Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)

ASTESJ

www.astesj.com

ISSN: 2415-6698

Special Issue on Innovation in Computing, Engineering Science & Technology

Acoustic Scene Classifier Based on Gaussian Mixture Model in the Concept Drift Situation
Ibnu Daqiqil Id*, Masanobu Abe, Sunao Hara
Graduate School of Interdisciplinary Science and Engineering in Health Systems, Okayama University, Okayama, 700-0001, Japan
ARTICLEINFO
Article history:
Received: 15 July, 2021
Accepted: 22 September, 2021
Online: 30 September, 2021
Keywords:
Acoustic Scene Classifier
Concept Drift
Kernel Density Estimation
Gaussian Mixture Model

1.

ABSTRACTThe data distribution used in model training is assumed to be similar with that when themodel is applied. However, in some applications, data distributions may change over time.
This situation is called the concept drift, which might decrease the model performance
because the model is trained and evaluated in different distributions. To solve this problem
for scene audio classification, this study proposes the kernel density drift detection (KD3)algorithm to detect the concept drift and the combine–merge Gaussian mixture model(CMGMM) algorithm to adapt to the concept drift. The strength of the CMGMM algorithm
is its ability to perform adaptation and continuously learn from stream data with a local
replacement strategy that enables it to preserve previously learned knowledge and avoid
catastrophic forgetting. KD3 plays an essential role in detecting the concept drift andsupplying adaptation data to the CMGMM. Their performance is evaluated for four types ofconcept drift with three systematically generated scenarios. The CMGMM is evaluated withand without the concept drift detector. In summary, the combination of the CMGMM andKD3 outperforms two of four other combination methods and shows its best performance ata recurring concept drift.

Introduction

Human–computer interaction through audition requires
devices to recognize the environment using acoustic soundanalysis. One of the primary research topics in this area is acoustic
scene classification (ASC), which attempts to classify digital audio
signals into mutually exclusive scene categories. ASC is an
important area of study covering various applications, including
smart homes, context-aware audio services, security surveillance,
mobile robot navigation, and wildlife monitoring in natural
habitats. Machine audition applications have a high potential tolead to more innovative context-aware services.
We intend to develop an ASC system for environmental or
scene audio in specific locations (i.e., beach, shop, bus station, andairport) with different acoustic characteristics. The scene audio
contains an ensemble of background and foreground sounds. Oneof the most important aspects of the audio scene in real life is theconcept drift [1], whose data distribution might evolve or change
in the future. For example, the foreground event sounds in a bus
station, such as an ambulance siren, wind noise, and rustlingsounds, might change because of the physical environment, humanactivities, or nature [2]. These changes cause the acoustic data*

Corresponding Author: Ibnu Daqiqil Id, Okayama, Japan, daqiqil@s.okayamau.ac.jp

www.astesj.com
https://dx.doi.org/10.25046/aj060519

distributions to change, potentially causing a lower performance inthe trained model [3].
The simplest solutions for handling the abovementioned
problems to maintain the model performance are periodic
retraining and redeployment of the model. Nevertheless, thesesolutions can be time consuming and costly. Moreover, thedecision for the frequency of retraining and redeployment is adifficult task. Another promising approach is to use an evolving or
incremental learning method [4], [5], where the model is updated
when a new subset of data arrives [6]. Each iteration is considered
as an incremental step toward revisiting the current model.
In this study, we propose a combine–merge Gaussian mixture
model (CMGMM) and kernel density drift detection (KD3) tosolve the concept drift problem [7]. The CMGMM is an algorithm
based on the Gaussian mixture model (GMM) that adapts to theconcept drift by adding or modifying its components toaccommodate the emerging concept drift. The algorithm’s
advantages are adaptation and continuous learning from stream
data with a local replacement strategy to preserve previously
learned knowledge and avoid catastrophic forgetting.
In [7], we compared the CMGMM to the incremental GMM(IGMM) [8] and KD3 to adaptive windowing (ADWIN) [9] andHDMM [10] in two approaches, namely the active and passive167

I. Daqiqil ID et al./Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)
approaches. In the active approach, the concept drift is detectedusing a specific algorithm, then adapts the model. In the passive
approach, the model is continuously adapted at a specific fixedinterval. The result is that the combination of CMGMM and KD3
outperforms other combinations in two of three evaluation
scenarios.
The work described herein extends and improves that ofprevious publications [7,11] in the following respects:•

The algorithm has been modified to use component pruning
to overcome the overfitting problem and support the ScikitMultiflow Framework [12].
• The KD3 hyperparameter is optimized, and the algorithm isevaluated using prequential evaluation for better results andonline performance monitoring in several concept drift types
and scenarios.
The rest of this paper is organized as follows: Section 2
presents the related work of this research and the fundamental
equations used in our proposed solutions; Section 3 describes the
proposed CMGMM and KD3; Section 4 outlines the experimental
setup; Section 5 discusses the experimental results; and finally,
Section 6 provides our conclusions.
2.

Related Work

This section provides a brief overview of the related work on
the concept drift and the fundamental theory used in the proposed
method.
2.1. Concept Drift in Audio Scenes
A concept is defined as a set of object instances [13].
Probabilistically, a concept is defined using prior classprobabilities 𝑝𝑝(𝑦𝑦) and class conditional probabilities 𝑝𝑝(𝑋𝑋|𝑦𝑦) [4].
𝑝𝑝(𝑦𝑦) and 𝑝𝑝(𝑋𝑋|𝑦𝑦) determine the joint distribution 𝑝𝑝(𝑋𝑋, 𝑦𝑦) [3];hence, a concept is defined as the joint probability distribution of
a set of input features 𝑋𝑋 and the corresponding label 𝑦𝑦 in dataset
𝔇𝔇. In this paper, 𝑋𝑋 is an acoustic scene sound defined as a mixtureof specific event sounds (𝑥𝑥�) perceived and defined by humans [14],and 𝑦𝑦 is the label of 𝑋𝑋. 𝑋𝑋 has numerous types of acoustic event
sounds and background noises 𝑥𝑥� that often overlap with eachother. In other words, the relationship between of 𝑋𝑋 and 𝑥𝑥�
determines 𝑝𝑝(𝑋𝑋, 𝑦𝑦) , 𝑋𝑋 ∈ (𝑥𝑥�1 , 𝑥𝑥�2 , 𝑥𝑥�3 , . 𝑥𝑥�𝑖𝑖 , ) , where 𝑖𝑖 denotes thenumber of 𝑥𝑥� in 𝑋𝑋.
In the future, the relationship of 𝑥𝑥� in 𝑋𝑋 might change, whichthen changes the relationship of 𝑝𝑝(𝑋𝑋, 𝑦𝑦). For example, anotherevent sound might appear, or some existing event sounds may
disappear. This situation is called the concept drift, which isexpressed as follows:∃𝑋𝑋: 𝑝𝑝𝑤𝑤0 (𝑋𝑋, 𝑦𝑦) ≠ 𝑝𝑝𝑤𝑤𝑛𝑛 (𝑋𝑋, 𝑦𝑦).

