Combining the classic vulnerability index and affinity propagation clustering algorithm to assess the intrinsic aquifer vulnerability of coastal aquifers on an integrated scale.

In the northern plains of Laizhou City, groundwater quality suffers dual threats from anthropogenic activities: seawater intrusion caused by overextraction of fresh groundwater, and vertical infiltration of agricultural pollutants. Groundwater management requires a comprehensive analysis of both horizontal and vertical pollution in coastal aquifers. In this paper, Intrinsic Aquifer Vulnerability (IAV) was assessed on an integrated scale using two classic IAV models (DRASTIC and GALDIT) separately based on a GIS database. Hydrogeological parameters from two classic IAV models were clustered using affinity propagation (AP) clustering algorithm, and silhouette coefficients were used to determine the optimal classification result. In our application, the objects of the AP algorithm are 3320 units divided from the whole study area with 500 m*500 m precision. A comparison of all four outputs in AP-DRASTIC shows that the clustering results of the 4-classification yielded the best silhouette coefficient of 0.406 out of all four. Cluster 4, which comprises 21% of the area, had relatively low level of groundwater contamination, despite its high level of vulnerability as indicated by the classic DRASTIC index. In the second level of vulnerability Cluster 3, 53.8% of all water samples were found to be contaminated, indicating a greater level of nitrate contamination. With respect to AP-GALDIT, the silhouette coefficient for result 7-classification reaches the highest value of 0.343. There was a high level of vulnerability identified in Clusters 2, 4 and 5 (34.7% of the study area) relating to the classic GALDIT index. The concentration of chloride in all water samples obtained in these areas was extremely high. Groundwater management should be addressed by AP-DRASTIC results on anthropogenic activity/contamination control, and by AP-GALDIT results on groundwater extraction limitation. Overall, this method allows for the evaluation of IAV in other coastal areas on an integrated scale, facilitating the development of groundwater management strategies based on a better understanding of the aquifer's essential characteristics.

In-Wheel Motor Fault Diagnosis Using Affinity Propagation Minimum-Distance Discriminant Projection and Weibull-Kernel-Function-Based SVDD.

To effectively ensure the operational safety of an electric vehicle with in-wheel motor drive, a novel diagnosis method is proposed to monitor each in-wheel motor fault, the creativity of which lies in two aspects. One aspect is that affinity propagation (AP) is introduced into a minimum-distance discriminant projection (MDP) algorithm to propose a new dimension reduction algorithm, which is defined as APMDP. APMDP not only gathers the intra-class and inter-class information of high-dimensional data but also obtains information on the spatial structure. Another aspect is that multi-class support vector data description (SVDD) is improved using the Weibull kernel function, and its classification judgment rule is modified into a minimum distance from the intra-class cluster center. Finally, in-wheel motors with typical bearing faults are customized to collect vibration signals under four operating conditions, respectively, to verify the effectiveness of the proposed method. The results show that the APMDP's performance is better than traditional dimension reduction methods, and the divisibility is improved by at least 8.35% over the LDA, MDP, and LPP. A multi-class SVDD classifier based on the Weibull kernel function has high classification accuracy and strong robustness, and the classification accuracies of the in-wheel motor faults in each condition are over 95%, which is higher than the polynomial and Gaussian kernel function.

Group-guided individual functional parcellation of the hippocampus and application to normal aging.

Aging is closely associated with cognitive decline affecting attention, memory and executive functions. The hippocampus is the core brain area for human memory, learning, and cognition processing. To delineate the individual functional patterns of hippocampus is pivotal to reveal the neural basis of aging. In this study, we developed a group-guided individual parcellation approach based on semisupervised affinity propagation clustering using the resting-state functional magnetic resonance imaging to identify individual functional subregions of hippocampus and to identify the functional patterns of each subregion during aging. A three-way group parcellation was yielded and was taken as prior information to guide individual parcellation of hippocampus into head, body, and tail in each subject. The superiority of individual parcellation of hippocampus is validated by higher intraregional functional similarities by compared to group-level parcellation results. The individual variations of hippocampus were associated with coactivation patterns of three typical functions of hippocampus. Moreover, the individual functional connectivities of hippocampus subregions with predefined target regions could better predict age than group-level functional connectivities. Our study provides a novel framework for individual brain functional parcellations, which may facilitate the future individual researches for brain cognitions and brain disorders and directing accurate neuromodulation.

