
series. In an ARMA model, the current sample is expressed as:
[ ] = ∑ [ − ] + ∑ [ − ]
(2)
=0
=1
where [ ] is the current input signal, and [ ] is the current
output. The perceptual linear prediction coefficients are created
from the linear prediction coefficients by performing perceptual
processing before performing the autoregressive modeling [
Voice database had 383 speakers (141 men and 242 women), where each speaker was represented by 3 recordings (419 recordings for men and 715 recordings for women) of sustained voicing of vowel /a/, each at least 2 seconds in length. Speaker age range was from 16 to 82 for HC and from 39 to 85 for PD. Detailed summary of voice recording database is in Table I. Recordings were collected in a sound-proof chamber using acoustic cardioid microphone (AKG Perception 220) placed at a distance of 10 cm from the mouth. Audio format was “.wav” (16-bit mono PCM
with 44.1 kHz sampling frequency). HC
voice subgroup encompassed healthy volunteer individuals who
considered their voice as normal, had no complaints concerning
their voice and no history of chronic laryngeal diseases or other
long-lasting voice disorders. Voices of these individuals were
also confirmed as healthy by clinical specialists. Furthermore,
no pathological alterations in the larynx of the subjects from HC
voice subgroup were found during video laryngostroboscopy.
decision trees, where the final decision is obtained by majority
voting. The core idea of RF is to combine many (
in total)
decision trees, built using different bootstrap samples of the
original data set, and a random subset (of predetermined size )
of features 1, … , . RF is known to be robust against
overfitting and as the number of trees increases, the generalization
error converges to a limit [
was set to ∙ √ ) were
The generalization performance of RF was evaluated using
internal out-of-bag (OOB) validation, where each observation is
classified only by the trees which did not have this observation
in bootstrap sample during construction. It is well known that
OOB validation provides an unbiased estimate of a test set error,
similar to leave-one-out scheme. Because of the “repeated
measures”
aspect in
voice
data,
where
each
subject is
represented by several recordings of sustained vowel, sampling
part of the RF algorithm [
RFs were built independently for each decomposition variant (EMD or VMD) and each frame location (center frame only or 3 frames in equally-spaced locations) and decisions of these individual experts were combined in a metalearner fashion. RF was used both as a base learner and as a meta learner. This implies that outputs from RF models from the first stage after compression of decisions for all IMFs of a single recording using statistical functionals are treated as inputs (meta-features) for another RF in the second stage.
For the detection task, a decision from base RF is the difference between class posteriori. Given a trained RF, this difference or variant of soft decision is estimated as: ∑ ( 1, … , ) = =1 ( , , = 2) − =1 ( , , = 1) ∑
, into which falls in the th tree of the forest: where is the object being classified, is the number of trees 2, . . . , in the RF for which observation is OOB, is a class label (label number 1 corresponds to HC and 2 to PD), and ( , , ) stands for the th class frequency in the leaf node, ( , , ) =
( , , ) ∑ =1 ( , , ) , (3) (4) where is the number of classes and ( , ) is the number of training data from class and falling into the same leaf node of as .
For a baseline solution, there was no need of decision-level fusion and a single base RF was enough. For a researched solution, decision-level fusion used decisions from the decomposition-based base RFs. Base RF was constructed using all components (IMFs) resulting from EMD or VMD in a specific frame. The number of decisions from a base RF corresponded to the number of extracted components. This varied number of base decisions was compressed into metafeatures using the following statistical functionals: min, max, mean, median, trimean, standard deviation, inter-quartile range (IQR), lower quartile (Qlo), upper quartile (Qup), lower range (IQlo), upper range (IQup), skewness, and kurtosis.
Meta-features in fusion RF were also investigated by performing
permutation-based variable importance analysis using mean decrease in accuracy as the variable importance measure. Values of each
meta-feature are permuted several times and the mean difference in fusion RF performance on
To evaluate the goodness of detection, detector’s scores for OOB data were used. Votes of RF were converted to a proper score vector by normalizing votes for a specific class through division by the total number of times the case was OOB, as in formula (3). A quick way to compare detectors is the equal error rate (EER).
The
cost of log-likelihood-ratio
(Cllr) is a
comprehensive detection metric, used here as the main criterion
for model selection. The log-likelihood-ratio is the logarithm of
the ratio between the likelihood that the target (PD) produced the
signal and the likelihood that a non-target (HC) produced the
signal. EER and Cllr measures were estimated using the ROC
convex hull method, available in the BOSARIS toolkit [
V. EXPERIMENTS
For our frame-based features several window sizes were tested: 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 milliseconds. For a researched solution, different quantity of windows were extracted and detection performance compared: 1 window from the center of recording versus 2 or 3 windows placed at equallyspaced locations to evenly cover all recording. For each setting of window size and quantity, three decision-level fusion variants were tested: EMD, VMD and EMD+VMD. The number PLPCCs used was 12 in both baseline and researched solutions.