(1)

Eq. (1) and Figure 1 describe concept drift as the change in the
joint probability distribution between two-time windows, 𝑤𝑤0
and 𝑤𝑤𝑛𝑛 . Models built on previous data at 𝑤𝑤0 might not be suitablefor predicting new incoming data at 𝑤𝑤𝑛𝑛 . This change may becaused by a change not only in the number of 𝑥𝑥�, but also in theunderlying data distribution of 𝑥𝑥�. These changes require model
adaptation because the model's error may no longer be acceptablewith the new data distribution [15].
www.astesj.com

Figure 1: Illustration of the concept drifts in an acoustic scene audio at a park

The change in the incoming data at 𝑤𝑤𝑛𝑛 depends on a variety ofdifferent internal or external influences (e.g., event sounds thatexist in a park depending on the season). The initial data recordedin the winter may only consist of people talking, bird calls, anddogs barking. However, the event sounds change in the summer,
and new event sounds, such as insect and wind sounds, emerge.
2.2. Concept Drift Detection Methods
Several methods have been proposed to detect concept drifts
from a data stream. This study focuses on window-based methods
that use fixed windows as a reference for summarizing previous
information. This approach has more accurate results than othermore straightforward methods, such as cumulative sum [16].
However, the computational time and space used are higher [17].
This approach usually utilizes statistical tests or mathematicalinequalities to compute the change in data. Some of the state-ofthe-art methods used in this paper is presented below:• ADWIN is a sliding window-based concept drift detection
algorithm. The size of ADWIN windows 𝑆𝑆𝑆𝑆 might change
depending on the instance in the distribution. Its size increases
when the instance in the stream continues in the same
distribution. 𝑆𝑆𝑆𝑆 shrinks when distribution changes occur [9].
ADWIN detects concept drifts when the averages between
these windows are higher than a given threshold.
• The HDDM is a concept drift detection algorithm based on
fixed windows and probability inequalities [10]. The author
proposes two types of HDDM, namely HDDMA andHDDMW. The HDDMA uses moving averages, whereas the
HDDMW uses weighted moving averages to detect the concept
drift. The HDDMA is suitable for detecting the abrupt concept
drift, whereas the HDDMW is suitable for detecting thegradual concept drift.
• KSWIN [18] is a window-based concept drift detection methodthat utilizes the Kolmogorov–Smirnov statistic test (KS-Test)
to compare the distances of two distributions. This test is a nonparametric test that does not require any assumptions about theunderlying data distribution.
Each method has its optimal hyperparameters, which differ
based on the datasets used and the type of drift in those datasets.
2.3. Merging Gaussian Mixture Component
A component of a Gaussian distribution is represented by(𝑤𝑤, 𝜇𝜇, 𝑃𝑃) and {(𝑤𝑤1 , 𝜇𝜇1 , 𝑃𝑃1 ), (𝑤𝑤2 , 𝜇𝜇2 , 𝑃𝑃2 ), … (𝑤𝑤𝑛𝑛 , 𝜇𝜇𝑛𝑛 , 𝑃𝑃𝑛𝑛 )} to denotea mixture of 𝑛𝑛 Gaussian components, where 𝑤𝑤, 𝜇𝜇, and 𝑃𝑃 are theweight or prior probability, distribution means, and covariancematrix, respectively. This mixture must satisfy 𝑤𝑤1 + 𝑤𝑤2 + ⋯ +𝑤𝑤𝑛𝑛 = 1 and has the pdf defined in Eq. (2).
168

I. Daqiqil ID et al./Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)

where,

𝑓𝑓(𝑋𝑋) = ∑𝑛𝑛𝑖𝑖=1 𝑤𝑤𝑖𝑖 𝑁𝑁(𝑥𝑥; 𝜇𝜇𝑖𝑖 , 𝑃𝑃𝑖𝑖 ),𝑁𝑁(𝑥𝑥; 𝜇𝜇𝑖𝑖 , 𝑃𝑃𝑖𝑖 ) =1�(2𝜋𝜋)𝑑𝑑 det 𝑃𝑃𝑖𝑖1𝑒𝑒 �−2(𝑥𝑥−𝜇𝜇𝑖𝑖 )𝑇𝑇 𝑃𝑃𝑖𝑖−1 (𝑥𝑥−𝜇𝜇𝑖𝑖 )�

(2)

Please refer to [19] for more details about the KL dissimilarityof the Gaussian distributions.
3.

.

(3)

Suppose we wish to merge two Gaussian components
�(𝑤𝑤𝑖𝑖 , 𝜇𝜇𝑖𝑖 , 𝑃𝑃𝑖𝑖 ), �𝑤𝑤𝑗𝑗 , 𝜇𝜇𝑗𝑗 , 𝑃𝑃𝑗𝑗 ��, where 𝑤𝑤𝑖𝑖 + 𝑤𝑤𝑗𝑗 ≤ 1 , and approximate
the result as a single Gaussian. The new Gaussian candidate(𝑤𝑤𝑖𝑖𝑖𝑖 , 𝜇𝜇𝑖𝑖𝑖𝑖 , 𝑃𝑃𝑖𝑖𝑖𝑖 ) must preserve the zeroth-, first-, and second-ordermoments of the original Gaussian. The moment-preserving merge
is shown in Eqs. (4)–(6).
𝑤𝑤𝑖𝑖𝑖𝑖 = 𝑤𝑤𝑖𝑖 + 𝑤𝑤𝑗𝑗
𝑤𝑤𝑗𝑗
𝑤𝑤𝑖𝑖
𝜇𝜇𝑖𝑖𝑖𝑖 =𝜇𝜇𝑖𝑖 +
𝜇𝜇
𝑤𝑤𝑖𝑖 + 𝑤𝑤𝑗𝑗
𝑤𝑤𝑖𝑖 + 𝑤𝑤𝑗𝑗 𝑗𝑗
𝑤𝑤𝑗𝑗
𝑤𝑤𝑖𝑖
𝑃𝑃𝑖𝑖𝑖𝑖 =𝑃𝑃𝑖𝑖 +
𝑃𝑃
𝑤𝑤𝑖𝑖 + 𝑤𝑤𝑗𝑗
𝑤𝑤𝑖𝑖 + 𝑤𝑤𝑗𝑗 𝑗𝑗
𝑤𝑤𝑖𝑖 𝑤𝑤𝑗𝑗𝑇𝑇+
2 �𝜇𝜇𝑖𝑖 − 𝜇𝜇𝑗𝑗 ��𝜇𝜇𝑖𝑖 − 𝜇𝜇𝑗𝑗 ��𝑤𝑤𝑖𝑖 + 𝑤𝑤𝑗𝑗 �Proposed Method

This study extends the combine–merge Gaussian mixture
model (CMGMM) [7] to classify audio scenes in concept drift
situations. The CMGMM was developed based on the GMM
algorithm that can incrementally adapt to the new identified
component. This algorithm can add new components as newconcepts and update existing components as a response to thechange of the current existing concept in the current data. The
CMGMM implementation is available in our public repository 1,
with the algorithm pipeline shown in Figure 2.

