Silhouette Method Research Articles

Brain Tissue Evaluation Based on Skeleton Shape and Similarity Analysis between Hemispheres

Background: The purpose of this article is to provide a new evaluation tool based on skeleton maps to assess the tumoral and non-tumoral regions of the 2D MRI in PD-weighted (proton density) and T2w (T2-weighted type) brain images. Methods: The proposed method investigated inter-hemisphere brain tissue similarity using a mask in the right hemisphere and its mirror reflection in the left one. At the hemisphere level and for each ROI (region of interest), a morphological skeleton algorithm was used to efficiently investigate the similarity between hemispheres. Two datasets with 88 T2w and PD images belonging to healthy patients and patients diagnosed with glioma were investigated: D1 contains the original raw images affected by Rician noise and D2 consists of the same images pre-processed for noise removal. Results: The investigation was based on structural similarity assessment by using the Structural Similarity Index (SSIM) and a modified Jaccard metrics. A novel S-Jaccard (Skeleton Jaccard) metric was proposed. Cluster accuracy was estimated based on the Silhouette method (SV). The Silhouette coefficient (SC) indicates the quality of the clustering process for the SSIM and S-Jaccard. To assess the overall classification accuracy an ROC curve implementation was carried out. Conclusions: Consistent results were obtained for healthy patients and for PD images of glioma. We demonstrated that the S-Jaccard metric based on skeletal similarity is an efficient tool for an inter-hemisphere brain similarity evaluation. The accuracy of the proposed skeletonization method was smaller for the original images affected by Rician noise (AUC = 0.883 (T2w) and 0.904 (PD)) but increased for denoised images (AUC = 0.951 (T2w) and 0.969 (PD)).

Tracing outliers in the dataset of Drosophila suzukii records with the Isolation Forest method

The analysis of big data is a fundamental challenge for the current and future stream of data coming from many different sources. Geospatial data is one of the sources currently less investigated. A typical example of always increasing data set is that produced by the distribution data of invasive species on the concerned territories. The dataset of Drosophila suzuki invasion sites in Europe up to 2011 was used to test a possible method to pinpoint its outliers (anomalies). Our aim was to find a method of analysis that would be able to treat large amount of data in order to produce easily readable outputs to summarize and predict the status and, possibly, the future development of a biological invasion. To do that, we aimed to identify the so called anomalies of the dataset, identified with a Python script based on the machine learning algorithm “Isolation Forest”. We used also the K-Means clustering method to partition the dataset. In our test, based on a real dataset, the Silhouette method yielded a number of clusters of 10 as the best result. The clusters were drawn on the map with a Voronoi tessellation, showing that 8 clusters were centered on industrial harbours, while the last two were in the hinterland. This fact led us to guess that: (1) the main entrance mechanisms in Europe may be the wares import fluxes through ports, occurring apparently several times; (2) the spreading into the inland may be due to road transportation of wares; (3) the outliers (anomalies) found with the isolation forest method would identify individuals or populations that tend to detach from their original cluster and hence represent indications about the lines of further spreading of the invasion. This type of analysis aims hence to identify the future direction of an invasion, rather than the center of origin as in the case of geographic profiling. Isolation Forest provides therefore complimentary results with respect to PGP. The recent records of the invasive species, mainly localized close to the outliers position, are an indication that the isolation forest method can be considered predictive and proved to be a useful method to treat large datasets of geospatial data.

Determining the number of states in dynamic functional connectivity using cluster validity indexes

BackgroundClustering analysis is employed in brain dynamic functional connectivity (dFC) to cluster the data into a set of dynamic states. These states correspond to different patterns of functional connectivity that iterate through time. Although several cluster validity index (CVI) methods to determine the best clustering partition exists, the appropriateness of methods to apply in the case of dynamic connectivity analysis has not been determined. New MethodCurrently employed indexes do not provide a crisp answer on what is the best number of clusters. In addition, there is a lack of CVI testing in the context of dFC data. This work tests a comprehensive set of twenty four cluster validity indexes applied to addiction data and suggest the best ones for clustering dynamic functional connectivity. ResultsOut of the twenty four considered CVIs, Davies-Bouldin and Ray-Turi were the most suitable methods to find the number of clusters in both simulation and real data. The solution for these two CVIs is to find a local minimum critical point, which can be automated using computational algorithms. Comparison with Existing MethodsElbow-Criterion, Silhouette and GAP-Statistic methods have been widely used in dFC studies. These methods are included among the tested CVIs where the performances of all twenty four CVIs are compared. ConclusionsDavies-Bouldin and Ray-Turi CVIs showed better performance among a group of twenty four CVIs in determining the number of clusters to use in dFC analysis.