From the results of initial experiments, the single best window size was selected. Sensitivity analysis was then performed by repeating decomposition for each recording 5 times. Each of the 5 different collections of IMFs, converted into EMD-PLPCCs or VMD-PLPCCs, were used in base RF and construction of base RF repeated 5 times. Finally, each of 25 results from decomposition and base RF runs was fused using meta RF and the fusion was repeated 5 times. All runs resulted in 125 detection performance measures (EER and Cllr) and statistical testing for equality of central tendencies (mean and median) was performed to compare the setting of using 1 central window only versus using 3 windows at equally-spaced locations. Parametric independent samples t-test was used to compare means. Non-parametric Wilcoxon rank-sum test (Mann-Whitney U-test) was used to compare medians.
From the results of initial experiment with various window sizes in Table II we decide that 30 ms window size, 1 or 3 windows and fusion of EMD+VMD could be a recommended setting for a researched solution. Both window sizes had same EER of 2.22%, but Cllr was slightly better for 3 windows (0.079) than 1 window (0.085). VMD consistently outperformed EMD, but the best overall performance was found when fusing EMD+VMD. The best window size was difficult to identify, because the results change from one window size to another sometimes rather erratically. This could be due to stochastic nature of EMD and VMD, where optimization results in suboptimal solutions and not identical IMFs when run repeatedly.
The summary of results from Table II for 1 and 3 windows is illustrated in Fig 2–3. Both settings of window quantity were able to provide the lowest EER of 2.2% with 30 ms window size, but performance when using 3 windows appear to be more stable and doesn’t fluctuate that much with respect to window sizes.
Fig. 3. EMD+VMD detection performance by EER and Cllr using 3 windows.
Results of the baseline solution (see Fig. 4), when extracting PLPCCs from all frames (without any decomposition) and compressing with statistical functionals, were rather stable irrespective of the window size. The best detection performance was 32.9% by EER and 0.895 by Cllr.
Fig. 4. Detection performance by EER and Cllr for the baseline solution.
Variable importance from the meta RF when using 3 windows and EMD+VMD type of decision-level fusion is shown in Fig 5. Both EMD and VMD types of decomposition are useful, but from statistical functionals variance-related measures (standard deviation and inter-quartile range with its lower part) of base decisions appear to be the most important for the detection.
Sensitivity analysis was performed by repeating detection task using 30 ms window size and EMD+VMD fusion. Distribution of the resulting Cllr and EER measures is illustrated by boxplots in Fig 6 – 7. Quartiles Median Mean lfr iiittrsoobunC D iiittrsoobEEnuR f D
Due to the lack of normality in Cllr and EER measures (see Tables III – IV), non-parametric statistical testing was performed. Medians of Cllr and EER were compared between 1 window and 3 windows setting using Wilcoxon rank-sum test and results are provided in Table V. Statistically significant difference with 99% confidence (p-value < 0.01) was indicated in favor of using 3 windows.
HYPOTHESIS OF EQUAL CENTRAL TENDENCIES TESTING FOR
CLLR AND EER USING WILCOXON RANK-SUM TEST
VI. CONCLUSIONS
Decomposition-based PLPCC features, namely, EMDPLPCC and VMD-PLPCC, were found useful for building expert system for Parkinson’s detection from sustained voice. The baseline solution without decomposition and decision-level fusion, where PLPCCs were obtained from all frames and compressed using statistical functionals, resulted in the lowest EER of 32.90% for 30 ms windows size. The researched solution using decision-level fusion of PLPCCs from EMD and VMD, obtained from 3 windows at equally-spaced locations, resulted in EER as low as 2.22% for 30 ms window size.
Sensitivity analysis was performed by fixing window size at 30 ms and repeating detection task 125 times to choose between fusion of components from 1 or 3 windows. Fusion of EMD+VMD from 1 window provided an average EER of 12.13%, whereas fusion of EMD+VMD from 3 windows provided an average EER of 6.48%. Detection performance when using decision-level fusion of decomposition results from 3 evenly located windows was better than using 1 central window and the difference in detection performance was statistically significant, as indicated by statistical tests.
Main challenge remains lack of numerical stability in decomposition output, where extracted IMFs were not identical between runs. This limitation leaves the choice of the window size questionable, but future work could exploit a multitude of sub-optimal IMFs and use them for boosting data amounts when building detectors. Not only the first stage detectors could be built on more data, but also statistical functionals when compressing decisions of base detectors for the second stage would certainly benefit from increased number of decisions – statistics for decision-level fusion would be obtained not from 6–12 components, as in a current solution, but from several times more. We speculate that meta-leaner in the second stage could achieve robustness by using all IMFs of several repeated decomposition runs.
Voice database was collected at Lithuanian University of Health Sciences (LUHS) under a grant (No. MIP-075/2015) from the Research Council of Lithuania. Authors would like to thank LUHS specialists – otorhinolaryngologist Evaldas Padervinskis and neurologist Jolita Čičelienė.