(4)
(5)
(6)

2.4. Kullback–Leibler (KL) Dissimilarity

Kullback–Leibler (KL) discrimination, known as KL
divergence or relative entropy, is a tool for measuring thediscrepancy between two probability distributions. The KL
discrimination between 𝑓𝑓(𝑥𝑥), a probability distribution for randomvariables 𝑋𝑋 and 𝑔𝑔(𝑥𝑥) , another probability distribution is the
expected value of the log-likelihood ratio. The KL divergence of𝑓𝑓(𝑥𝑥) and 𝑔𝑔(𝑥𝑥) is defined in Eq. (7), where ℜ𝑑𝑑 is the sample spaceof the random variable 𝑋𝑋.
𝑑𝑑𝐾𝐾𝐾𝐾 (𝑓𝑓, 𝑔𝑔) = � 𝑓𝑓(𝑥𝑥)𝑙𝑙𝑙𝑙𝑙𝑙ℜ𝑑𝑑

𝑓𝑓(𝑥𝑥)
𝑑𝑑𝑑𝑑.
𝑔𝑔(𝑥𝑥)(7)

Based on Eq. (7), KL is not a perfect distance metric because
it is asymmetric 𝑑𝑑𝐾𝐾𝐾𝐾 (𝑓𝑓, 𝑔𝑔) ≠ 𝑑𝑑𝐾𝐾𝐾𝐾 (𝑔𝑔, 𝑓𝑓) and does not satisfy thetriangle inequality, 𝑑𝑑𝐾𝐾𝐾𝐾 (𝑓𝑓, 𝑔𝑔) + 𝑑𝑑𝐾𝐾𝐾𝐾 (𝑔𝑔, ℎ) ≥ 𝑑𝑑𝐾𝐾𝐾𝐾 (𝑓𝑓, ℎ) .
However, we can use it as metric distance because the KL
discrimination of two probability distributions is larger than zero,
𝑑𝑑𝐾𝐾𝐾𝐾 (𝑓𝑓, 𝑔𝑔) ≥ 0 , and the discrimination of the identical two
probability distributions is zero, 𝑑𝑑𝐾𝐾𝐾𝐾 (𝑓𝑓, 𝑓𝑓) = 0.

Accordingly, we apply the KL dissimilarity by computing the
Kullback–Leibler discrimination upper bound of the post-merge
mixture with respect to the pre-merge mixture. In the case of theGaussian mixture, where 𝑓𝑓(𝑥𝑥) = 𝑁𝑁(𝑤𝑤1 , 𝜇𝜇1 , 𝑃𝑃1 ), 𝑔𝑔(𝑥𝑥) =𝑁𝑁(𝑤𝑤2 , 𝜇𝜇2 , 𝑃𝑃2 ) and 𝑤𝑤1 + 𝑤𝑤2 < 1 , the KL dissimilarity between
𝑓𝑓(𝑥𝑥) and 𝑔𝑔(𝑥𝑥) is shown in Eq. (8).
𝑑𝑑𝐾𝐾𝐾𝐾 ({(𝑤𝑤1 , 𝜇𝜇1 , 𝑃𝑃1 )}, {(𝑤𝑤2 , 𝜇𝜇2 , 𝑃𝑃2 )}).
1
= �𝑡𝑡𝑡𝑡( 𝑃𝑃2−1 [𝑃𝑃1 − 𝑃𝑃22+ (𝜇𝜇1 − 𝜇𝜇2 )(𝜇𝜇1 − 𝜇𝜇2 )𝑇𝑇 ])det(𝑃𝑃2 )+ 𝑙𝑙𝑙𝑙𝑙𝑙�det(𝑃𝑃1 )(8)

Figure 2: Combine–merge Gaussian mixture model (CMGMM) general
workflow

In the training process, we extract the feature of the scene audio
from the training dataset D0 and train an optimal model Μ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 .
We use the Expectation maximization (EM) [20] algorithm to train
the model and the Bayesian information criterion (BIC) [21] toselect the best model.
In the incremental process, the Μ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 performance isobserved through the prediction likelihood. When KD3 detects asignificant likelihood change, the model activates the concept drift
adaptation process. The concept drift adaptation process thenbegins by creating a local model Μ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 from the new coming
data. Μ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 represents the new concepts or concept updates in
the incoming data. Finally, we combine the Μ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 and Μ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
components to include any new concepts from Μ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 that may
not exist in the Μ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 at the initial training and merge similar
components to update the existing component in Μ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 .
The CMGMM pipeline process is detailed in the subsections
that follow.
3.1. Feature Extraction
Feature extraction is the first step of both the training andincremental processes. In this research, we use normalized Melfrequency cepstral coefficients (MFCCs) that represent the shortterm power spectrum of audio in the frequency domain of the Mel
scale. MFCCs are commonly used as features in audio processing
and speech recognition. The first step is pre-emphasis forenhancing the quantity of energy in high frequencies. The next stepis windowing the signal and computing the fast Fouriertransformation to transform the sample from the time domain to
the frequency domain. Subsequently, the frequencies are wrapped

1https://github.com/ibnudaqiqil/CMGMM

www.astesj.com

169

I. Daqiqil ID et al./Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)
on a Mel scale, and the inverse DCT is applied [22]. Finally, eachof the MFCCs is normalized using mean and variancenormalization based on Eq. (9):𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 =(𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀−𝜇𝜇)
𝑆𝑆

(9)

,

where, 𝜇𝜇 and 𝑆𝑆 denote the mean and the standard deviation of the
training samples, respectively.
3.2. Model Training

The training process is intended to build a set of models fromthe training dataset 𝐷𝐷0 containing training data 𝑥𝑥 ={𝑥𝑥1 , 𝑥𝑥2 , … , 𝑥𝑥𝑛𝑛 }, where 𝑥𝑥𝑛𝑛 denotes the MFCC vector. The models
are trained 𝑄𝑄 times using the EM algorithm. For each training
cycle, a different number of components 𝐾𝐾 ranging from Kmin to
Kmax is used, where 𝑄𝑄 = Kmax − Kmin. Consequently, a set of modelsℳ = �ℳ1 , ℳ2 , ℳ3 , . , ℳ𝑄𝑄 � is obtained based on the different
numbers of components.
The next step is model selection using the BIC. In [23], the BIC
value of a model ℳ𝐾𝐾 trained over the dataset X with K
components, BIC(X, 𝑀𝑀𝐾𝐾 ), is defined as follows:
𝐵𝐵𝐵𝐵𝐵𝐵(𝑋𝑋, 𝑀𝑀𝑘𝑘 ) ≡ − 2 log 𝐿𝐿(𝑋𝑋, 𝑀𝑀𝐾𝐾 ) + 𝑣𝑣 log 𝑁𝑁 ,(10)

where, L denotes the model likelihood; 𝑣𝑣 denotes the degree of
freedom of the model parameters; and 𝑁𝑁 denotes the number oftraining data points. The model with the lowest BIC value isselected because it maximizes the log-likelihood [6]. Algorithm 1presents the steps of the learning process.
Algorithm 1: Training the Optimal Model
Input: Initial Dataset Dinit, Minimum Component Number
Kmin, and Maximum Component Number Kmax
Result: Best GMM Model
BICbest = ∞for Kmin to Kmax do
Mcandidate= EMTrain(Dinit, k)
BICcandidate = ComputeBIC (Dinit, Mcandidate)
if BICcandidate < BICbest thenMbest = Mcandidate
end
end
return Mbest
3.3. Concept Drift Detection
We propose Kernel Density Drift Detection (KD3) to detect theconcept drift. KD3 is a window-based algorithm for concept drift
detection. It works based on estimating the window density using
the Kernel Density Estimation (KDE) or the Parzen’s window[24]. The KDE is a non-parametric probability density estimatorthat automatically estimates the shape of the data density without
assuming the underlying distribution. The concept drift can bedetected by comparing the probability functions between thesewindows. The greater the variation between the windows, the moreevidence obtained for the concept drifts. Aside from detecting
concept drifts, KD3 also collects data for adaptation (Ddrift) byidentifying a warning zone when data begin to show indications ofconcept drift.
KD3 requires three hyperparameters, namely α, β, and ℎ ,which denote the margins for detecting the concept drift andwww.astesj.com

