Microsoft Word - 1-V8N3(2023)-AITI#11169(163-176).docx Advances in Technology Innovation, vol. 8, no. 3, 2023, pp. 163-176 English language proofreader: Chih-Wen Teng Swarm Intelligence Algorithm Based on Plant Root System in 1D Biomedical Signal Feature Engineering to Improve Classification Accuracy Rui Gong1,2,*, Kazunori Hase2 1Organization of Liberal Arts Education, Mejiro University, Tokyo, Japan 2Faculty of Systems Design, Tokyo Metropolitan University, Tokyo, Japan Received 13 November 2022; received in revised form 02 February 2023; accepted 16 February 2023 DOI: https://doi.org/10.46604/aiti.2023.11169 Abstract The classification accuracy of one-dimensional (1D) biomedical signals is limited due to the lack of independence of the extracted features. To address this shortcoming, the study applies a swarm intelligence algorithm based on plant root systems (PRSs) to feature engineering. Some basic features of 1D biomedical signals are integrated into a digitized soil, and a root matrix is generated from this digitized soil and the PRS algorithm. The PRS features are extracted from the root matrix and used to classify the basic features. Following classification with the same biomedical signals and classifier, the accuracy of the added PRS set is generally higher than that of the base set. The result shows that the proposed algorithm can expand the application of 1D biomedical signals to include more biomedical signals in classification tasks for clinical diagnosis. Keywords: one-dimensional biomedical signal, feature engineering, plant root system algorithm, swarm intelligence 1. Introduction One-dimensional (1D) biomedical signals are widely used in the medical field and are crucial for clinical diagnosis and treatment. Electrocardiograms (ECGs) are commonly used to diagnose heart-related diseases, and electroencephalograms (EEGs) are used to determine sleep quality or mental state [1]. Electrical-based biomedical signals perform well, and magnetic, vibration, and acoustic-based biomedical signals are popularly used in clinical applications [2-3]. However, with increasingly shorter sampling intervals and longer signal lengths, analyzing 1D biomedical signals without the assistance of a computer has become a research limitation. Machine learning classification is a cutting-edge computer-assisted 1D technique for analyzing biomedical signals [4]. Supervised classification is a machine-learning technique that helps doctors improve diagnostic accuracy by training classifiers with features of biomedical signals [5]. This technique is effective for complex and large datasets, and a well-designed classifier training model combined with high-quality dataset features frequently generates unexpectedly good outcomes. However, feature extraction methods are not as versatile as model building; thus, related research has received less attention. Traditional and classical methods are often used for the extraction of 1D biomedical signals. The curve length of the signal in the time domain and the total spectral power in the frequency domain are common classification features of ECG signals [6]. Meanwhile, Shannon entropy is utilized as a classification feature of electromyography (EMG) signals in clinical settings [7]. * Corresponding author. E-mail address: r.gong@mejiro.ac.jp Advances in Technology Innovation, vol. 8, no. 3, 2023, pp. 163-176 164 Although these features may seem adequate, the naive Bayes classifier, which is the basis of machine learning theory, requires each condition to be independent during the classification process. In other words, features of biomedical signals extracted from classical feature engineering techniques should not be correlated [8]. This independence between features is undoubtedly challenging to achieve because both time- and frequency-domain features can always be connected by certain operations and their inverse. Therefore, new features with strong independence are needed to characterize 1D biomedical signals. After investigation, it was found that swarm intelligence computing might solve the above challenges. When a feature is extracted using swarm intelligence, the new feature has a distinguishing independence because each member of the swarm participates in making the choice. Moreover, the operations and transformations of the choice process are irreversible. The ant colony algorithm is a popular swarm intelligence algorithm, while the bee colony algorithm has been developed based on the swarming and social nature of bees [9]. Currently, dozens of swarm intelligence algorithms have been applied to feature selection [10]. However, they are all based on social animals, and the independence of extracted features is still lacking. Therefore, this study focuses on “social plants.” The root systems of plants are complex enough to form group intelligence as