RRH Clustering Using Affinity Propagation Algorithm with Adaptive Thresholding and Greedy Merging in Cloud Radio Access Network.

Affinity propagation (AP) clustering with low complexity and high performance is suitable for radio remote head (RRH) clustering for real-time joint transmission in the cloud radio access network. The existing AP algorithms for joint transmission have the limitation of high computational complexities owing to re-sweeping preferences (diagonal components of the similarity matrix) to determine the optimal number of clusters as system parameters such as network topology. To overcome this limitation, we propose a new approach in which preferences are fixed, where the threshold changes in response to the variations in system parameters. In AP clustering, each diagonal value of a final converged matrix is mapped to the position (x,y coordinates) of a corresponding RRH to form two-dimensional image. Furthermore, an environment-adaptive threshold value is determined by adopting Otsu's method, which uses the gray-scale histogram of the image to make a statistical decision. Additionally, a simple greedy merging algorithm is proposed to resolve the problem of inter-cluster interference owing to the adjacent RRHs selected as exemplars (cluster centers). For a realistic performance assessment, both grid and uniform network topologies are considered, including exterior interference and various transmitting power levels of an RRH. It is demonstrated that with similar normalized execution times, the proposed algorithm provides better spectral and energy efficiencies than those of the existing algorithms.

Power Control and Clustering-Based Interference Management for UAV-Assisted Networks.

Unmanned Aerial Vehicle (UAV) has been widely used in various applications of wireless network. A system of UAVs has the function of collecting data, offloading traffic for ground Base Stations (BSs) and illuminating coverage holes. However, inter-UAV interference is easily introduced because of the huge number of LoS paths in the air-to-ground channel. In this paper, we propose an interference management framework for UAV-assisted networks, consisting of two main modules: power control and UAV clustering. The power control is executed first to adjust the power levels of UAVs. We model the problem of power control for UAV networks as a non-cooperative game which is proved to be an exact potential game and the Nash equilibrium is reached. Next, to further improve system user rate, coordinated multi-point (CoMP) technique is implemented. The cooperative UAV sets are established to serve users and thus transforming the interfering links into useful links. Affinity propagation is applied to build clusters of UAVs based on the interference strength. Simulation results show that the proposed algorithm integrating power control with CoMP can effectively reduce the interference and improve system sum-rate, compared to Non-CoMP scenario. The law of cluster formation is also obtained where the average cluster size and the number of clusters are affected by inter-UAV distance.

An Affinity Propagation-Based Self-Adaptive Clustering Method for Wireless Sensor Networks.

A wireless sensor network (WSN) is an essential component of the Internet of Things (IoTs) for information exchange and communication between ubiquitous smart objects. Clustering techniques are widely applied to improve network performance during the routing phase for WSN. However, existing clustering methods still have some drawbacks such as uneven distribution of cluster heads (CH) and unbalanced energy consumption. Recently, much attention has been paid to intelligent clustering methods based on machine learning to solve the above issues. In this paper, an affinity propagation-based self-adaptive (APSA) clustering method is presented. The advantage of K-medoids, which is a traditional machine learning algorithm, is combined with the affinity propagation (AP) method to achieve more reasonable clustering performance. AP is firstly utilized to determine the number of CHs and to search for the optimal initial cluster centers for K-medoids. Then the modified K-medoids is utilized to form the topology of the network by iteration. The presented method effectively avoids the weakness of the traditional K-medoids in aspects of the homogeneous clustering and convergence rate. Simulation results show that the proposed algorithm outperforms some latest work such as the unequal cluster-based routing scheme for multi-level heterogeneous WSN (UCR-H), the low-energy adaptive clustering hierarchy using affinity propagation (LEACH-AP) algorithm, and the energy degree distance unequal clustering (EDDUCA) algorithm.

A Two-Level WiFi Fingerprint-Based Indoor Localization Method for Dangerous Area Monitoring.