accumulating the density distance and the window length,
respectively. α is used to determine the threshold of the density
variation in the concept drift, while β is employed to determine thethreshold of the density variation in the warning zone. Therefore,
α must be greater than β. KD3 accepts a set of likelihood windows
𝑧𝑧𝑐𝑐 as input. 𝑧𝑧𝑐𝑐 is the current likelihood window that contains asequence of log-likelihood ℓ from the model prediction, 𝑧𝑧𝑐𝑐 ={ℓ1 , ℓ2 , ℓ3 , … , ℓℎ }.

First, this algorithm aims to estimate the density (𝑓𝑓𝑘𝑘𝑘𝑘𝑘𝑘 ) of thecurrent 𝑧𝑧𝑐𝑐 and previous 𝑧𝑧𝑐𝑐−1 windows. Let ℓ𝑛𝑛 be the latest
generated ℓ . Let 𝑧𝑧𝑐𝑐 contain the ℎ -latest ℓ from ℓ𝑛𝑛 , 𝑧𝑧𝑐𝑐 ∈[ℓ𝑛𝑛−ℎ , ℓ𝑛𝑛 ], and let 𝑧𝑧𝑐𝑐−1 contain the ℎ-latest ℓ from ℓ𝑛𝑛−ℎ , 𝑧𝑧𝑐𝑐−1 ∈[ℓ𝑛𝑛−2ℎ , ℓ𝑛𝑛−ℎ ]. To detect a concept drift, the distance 𝑑𝑑̀𝑡𝑡 between
𝑓𝑓𝑘𝑘𝑘𝑘𝑘𝑘 of 𝑧𝑧𝑐𝑐 and 𝑧𝑧𝑐𝑐−1 is computed using Eq. (11) within the boundsof 𝑏𝑏1 and 𝑏𝑏2. The bounds are computed based on the maximum
and minimum values of the joined ℓ of 𝑧𝑧𝑐𝑐 and 𝑧𝑧𝑐𝑐−1 .
𝑏𝑏2

1𝑑𝑑̀𝑡𝑡 = � |𝑓𝑓𝑘𝑘𝑘𝑘𝑘𝑘 (𝑧𝑧𝑐𝑐 ) − 𝑓𝑓𝑘𝑘𝑘𝑘𝑘𝑘 (𝑧𝑧𝑐𝑐−1 )| 𝑑𝑑𝑑𝑑, where
2

(11)

𝑏𝑏1

𝑧𝑧𝑐𝑐 ∈ [ℓ𝑛𝑛−ℎ , ℓ𝑛𝑛 ], 𝑧𝑧𝑐𝑐−1 ∈ [ℓ𝑛𝑛−2ℎ , ℓ𝑛𝑛−ℎ ],𝑏𝑏1 = min(ℓ𝑛𝑛−2ℎ , ℓ𝑛𝑛 ) , 𝑏𝑏2 = max(ℓ𝑛𝑛−2ℎ , ℓ𝑛𝑛 ).

Finally, the algorithm compares 𝑑𝑑̀𝑡𝑡 to α and β.hen 𝑑𝑑̀𝑡𝑡 > β.
Suppose that the accumulative distance is equal to or greater thanα. In that case, the algorithm sends the collected data to the model
for adaptation. Figure 3 and Algorithm 2 illustrate the detailed
KD3 process.

Figure 3: Illustration of the Kernel density drift detection (KD3) concept

Algorithm 2: Detecting the Concept Drift
Input: Set of t likelihood ℓ, drift margin α, warning margin β (α> β), window length ℎ,
Result: Drift Concept Signal, Drifted Dataset (Ddrift)
Window1 = ℓ[𝑐𝑐 − ℎ: 𝑐𝑐];
Window2 = ℓ[𝑐𝑐 − 2ℎ: 𝑐𝑐 − ℎ];Bmin, Bmax = CalculateWindowBound(ℓ[𝑐𝑐 − 2ℎ: 𝑐𝑐]);
KDE1 = EstimateKDE(Window1)
KDE2 = EstimateKDE(Window2)
diff = distance(KDE1, KDE2, Bmin, Bmax)
if (diff ≥ α) thenresetWarningZoneData()
return true, [𝑐𝑐 − ℎ: 𝑐𝑐]
end
if (diff ≥ β) thenaccumulativeWarning += diffif (accumulativeWarning ≥ α) thenresetWarningZoneData();170

I. Daqiqil ID et al./Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)
return true, [𝑐𝑐 − ℎ: 𝑐𝑐]
end
return false, [𝑐𝑐 − ℎ: 𝑐𝑐]
end
return false, nullproximity of the ratio of 𝑤𝑤 2 and P 2 of the merged component tozero. In practice, components with 𝑤𝑤 that are very close to zero are
ignored by the model, whereas those with a large covariance tend
to overlap with other components. Algorithm 3 presents in detailthe steps of the proposed CMGMM-based method.

3.4. Model Adaptation

Algorithm 3: Model adaptation
Input: Current Model 𝑀𝑀, Drifted Dataset Ddrift
Result: Adapted Model
𝑀𝑀drift = findBestGMM(Ddrift)
𝑀𝑀combine = CombineGMMComponent(𝑀𝑀drift, 𝑀𝑀)distanceMatrix = KLDissimalarity(𝑀𝑀combine)
ds = Ddrift + 𝑀𝑀.generateData()
nCompmin = 𝑀𝑀.number_component
nCompmax = 𝑀𝑀combine.number_component
BICbest = ∞for targetComponent = nCompmin to nCompmax
𝑀𝑀merge = mergeComponent(target, distanceMatrix)
if useComponentPrune thenComponentPrune(𝑀𝑀merge)
End
BICcandidate = ComputeBIC (𝑀𝑀merge, ds)
if BICcandidate < BICbest thenMbest = Mmerge
End
end
return Mbest

Model adaptation aims to revise the current model upon newly
incoming data that might contain new concepts or conceptchanges. The result of this adaptation is an adapted weighted
mixture component that respects the original mixture.
The model adaptation method starts by training a new model𝑀𝑀drift from data drifts Ddrift using Algorithm 1, and then combining
the existing model ℳ. Consequently, the newly adapted model ℳ
accommodates the new concept represented by the components inℳ drift. The next step is to calculate the pairwise distance between
the components in ℳ using KL discrimination. The KL
discrimination formula (Eq. (8)) enables us to set an upper boundon the discrimination of the mixture before and after the merging
process. According to this formula, components with low weights
means close to their variances, and similar covariance matrices are
selected for merging. When two components are merged, themoment-preserving merging method [25] is used to preserve themean and the covariance of the overall mixture (Eqs. (4)–(6)).
Figure 4 illustrates the CMGM adaptation process.