Analyze K-Value Selected Method of K-Means Clustering Algorithm to Clustering Province Based on Disease Case

Disease cases throughout Indonesia has increased as seen from the Indeks Pembangunan Masyarakat (IPKM). Globalization has the effect of increasing human mobility across provinces, thus accelerating the process of spreading epidemics that could pose a threat for Indonesia. The speed of action from government is needed to reducing the level if outbreaks of the disease. For this reason, accuracy from the government is needed to solving this problem. The data were taken from data disease cases in 2015 which consisted of 34 provinces in Indonesia based on the Central Statistics Agency in Indonesian. In K-Means clustering, determining of K-value is needed because it affects in convergence results. To solve this problem, this research analyzes three methods of K-Value, there are Silhouette, Elbow, and Gap Statistics Methods.The result of testing three methods of determining K-value obtained execution times on Silhouette 13.09s, Elbow 14.76s, and Gap Statistics 20.28s. So, choosing Silhouette method produces 2 optimal clusters, there are low cluster level (C1) and high cluster level (C2). The correlation matrix to understand the relationship between each disease is performed and a value of 0.88 is obtained there is the strong linear correlation between Pneumonia and Pulmonary TB. Then, modeling the relationship between these two variables by fitting linear equations. The results of C1 cluster based on disease cases were obtained 32 provinces and for C2 cluster were 2 provinces there areWest Java and East Java. Based on the results of the clustering can be input to the Indonesian government to tackle disease cases in all provinces in Indonesia

Information System for Evaluating Specific Interventions of Stunting Case Using K-means Clustering

One of the causes of death of children under five is chronic malnutrition or stunting. The government has made a policy as an effort to reduce stunting. Specific intervention nutrition programs are activities that directly address the occurrence of stunting. Evaluation of edit interventions that have currently been carried out but have not separated the process based on intervention indicators so that it results in a long processing time and large exit costs so we need a system that can accelerate the process of evaluating specific interventions. Information systems for evaluating specific interventions can be a solution to this problem. In this study, an information system for evaluating specific interventions of stunting cases was developed web-based to facilitate real-time operation. The evaluation information system is designed to collect national data and carry out a clustering process using the k-means method and evaluation stucture cluster using silhouette method. In this study an evaluation value of 34 provinces was obtained which was divided into several clusters as a result of evaluation process in the information system.

Finding Best Possible Number of Clusters using K-Means Algorithm

Customers are assets for business. The companies are investing more for customer relationship management. Retaining customer for long time is a difficult process in today’s trend. On line shopping is also increasing day by day. People are more interested to visit popular web sites and they are spending very less time to choose their products. On line shops are paying more interest to analyze customer preferences, their needs, shopping behaviors through data mining technique. Proper classification is necessary for organizing such data. In this work, Customer with the same buying behavior is grouped based on the features age and salary. K-Means algorithm is applied to form clusters with different K values for original data and normalized data. The within sum of square (wss) is calculated for both the data for different cluster size. The minimum wss is considered to be better which is achieved in normalized data. The validity of cluster is evaluated by elbow, silhouette and gap statistic method to choose the optimal number of clusters. This work is implemented in R software.

Uncertainty quantification of channel reservoirs assisted by cluster analysis and deep convolutional generative adversarial networks