Localization technologies play an important role in disaster management and emergence response. In areas where the environment does not change much after an accident or in the case of dangerous areas monitoring, indoor fingerprint-based localization can be used. In such scenarios, a positioning system needs to have both a high accuracy and a rapid response. However, these two requirements are usually conflicting since a fingerprint-based indoor localization system with high accuracy usually has complex algorithms and needs to process a large amount of data, and therefore has a slow response. This problem becomes even worse when both the size of monitoring area and the number of reference nodes increase. To address this challenging problem, this paper proposes a two-level positioning algorithm in order to improve both the accuracy and the response time. In the off-line stage, a fingerprint database is divided into several sub databases by using an affinity propagation clustering (APC) algorithm based on Shepard similarity. The online stage has two steps: (1) a coarse positioning algorithm is adopted to find the most similar sub database by matching the cluster center with the fingerprint of the node tested, which will narrow the search space and consequently save time; (2) in the sub database area, a support vector regression (SVR) algorithm with its parameters being optimized by particle swarm optimization (PSO) is used for fine positioning, thus improving the online positioning accuracy. Both experiment results and actual implementations proved that the proposed two-level localization method is more suitable than other methods in term of algorithm complexity, storage requirements and localization accuracy in dangerous area monitoring.

Lightweight Workload Fingerprinting Localization Using Affinity Propagation Clustering and Gaussian Process Regression.

Fingerprinting localization approach is widely used in indoor positioning applications owing to its high reliability. However, the learning procedure of radio signals in fingerprinting is time-consuming and labor-intensive. In this paper, an affinity propagation clustering (APC)-based fingerprinting localization system with Gaussian process regression (GPR) is presented for a practical positioning system with the reduced offline workload and low online computation cost. The proposed system collects sparse received signal strength (RSS) data from the deployed Bluetooth low energy beacons and trains them with the Gaussian process model. As the signal estimation component, GPR predicts not only the mean RSS but also the variance, which indicates the uncertainty of the estimation. The predicted RSS and variance can be employed for probabilistic-based fingerprinting localization. As the clustering component, the APC minimizes the searching space of reference points on the testbed. Consequently, it also helps to reduce the localization estimation error and the computational cost of the positioning system. The proposed method is evaluated through real field deployments. Experimental results show that the proposed method can reduce the offline workload and increase localization accuracy with less computational cost. This method outperforms the existing methods owing to RSS prediction using GPR and RSS clustering using APC.

An Adaptive Weighted KNN Positioning Method Based on Omnidirectional Fingerprint Database and Twice Affinity Propagation Clustering.

The human body has a great influence on Wi-Fi signal power. A fixed K value leads to localization errors for the K-nearest neighbor (KNN) algorithm. To address these problems, we present an adaptive weighted KNN positioning method based on an omnidirectional fingerprint database (ODFD) and twice affinity propagation clustering. Firstly, an OFPD is proposed to alleviate body's sheltering impact on signal, which includes position, orientation and the sequence of mean received signal strength (RSS) at each reference point (RP). Secondly, affinity propagation clustering (APC) algorithm is introduced on the offline stage based on the fusion of signal-domain distance and position-domain distance. Finally, adaptive weighted KNN algorithm based on APC is proposed for estimating user's position during online stage. K initial RPs can be obtained by KNN, then they are clustered by APC algorithm based on their position-domain distances. The most probable sub-cluster is reserved by the comparison of RPs' number and signal-domain distance between sub-cluster center and the online RSS readings. The weighted average coordinates in the remaining sub-cluster can be estimated. We have implemented the proposed method with the mean error of 2.2 m, the root mean square error of 1.5 m. Experimental results show that our proposed method outperforms traditional fingerprinting methods.

pySAPC, a python package for sparse affinity propagation clustering: Application to odontogenesis whole genome time series gene-expression data.

BACKGROUND: Developmental dental anomalies are common forms of congenital defects. The molecular mechanisms of dental anomalies are poorly understood. Systematic approaches such as clustering genes based on similar expression patterns could identify novel genes involved in dental anomalies and provide a framework for understanding molecular regulatory mechanisms of these genes during tooth development (odontogenesis). METHODS: A python package (pySAPC) of sparse affinity propagation clustering algorithm for large datasets was developed. Whole genome pair-wise similarity was calculated based on expression pattern similarity based on 45 microarrays of several stages during odontogenesis. RESULTS: pySAPC identified 743 gene clusters based on expression pattern similarity during mouse tooth development. Three clusters are significantly enriched for genes associated with dental anomalies (with FDR <0.1). The three clusters of genes have distinct expression patterns during odontogenesis. CONCLUSIONS: Clustering genes based on similar expression profiles recovered several known regulatory relationships for genes involved in odontogenesis, as well as many novel genes that may be involved with the same genetic pathways as genes that have already been shown to contribute to dental defects. GENERAL SIGNIFICANCE: By using sparse similarity matrix, pySAPC use much less memory and CPU time compared with the original affinity propagation program that uses a full similarity matrix. This python package will be useful for many applications where dataset(s) are too large to use full similarity matrix. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.