4.

ExperimentThis section provides information about the datasets andexperimental setup used in this study to train, optimize, andevaluate the proposed method.
4.1. Datasets
We used three types of datasets in this experiment, that is,training, optimization, and evaluation. The training dataset
consisted of audio signals extracted with a 10-seconds window
from 15 scenes in the TUT Acoustic Scenes 2017 [26] and TAU
Urban Acoustic Scenes 2019 datasets [26]. The scenes were home,
airport, beach, office, cafe, grocery store, bus, tram, metro, city
center, residential area, street pedestrian, and shopping mall.
Figure 4: Illustration of the combine–merge Gaussian mixture model (CMGMM)
adaptation process

As a result, the reduction process generates a set of merged
models ℳ merge. To select the best ℳ merge model, the accumulative
BIC is computed by combining sampling data from ℳ curr. Ddriftthen computes the BIC value using Eq. (10). The smaller the valueof the accumulative BIC, the better the newly adapted model.

To simulate the concept drift in the datasets, the optimizationand evaluation datasets were generated by overlay new additional
event sounds from and UrbanSound8K datasets [27] and the BBC
Sound Class Library [28]. When the sounds were added, thenumbers of additions (1–10), positions in the time axis (0–9000ms), and loudness (−20,0) of the sounds were randomly changed
at random. In total, the dataset had 46 new event classes and 371
added event sounds.

Based on [7] and [11], the CMGMM tends to increase thenumber of components because it combines and merges them. Thismechanism leads to an overfitting problem because the adaptation
frequency increases due to the sensitive KD3 hyperparameter.

We generated four concept drift types with three scenarios. The
four types of concept drift are as follows:•

abrupt concept drift (AB), where ongoing concepts are
replaced with new concepts at a particular time;

To maintain the compactness of the CMGMM and avoid
overfitting, we design a strategy to merge statistically equivalent
components into one component, then prune the inactive
components. The inactive components are identified by the•gradual concept drift (GR), where new concepts are added toan ongoing concept at a particular time;

www.astesj.com

171

I. Daqiqil ID et al./Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)•

recurring concept drift type 1 (R1), where an ongoing
concept is replaced at a particular time with concepts that
previously appeared; and•recurring concept drift type 2 (R2), where concepts that
previously appeared are added to an ongoing concept at aparticular time.

Figure 5 illustrates the scenario generation. The three scenarios
were designed to have different data distribution complexities. The
scenario details are described below:•

Scenario 1 (Sc1): A unique event sounds from a specific
event sounds is repeatedly introduced with a random numberof times, gain, and timing. For example, in the airport scene,
unique sounds representing the airplane sound, crowd
background, and construction site are overlaid with a random
number of times (1–10), position (0–9000 ms), and loudness(−20,0).

•

Scenario 2 (Sc2): Several event sounds are randomly
selected from a set of the same sound labels in Sc1 and addedusing the same rule as Sc1.

•

Scenario3 (Sc3): This scenario differs from Sc1 and Sc2 inthat event sounds coexist among scenes. For example, a setof rain sounds exists in other scenes (e.g., beach, city center,and forest paths). The methods of selection and addition are
the same as those in Sc2.

Café
/restaurant

Washing machine, foodmixer, and kitchenware

Phone ringing, children
playing, and teenage
crowd

City centerSound of bird, ambulance,
and windFootsteps, phone ringing,and children playing

Grocery
store

Footsteps, children playing, Vacuum cleaner, phoneand shopping cart
ringing, and footstep

Home

Frying, door, and vacuum
cleanerMetrostationSiren, road car, and thunder Footsteps, crowd, andwind

OfficeTyping, phone ringing, andsneezeBroom, camera, andfootsteps

PublicsquarePeople running, music, andairplane

Birds, rain, and teenagers
talking

Residential Wind, camera, and cat
area

Clock and phone ringing

Birds, sneeze, and clock

Shopping
mall

Clock, camera, and teenage Children playing, phone
crowd
ringing, dog

Streetpedestrian

Dog, bicycle, and bird

Street traffic Motorcycle, horn, and train
Tram

Coughing, bell, andfootsteps on the pavement

Footsteps and children
playing
Siren, airplane, and bell
Teenage crowd andchildren playing

Finally, we have one training dataset, four optimization
datasets, and 12 evaluation datasets in this experiment. Eachtraining dataset contained 3,000 scene audio, while theoptimization and evaluation dataset contained 15,000 scene audio.
The datasets are available in our repository 2.
4.2. Experimental Setup
The CMGMM accuracy was evaluated under four concept drift
types in three scenarios (i.e., Sc1, Sc2, and Sc3). The evaluations
are performed using the two following approaches:

Figure 5: Concept drift scenario

Table 1 shows a list of event sounds that appear at scene types
in every concept drift scenario. The mutually exclusive event
sounds appear in all scenarios, but coexisting sounds only appear
for Sc3.
Table 1: Setting of the novel sounds in scene audio for Sc1, Sc2, and Sc3

Scene

AirportMutually Exclusive
Sounds in Sc1, Sc2, andSc3
Helicopter, crowd, andconstruction site

Additional CoexistingSounds in Sc3
Airplane, footsteps, andchildren playing

BeachPeople swimming, footsteps Teenage crowd, dog, andbirds
on the sand, and rainBus

Car horn, engine, and citycar

Kitchenware, phoneringing, children playing,
and teenage crowd• Active CMGMM adaptation: In this approach, the CMGMM
actively detects the concept drift using a certain method andonly adapts the model when the concept drift is detected. In
this study, we compared KD3 to ADWIN [9], HDDMA,HDDMW [10], and KSWIN [18].
• Passive CMGMM adaptation: In this approach, the CMGMM
adapts as soon as a particular datum is received without
requiring the explicit prior detection of the concept drift.
Several adaptation cycle sizes were tested, that is, 25, 50, 100,
150, and 200.
5.

Experiment Result

The experimental result of the proposed method are presented
herein.
5.1. Hyperparameter Optimization
The first step in this experiment is the systematic optimizationof the KD3 hyperparameter. We used the grid-search method using
a combination of hyperparameters α from 0.1 to 0.001, β from
0.0001 to 0.000001, and ɦ from 45 to 300. We prepared a particular

2https://bit.ly/CMGMM_Dataset

www.astesj.com

172

I. Daqiqil ID et al./Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)
dataset for the KD3 hyperparameter optimization in four types ofconcept drift.
In [11], we reported that hyperparameters β and ɦ did not havea significant effect on accuracy. Therefore, during the initial step,
we observed the performance change according to β and ɦ. Figure
6 shows the average accuracy in all concept drift types according
to hyperparameters β and ɦ. In this experiment, the best β and ɦ
were set at 0.0001 and 45, respectively.

scenarios. The adaptations of the CMGMM on R1 and R2 showed
better accuracy than those on AB and GR. On average, AB
exhibited the lowest accuracy, while R2 showed the highest
accuracy. This high accuracy on recurring was caused by the
CMGMM being designed to preserve the old concept, even though
the new concept is adapted in the model. Thus, the model canrecognize the previously learned concept if it is repeated in the
future.
The CMGMM experiment result depicted that KD3
outperformed other combinations in two of the four concept drift
types in GR and R2. Meanwhile, ADWIN showed the best
accuracy in AB. KSWIN demonstrated the best accuracy in R1,
whereas HDDM was unsuitable for this case. Despite getting thehighest overall accuracy score, the combination of the CMGMM
and KD3 needed more frequent adaptations than ADWIN and
KSWIN. In contrast, both HDDM-based methods showed worse
performances compared to all others. HDDMA overdetected theconcept drift in all concept drift types for more than 3000 times inGR.