well. Holker et al. [11] hypothesized that the root system of plants is a type of swarm intelligence system. The root apices communicate with each other through electrical signals or chemical pheromones and build a massive “brain-like” system underground. Within such a complex root system, independent roots acquire water and nutrients through cooperation. To support proper growth and development, the root system competes with other root systems, beginning a “war” when it has an advantage and retreating when it is at a disadvantage [11]. A swarm intelligence algorithm based on a plant root system (PRS) is proposed and applied to feature engineering in this study. Specifically, the proposed PRS approach imitates the growth of plant roots, in which the root apices cooperate to absorb as much of the sustaining nutrients as possible. In the proposed approach, the base features used by the selected machine learning model to classify biomedical signals are equivalent to the nutrients in digitized soil. These base features are obtained using common feature extraction methods. The sum of the nutrients absorbed during growth also serves as the first auxiliary feature, and the growth area of the root system is the second auxiliary feature. These auxiliary features are referred to as auxiliary PRS features. During model training, the most significant advantage of the PRS features based on swarm intelligence is that they are ideally independent (with a low correlation with the other features) and highly correlated with the dependent variable. The independence of the PRS features is derived from the brain-like structure of the root system, where the co-determination of the root tips reduces the correlation with the base features. As an advantage, PRS auxiliary features of biomedical signals are obtained from the proposed algorithm. After appending these features to the training set, the correlation between the features decreases and leads to reduced bias and variance and improved accuracy in machine learning classification. Most importantly, the PRS algorithm is universally applicable for the feature engineering of most 1D biomedical signals. This technology also enables 1D biomedical signals to become more competitive in the clinical field by improving the accuracy of machine learning classification. 2. Method 2.1. Extraction of base features The growth of natural plants requires suitable soil; similarly, the extraction of PRS features requires digitized soil (a feature matrix) composed of base features. When extracting base features, time-domain features are generally preferred over frequency-domain and nonlinear features. Time-domain features are more reliable than nonlinear features for involving a lower computational burden for nonstationary 1D biomedical signals. [12]. Moreover, time-domain features are more dependable than frequency-domain features because they avoid the risk of spectral leakage caused by signal decomposition [13]. Advances in Technology Innovation, vol. 8, no. 3, 2023, pp. 163-176 165 Time-domain feature selection is essential for base feature extraction. The number of features needs to be carefully considered: a small number of features limits the growth of the root system, while a large number of features may adversely affect classifier performance [14]. For the base features, this study selected 12 features that have relatively low computational complexity and have been successfully used for classification [15-16]. The definitions of the base features are listed in Table 1, which �� represents the 1D biomedical signal in the segment �̅, N is the length of the signal, and �̅ is the average value of ��. Table 1 Time-domain features Base feature Definition Standard deviation (STD) 2 1 1 1 1 STD N N i i i i x x N N= = = −  Variance of signal (VAR) 2 1 1 VAR 1 N n n x N = = −  Root mean square (RMS) 2 1 1 RMS N n n x N = =  Skewness (SKW) ( ) ( ) 3 2 3 2 1 1 1 1 SKW N N n n n n x x x x N N= =   = − −      Kurtosis (KURT) ( ) ( ) 2 4 2 1 1 1 1 KURT = =   = − × −      N N n n n n x x x x N N Mean absolute value (MAV) 1 1 MAV N n n x N = =  Zero crossing (ZC) ( ) 1 1 1 1 ZC sgn threshold N n n n n n x x x x − + + = =  × ∩ − ≥   Slope sign change (SSC) ( ) ( ){ } ( ) 1 1 1 2 1, if threshold SSC , 0, otherwise − − + = ≥ = − × − =      N n n n n n x f x x x x f x Willison amplitude (WAMP) ( ) ( ) 1 1 1 1, if threshold WAMP , 0, otherwise − + = ≥ = − =    N n n n x f x x f x Simple sign integral (SSI) 2 1 SSI N n n x = = Nonlinear energy (NLE) ( ) ( ) ( ) ( ) 1 2 2 1 NLE 1 1 2 − = = − − + −  N n n n n i x x i x i x i N Waveform length (WL) 1 1 1 WL N n n n x x − + = = − Among the 12 features comprising the base features set, the statistical features are the most basic, including VAR, STD, RMS, SKW, KURT, and the MAV, which is similar to the average rectified value. Three features related to frequency are also included: ZC, i.e., the amplitude value of a signal that crosses the zero-amplitude axis; SSC, i.e., the frequency of a signal within the time domain; and the WAMP, i.e., the sum difference between the signal amplitudes for two adjacent samples. The last three features indicate energy and complexity: SSI represents signal segment energy, NLE approximates signal amplitude energy, and WL measures signal complexity. These twelve base features collectively represent a 1D biomedical signal series. The new features derived from these representative values closely approximate the actual measurement values. 