Constructing an Indoor Floor Plan Using Crowdsourcing Based on Magnetic Fingerprinting.

A large number of indoor positioning systems have recently been developed to cater for various location-based services. Indoor maps are a prerequisite of such indoor positioning systems; however, indoor maps are currently non-existent for most indoor environments. Construction of an indoor map by external experts excludes quick deployment and prevents widespread utilization of indoor localization systems. Here, we propose an algorithm for the automatic construction of an indoor floor plan, together with a magnetic fingerprint map of unmapped buildings using crowdsourced smartphone data. For floor plan construction, our system combines the use of dead reckoning technology, an observation model with geomagnetic signals, and trajectory fusion based on an affinity propagation algorithm. To obtain the indoor paths, the magnetic trajectory data obtained through crowdsourcing were first clustered using dynamic time warping similarity criteria. The trajectories were inferred from odometry tracing, and those belonging to the same cluster in the magnetic trajectory domain were then fused. Fusing these data effectively eliminates the inherent tracking errors originating from noisy sensors; as a result, we obtained highly accurate indoor paths. One advantage of our system is that no additional hardware such as a laser rangefinder or wheel encoder is required. Experimental results demonstrate that our proposed algorithm successfully constructs indoor floor plans with 0.48 m accuracy, which could benefit location-based services which lack indoor maps.

A Smartphone Indoor Localization Algorithm Based on WLAN Location Fingerprinting with Feature Extraction and Clustering.

With the development of communication technology, the demand for location-based services is growing rapidly. This paper presents an algorithm for indoor localization based on Received Signal Strength (RSS), which is collected from Access Points (APs). The proposed localization algorithm contains the offline information acquisition phase and online positioning phase. Firstly, the AP selection algorithm is reviewed and improved based on the stability of signals to remove useless AP; secondly, Kernel Principal Component Analysis (KPCA) is analyzed and used to remove the data redundancy and maintain useful characteristics for nonlinear feature extraction; thirdly, the Affinity Propagation Clustering (APC) algorithm utilizes RSS values to classify data samples and narrow the positioning range. In the online positioning phase, the classified data will be matched with the testing data to determine the position area, and the Maximum Likelihood (ML) estimate will be employed for precise positioning. Eventually, the proposed algorithm is implemented in a real-world environment for performance evaluation. Experimental results demonstrate that the proposed algorithm improves the accuracy and computational complexity.

Classifier ensemble selection based on affinity propagation clustering.

A small number of features are significantly correlated with classification in high-dimensional data. An ensemble feature selection method based on cluster grouping is proposed in this paper. Classification-related features are chosen using a ranking aggregation technique. These features are divided into unrelated groups by an affinity propagation clustering algorithm with a bicor correlation coefficient. Some diversity and distinguishing feature subsets are constructed by randomly selecting a feature from each group and are used to train base classifiers. Finally, some base classifiers that have better classification performance are selected using a kappa coefficient and integrated using a majority voting strategy. The experimental results based on five gene expression datasets show that the proposed method has low classification error rates, stable classification performance and strong scalability in terms of sensitivity, specificity, accuracy and G-Mean criteria.

Node Detection and Internode Length Estimation of Tomato Seedlings Based on Image Analysis and Machine Learning.