Figure 6: Result of hyperparameters β and ɦ in four types of concept drift

Table 2 lists the experimental results of α in the optimization
dataset in four types of concept drift. Based on this experiment,
every concept drift type has its respective hyperparameter αaccording to the concept drift characteristics. AB and GR have
similar characteristics. There are no repeating concepts in the
future; hence, a more sensitive concept drift detector than R1 andR2 is required.
Table 2: KD3 hyperparameter optimization result

Hyperparameter α (β = 0.001, ɦ = 45)
Concept
Drift Types α = 0.1 α = 0.05 α = 0.01 α = 0.005 α = 0.001
AB
GR
R1
R2

0.65680.60070.73320.72680.71130.61730.72320.71330.70690.70500.71580.72280.71370.69220.70540.70900.70660.7002
0.69270.6823Overall

0.67930.69120.71260.70500.6950In AB and GR, a sensitive hyperparameter α accelerated the
update frequency. In the experimental result for these types ofconcept drifts, a high adaptation frequency reduced the loss
received. However, a less-sensitive hyperparameter showed abetter result in recurring concept drifts, where an old concept
reappears in the future. A less-sensitive hyperparameter α provided
the model with longer data compared to the sensitive
hyperparameter.
We also selected the overall hyperparameter setting based on
this experiment. The overall hyperparameter was selected from thebest average performance of the hyperparameter optimization (α =0.01, β = 0.001, and ɦ = 45). We used this hyperparameter for
further CMGMM and KD3 evaluations.
5.2. Active Combine–Merge Gaussian Mixture Model (CMGMM)
Adaptation Result
Table 3 presents the experimental results of the active
CMGMM adaptation. In general, the model performance without
a concept drift detector is low in all concept drift types andwww.astesj.com

The abovementioned results illustrated that the concept drift
detector plays a vital role in the concept drift adaptation. The
model performance decreased over time if the drift detector failed
to detect or delay detecting or over detecting the concept drift.
Performance of the combine–merge Gaussian mixture model(CMGMM) and kernel density drift detection (KD3)
KD3 showed the best average accuracy of 0.6983 compared to
ADWIN, KSWIN, and HDMM with 209 adaptations. This
combination also showed its best results on R2 with 0.7321
accuracy, followed by R1 with 0.7373 accuracy, GR with 0.6999
accuracy, and AB with accuracy 0.6469. Furthermore, thiscombination was the most stable in all scenarios. The maximum
performance decrements in AB, GR, R1, and R2 were 1.38%,
1.2%, 1.34%, and 0.94%, respectively.
Despite achieving a good performance in all concept drift
types, the number of concept drifts detected in this combination
was higher than ADWIN and KSWIN. The most significant
number of adaptations occurred in AB. The disadvantage of a highnumber of adaptations is the higher computation time required tofinish the task and possible overfitting. In this case, the higher
numbers of adaptations in AB and GR are obtained because theconcept constantly changes over time, and the learned concept
becomes obsolete in the future; hence, the higher the adaptation,
the better the performance.
Performance of the combine–merge Gaussian mixture model(CMGMM) and ADWIN
In general, the combination of CMGMM and ADWIN showed
a good performance in every concept drift type, especially on theabrupt datasets, where this combination showed its best
performance. The overall accuracy was 0.6371 with 83 times ofadaptation. The overall accuracies of this combination in AB, GR,
R1, and R2 were 0.6369, 0.6475, 0.6912, and 0.7169, respectively.
Furthermore, this combination had the advantage of a small
number of adaptations in all concept drift types. Hence, ADWIN
showed an effective performance in using resources and had areasonably good performance. This combination performed very
well on Sc1, but showed a performance drop in Sc2 and Sc3. For
173

I. Daqiqil ID et al./Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)
Table 3: Experiment result of the CMGMM with the concept drift detector

Accuracy

Concept Drift Detector

AB

GR

R1

Overall

R2

ADWIN
HDDM_A
HDDM_W
KD3*
KSWIN
Without Detector
ADWIN
HDDM_A
HDDM_W
KD3*
KSWIN
Without Detector
ADWIN
HDDM_A
HDDM_W
KD3*
KSWIN
Without Detector
ADWIN
HDDM_A
HDDM_W
KD3*
KSWIN
Without Detector
ADWIN
HDDM_A
HDDM_W
KD3*
KSWIN
Without Detector

Sc1
0.69890.41570.40410.64690.6611
0.41210.67230.41340.41310.69990.65320.35540.72220.4721
0.48470.73730.78180.45120.73530.59190.57890.7321
0.69140.42540.70720.47330.47020.70410.69690.4110Sc2
0.65250.44760.44550.63590.62410.4054
0.63410.44630.44970.69420.62410.35240.69480.52040.48150.73340.73510.44580.7066
0.60340.59960.73250.69640.42050.67200.50440.49410.69900.66990.4060

Sc3 Overall
0.6214 0.6369
0.4345 0.4326
0.4546 0.4347
0.6331 0.6386
0.6345 0.6317
0.4095 0.4090
0.6363 0.6475
0.4311 0.4302
0.45440.439
0.68790.694
0.618 0.6322
0.3489 0.3522
0.6568 0.6912
0.48960.494
0.50680.491
0.7239 0.7315
0.7357 0.7508
0.4257 0.4409
0.7089 0.7169
0.62590.607
0.5875 0.5886
0.7227 0.7291
0.677 0.6882
0.3985 0.4148
0.6559 0.6731
0.4953 0.4910
0.5008 0.4883
0.6919 0.6983
0.6663 0.6757
0.3956 0.4042

F1
Sc1
0.713
0.45860.44850.6476
0.67220.42350.68450.45800.45240.7044
0.66310.35710.73930.52060.53050.73890.78760.45120.73980.63690.63690.7352
0.69770.42790.71910.51850.51700.70650.70510.4149Sc20.64950.48040.49020.6467
0.63690.41250.65060.49460.487
0.7004
0.63260.3542
0.69810.5566
0.52150.73410.74040.44580.71310.63980.63980.73150.6976
0.41980.67780.54280.53460.70310.67680.4080

Sc3 Overall
0.6353 0.6599
0.477
0.472
0.5004 0.4797
0.6395 0.6446
0.6411 0.6501
0.4095 0.4151
0.6478 0.6609
0.4701 0.4742
0.4816 0.4736
0.6867 0.6971
0.6204 0.6387
0.3501 0.3538
0.6333 0.6902
0.5392 0.5388
0.5357 0.5292
0.7247 0.7325
0.7416 0.7565
0.4257 0.4409
0.71630.723
0.6658 0.6475
0.6658 0.6475
0.7221 0.7296
0.6811 0.6921
0.3968 0.4148
0.6581 0.6835
0.5380 0.5331
0.5458 0.5325
0.6932 0.7009
0.6710 0.6843
0.3955 0.4061

Number of Concept Drift
Detection
Sc1 Sc2 Sc3 Overall
83
89
85
85
3287 3350 3359
3332
489 413 409
437
207 236 220
221
132 121 123
125
92
81
83
3306 3308 3265
0 409 401
190 218 221
129 125 107

85
3293
270
209
120

78
83
87
3154 3258 3201
0 662 647
208 201 204
142 135 126

82
3204
436
204
134

75
86
82
3052 2957 3017
759 604 543
195 207 205
156 143 141

81
3008
635
202
146

82
84
84
3199 3218 3210
312 522 500
200 215 212
139 131 124

83
3209
444
209
131

(*) Proposed method

example, the accuracies of AB, GR, R1, and R2 decreased in Sc3
by 4.64%, 3.82%, 2.74%, and 287%, respectively.