2.2. Feature sorting For the development of a root system, the site where the seed is planted requires nutritious soil. In this study, the base features were modeled based on the distribution of nutrients. Each element ��,� of the base feature set ��×�〈 〉 must be sorted. First, the dataset must be normalized using a scaling technique during the preprocessing stage to eliminate scale Advances in Technology Innovation, vol. 8, no. 3, 2023, pp. 163-176 166 differences among various elements while sorting. Min-max normalization was used to scale the data within the range [0,1] and maintain the relationships that existed among the original data [17]. The min-max normalization based on the feature set ���×�〈 〉 can be expressed as: , min max min m n m n B B B B × −   =  −  ɺ β (1) where n = 1, 2, …, 12 and m = 1, 2, …, the length of ��. Feature importance measurements can reduce the initial number of features by eliminating those features with a low importance score and improving classifier performance [18]. In this study, the features were sorted based on their worth. To score a feature’s worth, the information associated with the feature was used. Features with higher scores were those closest to the center location. Information gain was first input into a decision tree and used to rank the priority of feature nodes; this was then expanded and applied to importance measurement. Assuming the class label of a feature has two distinct values that define binary classes �C1,C2�. Info��� �, also known as the entropy of ���×�〈 〉, can be defined as ( ) ( ) ( )1 2 1 2 2 2 Info log logB p p p p= − −ɺ (2) where �� , �� are the nonzero probabilities that an arbitrary tuple ���×�〈 〉 belongs to classes C1,C2 and are estimated using ��� or 2,�� � ∕ ��� �. Because each feature column ��� is a set of discontinuous values, these discrete values of ��� need to be split into two sets using an unsupervised algorithm. The K-means clustering method can partition a given dataset into k groups prespecified by the analyst [19]. In this study, this process was repeated 25 times to produce a lower within-cluster variation and a more stable result. Each ���×� now belongs to the split set � ��, ��� and has a class label. The expected information required to classify the tuple from �� based on feature ��� is ( ) ( ) 2 1 Info Info β = = ×ɺ ɺ ɺ ɺ ɺ i n i nn i s s B B B B (3) ( ) ( ) ( )Gain Info Info β β = − ɺ ɺ ɺ ɺ n n B B (4) The ��� with the highest information gain was chosen to replace the center of !���, ���, … , ����# and the other features were sorted individually from the center to the two sides with decreasing information gain. Thus, a sorted base feature set was obtained. 2.3. Generating nutritious soil based on features Digitized soil consisting of the sorted base feature set cannot only be wide; it must also have depth. Therefore, continuous feature discretization (from scalar to vector) is necessary. In this process, equal-width interval binning is the most common method used for discretizing data to produce nominal values from continuous features [20]. With this binning method, if feature $ has values bounded by $�%& and $�'� , the method computes k equally sized bin widths as follows: max mina a k − =δ (5) And it constructs bin boundaries at $�'� + )*, where ) = 1, 2, … , , − 1. To imitate the natural environment of the root system, this study set , = 15. Advances in Technology Innovation, vol. 8, no. 3, 2023, pp. 163-176 167 In addition, the vertical distribution of soil nutrients should follow the laws of nature. Most nutrients are concentrated in the shallowest layer and decrease with depth because nutrients return to the soil through biocycles. Thus, the discrete feature set /�0×�� was arranged in decreasing order from top to bottom. By contrast, the horizontal distribution of nutrients is associated with crustal movement. The kernel convolution values 12 and 1� were used to calculate the reconstituted nutrient distributions. Nutritional reconstructions are divided into two types: 12, which affects the nutrient distribution in shallower layers; and 1�, which affects the nutrient distribution in deeper layers. The convolution kernel is then defined as: 1 1 1 1 0 1 0 2 0.5 0.5 0.5 A    =      τ (6) 0.5 0.5 0.5 1 0 1 0 2 1 1 1 B    =      τ (7) The nutritious soil used to generate the root system is written as 3�0×��, which is a result of the /�0×�� convolution with kernels 12 and 1� . The calculated target matrix requires zero padding with a size of 1 before each convolution. The completed soil with the mineral nutrition generation process is shown in Fig. 1. The following matrix for the distribution of nutrients in the soil is referred to as the nutrient matrix. The elements of the base feature set are arranged in order of importance, from the center to either side. Each element in the set is then discretized. Finally, the soil matrix is obtained using two convolution calculations. Fig. 1 Top-to-bottom order of soil matrix construction 2.4. Plant root system algorithm In plants, either the radicle or primary root is the first organ to emerge from the seed coat. Before the first leaf grows, the energy required by the cotyledon for root development comes from the seed itself. Additional inorganic nutrients (including water) are essential. Only a small fraction of these nutrients come from the seed itself, and the rests are from the surrounding soil which contains mineral nutrients [21]. The rule that is inherent in the genes of higher plants is to develop a sufficiently large first leaf and long roots before the energy stored in the seed is exhausted. The proposed algorithm follows this rule. As organic matter cannot be synthesized by photosynthesis before the first leaf has grown, the task is to absorb more mineral nutrients by growing a sufficient large root system with limited energy (root division) in a limited time. The matrix distribution for the roots in the soil is hereafter referred to as the root matrix. In the proposed approach, the aforementioned natural processes must be transformed into a data-processing program. First, the root and nutrient matrices form a four-dimensional tensor, as shown in Fig. 2. The initial root matrix is a zero matrix, where the upper-center location assigning values can create a radicle matrix. To absorb more nutrients, the rule of root division Advances in Technology Innovation, vol. 8, no. 3, 2023, pp. 163-176 168 is to preferentially proliferate at the global maximum in the mapping nutrient matrix. Neighboring root tips are also necessary. The radicle matrix, photosynthetic day, and daily root division are used as modification parameters. The developmental process can be characterized by the root distribution area and total nutrient absorption. Fig. 3 shows the natural and digital processes used to build a brain-like root system. The figure also depicts that the growth of digital roots is dependent on the base features in this study. By extracting the PRS features from the brain-like root system, the correlation with the base features is reduced. Fig. 2 Four-dimensional data tensor of biomedical signals Fig. 3 Natural and digital processes for building brain-like root systems In Table 2, the root growth process can be written as a pseudocode. In the proposed algorithm, the core steps of root development involve seeking the global maximum location of the nutrient matrix map relative to the root matrix location using a tensor of a biomedical signal base feature set. The entire root system makes decisions in a brain-like fashion to improve total nutrient absorption. The root distribution can be drawn in the coordinate system as a polygon. The area of this polygon serves as a feature. This study uses a well-known tool to calculate the polygon area proposed by Paul Bourke in 1988. The procedure provided two results, which are both referred to as PRS features: nutrient feature (NF), representing the total number of nutrients absorbed during root system development in the digitized soil; and root feature (RF), representing the area of root distribution. The calculations of NF and RF are shown in Table 2 as the nutrient amount (na) and area (A). A is calculated based on Eq. (8) and Fig. 4, wherein the polygon is closed and composed of line segments between N vertices 4�' , 5'6, 7 = 0 to 9 − 1. ( ) 1 1 1 0 1 2 N i i i i i A p q p q − + + = = − (8) Advances in Technology Innovation, vol. 8, no. 3, 2023, pp. 163-176 169 Fig. 4 Example of 10-vertex closed polygon constructed from a root matrix Table 2 Plant root system algorithm Algorithm 1 Plant root system Pseudocode Comments 1 Input: 2 :ℝ&×<: distribution of the radicle in soil (initial root matrix); x, y are the number of rows and columns of the distribution matrix 3 :ℕ&×<: distribution of nutrients in the soil (nutrient matrix); 4 Output: 5 na: nutrients absorbed by the roots; 6 A: root distribution area; 7 @$ ← 0; 8 ℝ&×< ← :ℝ&×<; ℝ&×< : distribution of the growing root in the soil (root matrix) 9 for 7 = 1 → /$C do day is the number of days for the first leaf to appear 10 for each ℝD&EF,