Seedling vigor in tomatoes determines the quality and growth of fruits and total plant productivity. It is well known that the salient effects of environmental stresses appear on the internode length; the length between adjoining main stem node (henceforth called node). In this study, we develop a method for internode length estimation using image processing technology. The proposed method consists of three steps: node detection, node order estimation, and internode length estimation. This method has two main advantages: (i) as it uses machine learning approaches for node detection, it does not require adjustment of threshold values even though seedlings are imaged under varying timings and lighting conditions with complex backgrounds; and (ii) as it uses affinity propagation for node order estimation, it can be applied to seedlings with different numbers of nodes without prior provision of the node number as a parameter. Our node detection results show that the proposed method can detect 72% of the 358 nodes in time-series imaging of three seedlings (recall = 0.72, precision = 0.78). In particular, the application of a general object recognition approach, Bag of Visual Words (BoVWs), enabled the elimination of many false positives on leaves occurring in the image segmentation based on pixel color, significantly improving the precision. The internode length estimation results had a relative error of below 15.4%. These results demonstrate that our method has the ability to evaluate the vigor of tomato seedlings quickly and accurately.

A Mixed Approach to Similarity Metric Selection in Affinity Propagation-Based WiFi Fingerprinting Indoor Positioning.

The weighted k-nearest neighbors (WkNN) algorithm is by far the most popular choice in the design of fingerprinting indoor positioning systems based on WiFi received signal strength (RSS). WkNN estimates the position of a target device by selecting k reference points (RPs) based on the similarity of their fingerprints with the measured RSS values. The position of the target device is then obtained as a weighted sum of the positions of the k RPs. Two-step WkNN positioning algorithms were recently proposed, in which RPs are divided into clusters using the affinity propagation clustering algorithm, and one representative for each cluster is selected. Only cluster representatives are then considered during the position estimation, leading to a significant computational complexity reduction compared to traditional, flat WkNN. Flat and two-step WkNN share the issue of properly selecting the similarity metric so as to guarantee good positioning accuracy: in two-step WkNN, in particular, the metric impacts three different steps in the position estimation, that is cluster formation, cluster selection and RP selection and weighting. So far, however, the only similarity metric considered in the literature was the one proposed in the original formulation of the affinity propagation algorithm. This paper fills this gap by comparing different metrics and, based on this comparison, proposes a novel mixed approach in which different metrics are adopted in the different steps of the position estimation procedure. The analysis is supported by an extensive experimental campaign carried out in a multi-floor 3D indoor positioning testbed. The impact of similarity metrics and their combinations on the structure and size of the resulting clusters, 3D positioning accuracy and computational complexity are investigated. Results show that the adoption of metrics different from the one proposed in the original affinity propagation algorithm and, in particular, the combination of different metrics can significantly improve the positioning accuracy while preserving the efficiency in computational complexity typical of two-step algorithms.

Affinity Propagation Clustering of Measurements for Multiple Extended Target Tracking.

More measurements are generated by the target per observation interval, when the target is detected by a high resolution sensor, or there are more measurement sources on the target surface. Such a target is referred to as an extended target. The probability hypothesis density filter is considered an efficient method for tracking multiple extended targets. However, the crucial problem of how to accurately and effectively partition the measurements of multiple extended targets remains unsolved. In this paper, affinity propagation clustering is introduced into measurement partitioning for extended target tracking, and the elliptical gating technique is used to remove the clutter measurements, which makes the affinity propagation clustering capable of partitioning the measurement in a densely cluttered environment with high accuracy. The Gaussian mixture probability hypothesis density filter is implemented for multiple extended target tracking. Numerical results are presented to demonstrate the performance of the proposed algorithm, which provides improved performance, while obviously reducing the computational complexity.

Automatic detection of arterial input function in dynamic contrast enhanced MRI based on affinity propagation clustering.

PURPOSE: To automatically and robustly detect the arterial input function (AIF) with high detection accuracy and low computational cost in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). MATERIALS AND METHODS: In this study, we developed an automatic AIF detection method using an accelerated version (Fast-AP) of affinity propagation (AP) clustering. The validity of this Fast-AP-based method was proved on two DCE-MRI datasets, i.e., rat kidney and human head and neck. The detailed AIF detection performance of this proposed method was assessed in comparison with other clustering-based methods, namely original AP and K-means, as well as the manual AIF detection method. RESULTS: Both the automatic AP- and Fast-AP-based methods achieved satisfactory AIF detection accuracy, but the computational cost of Fast-AP could be reduced by 64.37-92.10% on rat dataset and 73.18-90.18% on human dataset compared with the cost of AP. The K-means yielded the lowest computational cost, but resulted in the lowest AIF detection accuracy. The experimental results demonstrated that both the AP- and Fast-AP-based methods were insensitive to the initialization of cluster centers, and had superior robustness compared with K-means method. CONCLUSION: The Fast-AP-based method enables automatic AIF detection with high accuracy and efficiency.