Performance of the combine–merge Gaussian mixture model(CMGMM) and KSWIN

Performance of the combine–merge Gaussian mixture model(CMGMM) and Hoeffding’s bounds-based method (HDDM)

The combination of CMGMM and KSWIN showed the best
performance in R1, with an overall accuracy of 0.750 with 134
adaptations. The accuracies of this combination in AB, GR, R1,
and R2 were 0.6317, 0.6322, 0.7508, and 0.6882, respectively. On
average, KSWIN required eight to nine adaptations per scene in all
dataset types. This algorithm seems able to detect occurringchanges in data and supports the concept drift handling processwith good indicators at a given time.

In this experiment, both Hoeffding's inequality-basedalgorithms showed underperformance results for all concept drift
types. Both algorithms were less effective in detecting the concept
drift in this case. The overall accuracies of HDDMA in AB, GR,
R1, and R2 were 0.4326, 0.4302, 0.494, and 0.607, respectively.
The number of HDDMA adaptations exceeded 3000 times ofadaptation. This high adaptation process was ineffective because
the amount of trained data for each adaptation was too small. Thiscondition led to an overfitting and decreased the model
performance.
HDDM W also experienced the same problem. In some cases,
HDDMA failed to detect the drift concepts, such as GR, R1, andR2 in Sc1. The overall accuracies of this HDDMW in AB, GR, R1,
and R2 were 0.4347, 0.439, 0.491, and 0.5886, respectively.
www.astesj.com

5.3. Passive Combine–Merge Gaussian Mixture Model(CMGMM) Adaptation Result
Table 4 lists the experimental results of the passive CMGMM
adaptation. The best performance in AB, GR, and R1 was obtainedwith a cycle size of 50, and that in R2 was obtained with a cycle
size of 100. The best accuracies of AB, GR, R1, and R2 were0.7152, 0.7139, 0.7323, and 0.7155, respectively.

174

I. Daqiqil ID et al./Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)
Table 4: The experiment result of CMGMM without concept drift detector

Concept
Drift
Types

AB

GR

R1

R2

Accuracy

Cycle
Size

Sc1

Sc2

Sc3

Average

25
50
100
150
200
25
50
100
150
200
25
50
100
150
200
25
50
100
150
200

0.62900.71220.62850.6361
0.55800.62940.71330.61730.6371
0.53340.6186
0.72350.72110.7332
0.66390.51330.73960.74310.68650.65020.62360.71590.59250.57760.50590.62320.71690.58870.58180.50940.57990.73200.71050.70860.70180.54440.69910.7012
0.66390.60110.62560.71770.59550.5851
0.51190.60040.71150.60890.57970.50760.56080.7416
0.69880.71200.7146
0.56690.70110.70230.68030.60890.62600.71520.60550.5996
0.52520.6176
0.71390.60490.59950.51680.58640.73230.71010.71790.69340.54150.71320.71550.67690.6200Similar to active adaptation, R1 and R2 showed good
performances compared to AB and GR, but better performances inpassive adaptation. Although R1 exhibited the best adaptation at
cycle size 50, it also showed good result at cycle sizes 100 and 150.
If you consider the time and the computing resources used, thencycle sizes 100 and 150 are recommended.
In passive adaptation, the cycle size is vital in achieving a good
performance. This cycle size determines the adequacy of the data
for adaptation. If the cycle size is too short, the number of data
adapted is small, leading to overfitting problems.
5.4. Suggestions and Limitations
The experiment results showed that the combination of
CMGMM and KD3 has a higher number of adaptations comparedto that of ADWIN and KSWIN due to the selection of KD3
hyperparameters that are sensitive to accommodating GR and AB.
When the number of adaptations is increased, then in certain cases,
such as GR and AB, the accuracy is improved, albeit with a higher
computing cost. The advantage of KD3 compared to the othermethods is that it could be applied in multi-dimensional probability
distribution; hence, it is more flexible to apply in other models andcases.
In cases where the time or location of the concept drift can bepredicted, the use of a passive adaptation strategy is more
beneficial and has a lower computational cost than the active
strategy. However, if the adaptation cycle is too far from theconcept drift, then the model performance will decrease over time.
6.

Conclusion

This paper presented KD3 hyperparameter optimization and
the CMGMM performance evaluation in four types of concept
drift. All concept drift types had optimum hyperparameter
configurations. AB and GR showed similar patterns that requireda smaller α value than the recurring concept drift. In this type of
www.astesj.com

concept drift, concepts continuously appear; hence, a sensitive drift
detector is needed to update the model early or have a highfrequency model adaptation. However, in recurring concepts, the
new concept may be repeated in the future; thus, a lower-frequency
adaptation shows a better performance.
The evaluation results demonstrated that the proposed
algorithms work well in detecting and adapting to four types ofconcept drift and three scenarios. Overall, the CMGMM works
better in R1 and R2 than in AB and GR because it is designed topreserve old concepts to preserve previously learned knowledge.
Component pruning is only performed on components with aminimal impact on the prediction.
In the active adaptation strategy, the proposed combined
method of CMGMM and KD3 outperformed two of four othercombination methods in GR and R1. These methods showed themost stable performance among Sc1, Sc2, and Sc3 in all concept
drift types. Furthermore, ADWIN showed the best results on AB.
This algorithm is efficient in computing resources, but less stablein more challenging scenarios, such as Sc2 and Sc3. KSWIN
showed the best results in recurring drift and good performancefor all concept drift types. HDDM overdetected or failed to detect
the concept drift and was not suitable in this case.
In the passive adaptation strategy, a short or long adaptation
cycle could reduce the performance, and a short cycle size makes
the adaptation less effective. A short cycle could disrupt the modelcomponent because the model is trained with insufficient data,
leading to an underfitting problem.
In AB and GR, the model requires a high-frequency adaptation
to maintain the performance; therefore, sensitive hyperparameters
or a short cycle size is required. Based on the experimental results,
the passive method is more suitable in these concept drift types.
However, the computational costs are higher than those of theactive method. Furthermore, in recurring drift scenarios, a lesssensitive hyperparameter, or a moderate cycle size is needed. The
active method is recommended for recurring drift types
considering the computation cost and better accuracy inexperiments.
As part of our future work, we plan to improve the proposed
KD3 concept drift detection algorithm to achieve adaptive weight,
reduce the kernel density computation, and optimize the numberof data points considered when detecting the concept drift anddecreasing the computation time.
Conflict of Interest
The authors declare no conflict of interest.
Acknowledgment
This work was supported by JSPS KAKENHI Grant Number
JP20K12079.
References
[1]

[2]

R. Elwell, R. Polikar, “Incremental Learning of Concept Drift in
Nonstationary Environments,” IEEE Transactions on Neural Networks,
22(10), 1517–1531, 2011, doi:10.1109/TNN.2011.2160459.
S. Ntalampiras, “Automatic analysis of audiostreams in the concept drift
environment,” in 2016 IEEE 26th International Workshop on Machine
Learningfor
Signal
Processing(MLSP),
IEEE,2016,
doi:10.1109/MLSP.2016.7738905.