An improved differential evolution algorithm for multi-modal multi-objective optimization.

Multi-modal multi-objective problems (MMOPs) have gained much attention during the last decade. These problems have two or more global or local Pareto optimal sets (PSs), some of which map to the same Pareto front (PF). This article presents a new affinity propagation clustering (APC) method based on the Multi-modal multi-objective differential evolution (MMODE) algorithm, called MMODE_AP, for the suit of CEC'2020 benchmark functions. First, two adaptive mutation strategies are adopted to balance exploration and exploitation and improve the diversity in the evolution process. Then, the affinity propagation clustering method is adopted to define the crowding degree in decision space (DS) and objective space (OS). Meanwhile, the non-dominated sorting scheme incorporates a particular crowding distance to truncate the population during the environmental selection process, which can obtain well-distributed solutions in both DS and OS. Moreover, the local PF membership of the solution is defined, and a predefined parameter is introduced to maintain of the local PSs and solutions around the global PS. Finally, the proposed algorithm is implemented on the suit of CEC'2020 benchmark functions for comparison with some MMODE algorithms. According to the experimental study results, the proposed MMODE_AP algorithm has about 20 better performance results on benchmark functions compared to its competitors in terms of reciprocal of Pareto sets proximity (rPSP), inverted generational distances (IGD) in the decision (IGDX) and objective (IGDF). The proposed algorithm can efficiently achieve the two goals, i.e., the convergence to the true local and global Pareto fronts along with better distributed Pareto solutions on the Pareto fronts.

A clustering effectiveness measurement model based on merging similar clusters.

This article presents a clustering effectiveness measurement model based on merging similar clusters to address the problems experienced by the affinity propagation (AP) algorithm in the clustering process, such as excessive local clustering, low accuracy, and invalid clustering evaluation results that occur due to the lack of variety in some internal evaluation indices when the proportion of clusters is very high. First, depending upon the "rough clustering" process of the AP clustering algorithm, similar clusters are merged according to the relationship between the similarity between any two clusters and the average inter-cluster similarity in the entire sample set to decrease the maximum number of clusters Kmax. Then, a new scheme is proposed to calculate intra-cluster compactness, inter-cluster relative density, and inter-cluster overlap coefficient. On the basis of this new method, several internal evaluation indices based on intra-cluster cohesion and inter-cluster dispersion are designed. Results of experiments show that the proposed model can perform clustering and classification correctly and provide accurate ranges for clustering using public UCI and NSL-KDD datasets, and it is significantly superior to the three improved clustering algorithms compared with it in terms of intrusion detection indices such as detection rate and false positive rate (FPR).

Vocal complexity in the long calls of Bornean orangutans.

Vocal complexity is central to many evolutionary hypotheses about animal communication. Yet, quantifying and comparing complexity remains a challenge, particularly when vocal types are highly graded. Male Bornean orangutans (Pongo pygmaeus wurmbii) produce complex and variable "long call" vocalizations comprising multiple sound types that vary within and among individuals. Previous studies described six distinct call (or pulse) types within these complex vocalizations, but none quantified their discreteness or the ability of human observers to reliably classify them. We studied the long calls of 13 individuals to: (1) evaluate and quantify the reliability of audio-visual classification by three well-trained observers, (2) distinguish among call types using supervised classification and unsupervised clustering, and (3) compare the performance of different feature sets. Using 46 acoustic features, we used machine learning (i.e., support vector machines, affinity propagation, and fuzzy c-means) to identify call types and assess their discreteness. We additionally used Uniform Manifold Approximation and Projection (UMAP) to visualize the separation of pulses using both extracted features and spectrogram representations. Supervised approaches showed low inter-observer reliability and poor classification accuracy, indicating that pulse types were not discrete. We propose an updated pulse classification approach that is highly reproducible across observers and exhibits strong classification accuracy using support vector machines. Although the low number of call types suggests long calls are fairly simple, the continuous gradation of sounds seems to greatly boost the complexity of this system. This work responds to calls for more quantitative research to define call types and quantify gradedness in animal vocal systems and highlights the need for a more comprehensive framework for studying vocal complexity vis-à-vis graded repertoires.