175

I. Daqiqil ID et al./Advances in Science, Technology and Engineering Systems Journal Vol. 6, No. 5, 167-176 (2021)
J. Gama, I. Žliobaitė, A. Bifet, M. Pechenizkiy, A. Bouchachia, “A Survey
on Concept Drift Adaptation,” ACM Computing Surveys, 46(4), 1–37, 2014,
doi:10.1145/2523813.
[4] T.R. Hoens, R. Polikar, N. V. Chawla, “Learning from Streaming Data withConcept Drift and Imbalance: An Overview,” Progress in Artificial
Intelligence, 1(1), 89–101, 2012, doi:10.1007/s13748-011-0008-0.
[5] I. Žliobaitė, “Learning under Concept Drift: an Overview,” 1–36, 2010,
doi:10.1002/sam.
[6] C. Chen, C. Wang, J. Hou, M. Qi, J. Dai, Y. Zhang, P. Zhang, “Improving
Accuracy of Evolving GMM under GPGPU-Friendly Block-Evolutionary
Pattern,” International Journal of Pattern Recognition and Artificial
Intelligence, 34(3), 1–34, 2020, doi:10.1142/S0218001420500068.
[7] I.D. Id, M. Abe, S. Hara, “Concept Drift Adaptation for Acoustic Scene
Classifier based on Gaussian Mixture Model,” in IEEE Region 10 Annual
International Conference, Proceedings/TENCON, IEEE, Osaka: 450–455,
2020, doi:10.1109/TENCON50793.2020.9293766.
[8] J.M. Acevedo-Valle, K. Trejo, C. Angulo, “Multivariate regression withincremental learning of Gaussian mixture models,” Frontiers in Artificial
Intelligence and Applications, 300, 196–205, 2017, doi:10.3233/978-161499-806-8-196.
[9] A. Bifet, R. Gavaldà, “Learning from Time-changing Data with Adaptive
Windowing,” Proceedings of the 7th SIAM International Conference on
Data Mining, (April), 443–448, 2007, doi:10.1137/1.9781611972771.42.
[10] I. Frías-Blanco, J. Del Campo-Ávila, G. Ramos-Jiménez, R. Morales-Bueno,
A. Ortiz-Díaz, Y. Caballero-Mota, “Online and Non-Parametric Drift
Detection Methods Based on Hoeffding’s Bounds,” IEEE Transactions on
Knowledge and Data Engineering, 27(3), 810–823, 2015,
doi:10.1109/TKDE.2014.2345382.
[11] I.D. Id, M. Abe, S. Hara, “Evaluation of Concept Drift Adaptation for
Acoustic Scene Classifier Based on Kernel Density Drift Detection andCombine Merge Gaussian Mixture Model,” in 2021 Spring meeting of the
Acoustical Society of Japan, 2021.
[12] J. Montiel, J. Read, A. Bifet, T. Abdessalem, “Scikit-multiflow: A Multioutput Streaming Framework,” Journal of Machine Learning Research, 19,
1–5, 2018, doi:10.5555/3291125.3309634.
[13] G.I. Webb, R. Hyde, H. Cao, H.L. Nguyen, F. Petitjean, “Characterizing
Concept Drift,” Data Mining and Knowledge Discovery, 30(4), 964–994,
2016, doi:10.1007/s10618-015-0448-4.
[14] T. Zhang, J. Liang, B. Ding, “Acoustic scene classification using deep CNN
with fine-resolution feature,” Expert Systems with Applications, 143(1),113067, 2020, doi:10.1016/j.eswa.2019.113067.
[15] A. Tsymbal, “The Problem of Concept Drift: Definitions and Related Work,”
2004.
[16] E.S. Page, “Continuous Inspection Schemes,” Biometrika, 41(1/2), 100,
1954, doi:10.2307/2333009.
[17] Y. Yuan, Z. Wang, W. Wang, “Unsupervised concept drift detection basedon multi-scale slide windows,” Ad Hoc Networks, 111, 102325, 2021,
doi:10.1016/j.adhoc.2020.102325.
[18] C. Raab, M. Heusinger, F.M. Schleif, “Reactive Soft Prototype ComputingforConcept
Drift
Streams,”
Neurocomputing,2020,
doi:10.1016/j.neucom.2019.11.111.
[19] A.R. Runnalls, “Kullback-Leibler Approach to Gaussian Mixture Reduction,”
IEEE Transactions on Aerospace and Electronic Systems, 43(3), 989–999,
2007, doi:10.1109/TAES.2007.4383588.
[20] A.P. Dempster, N.M. Laird, D.B. Rubin, “Maximum Likelihood from
Incomplete Data via the EM Algorithm,” Journal of the Royal StatisticalSociety. Series B (Methodological), 39(1), 1–38, 1977.
[21] A.D.R. McQuarrie, C.-L. Tsai, Regression and Time Series Model Selection,WORLD SCIENTIFIC, 1998, doi:10.1142/3573.
[22] P. Pal Singh, “An Approach to Extract Feature using MFCC,” IOSR Journalof Engineering, 4(8), 21–25, 2014, doi:10.9790/3021-04812125.
[23] C. Fraley, “How Many Clusters? Which Clustering Method? Answers Via
Model-Based Cluster Analysis,” The Computer Journal, 41(8), 578–588,
1998, doi:10.1093/comjnl/41.8.578.
[24] E. Parzen, “On Estimation of a Probability Density Function and Mode,” The
Annals of Mathematical Statistics, 33(3), 1065–1076, 1962,
doi:10.1214/aoms/1177704472.
[25] J.L. Williams, P.S. Maybeck, “Cost-function-based Gaussian mixture
reduction for target tracking,” Proceedings of the 6th International
Conferenceon
Information
Fusion,2,1047–1054,
2003,
doi:10.1109/ICIF.2003.177354.
[26] A. Mesaros, T. Heittola, T. Virtanen, TUT Acoustic scenes 2017,
Development dataset, 2017, doi:10.5281/ZENODO.400515.
[27] J. Salamon, C. Jacoby, J.P. Bello, “A Dataset and Taxonomy for Urban
Sound Research,” MM 2014 - Proceedings of the 2014 ACM Conference on[3]

www.astesj.com

Multimedia, (November), 1041–1044, 2014, doi:10.1145/2647868.2655045.
[28] BBC, BBC Sound Effects, https://sound-effects.bbcrewind.co.uk/search,
Mar. 2019.

176