Reservoir characterization is to find reservoir properties of interest by combining available geological information. In channel reservoirs, flow responses are very sensitive depending on the characteristics of channels. Therefore, it is crucial to characterize the distribution and connectivity of channels to estimate future production performances.In this paper, we propose a method of uncertainty quantification on channel reservoir models. This novel method is based on a sequential combination of 3 machine learning methods: principal component analysis (PCA), K-means clustering, and deep convolutional generative adversarial networks (DCGAN). PCA and K-means clustering are used for classification of reservoir models and DCGAN replicates a group of new models based on the selected data from the PCA and K-means clustering.The cluster analysis by PCA and K-means clustering is to select some of realizations, which have similar production performance with the true response. After feature extraction by the two largest components from PCA, K-means clustering makes several groups among which we use silhouette method to determine the number of clusters. Then, we can find a group of models showing similar production performances with the true in an efficient way by using a representative model from each cluster.Based on the selected models, we train DCGAN to generate new realizations that do not exist among the initial models. After the cluster analysis on the regenerated models to filter out again, we can get calibrated models without using any conventional inverse algorithm. We apply the proposed method in 2 two-dimensional channel reservoir cases. In the both case, the proposed method reduces prediction uncertainty as well as characterizes channels’ pattern and connectivity reliably.

Unsupervised Learning Used in Automatic Detection and Classification of Ambient‐Noise Recordings from a Large‐N Array

AbstractWe present a method for automatic detection and classification of seismic events from continuous ambient‐noise (AN) recordings using an unsupervised machine‐learning (ML) approach. We combine classic and recently developed array‐processing techniques with ML enabling the use of unsupervised techniques in the routine processing of continuous data. We test our method on a dataset from a large‐number (large‐N) array, which was deployed over the Kylylahti underground mine (Finland), and show the potential to automatically process and cluster the volumes of AN data. Automatic sorting of detected events into different classes allows faster data analysis and facilitates the selection of desired parts of the wavefield for imaging (e.g., using seismic interferometry) and monitoring. First, using array‐processing techniques, we obtain directivity, location, velocity, and frequency representations of AN data. Next, we transform these representations into vector‐shaped matrices. The transformed data are input into a clustering algorithm (called k‐means) to define groups of similar events, and optimization methods are used to obtain the optimal number of clusters (called elbow and silhouette tests). We use these techniques to obtain the optimal number of classes that characterize the AN recordings and consequently assign the proper class membership (cluster) to each data sample. For the Kylylahti AN, the unsupervised clustering produced 40 clusters. After visual inspection of events belonging to different clusters that were quality controlled by the silhouette method, we confirm the reliability of 10 clusters with a prediction accuracy higher than 90%. The obtained division into separate seismic‐event classes proves the feasibility of the unsupervised ML approach to advance the automation of processing and the utilization of array AN data. Our workflow is very flexible and can be easily adapted for other input features and classification algorithms.

A methodology for evaluating human operator's fitness for duty in nuclear power plants

Abstract It is reported that about 20% of accidents at nuclear power plants in Korea and abroad are caused by human error. One of the main factors contributing to human error is fatigue, so it is necessary to prevent human errors that may occur when the task is performed in an improper state by grasping the status of the operator in advance. In this study, we propose a method of evaluating operator's fitness-for-duty (FFD) using various parameters including eye movement data, subjective fatigue ratings, and operator's performance. Parameters for evaluating FFD were selected through a literature survey. We performed experiments that test subjects who felt various levels of fatigue monitor information of indicators and diagnose a system malfunction. In order to find meaningful characteristics in measured data consisting of various parameters, hierarchical clustering analysis, an unsupervised machine-learning technique, is used. The characteristics of each cluster were analyzed; fitness-for-duty of each cluster was evaluated. The appropriateness of the number of clusters obtained through clustering analysis was evaluated using both the Elbow and Silhouette methods. Finally, it was statistically shown that the suggested methodology for evaluating FFD does not generate additional fatigue in subjects. Relevance to industry The methodology for evaluating an operator's fitness for duty in advance is proposed, and it can prevent human errors that might be caused by inappropriate condition in nuclear industries.

Personas Design for Conversational Systems in Education

This research aims to explore how to enhance student engagement in higher education institutions (HEIs) while using a novel conversational system (chatbots). The principal research methodology for this study is design science research (DSR), which is executed in three iterations: personas elicitation, a survey and development of student engagement factor models (SEFMs), and chatbot interaction analysis. This paper focuses on the first iteration, personas elicitation, which proposes a data-driven persona development method (DDPDM) that utilises machine learning, specifically the K-means clustering technique. Data analysis is conducted using two datasets. Three methods are used to find the K-values: the elbow, gap statistic, and silhouette methods. Subsequently, the silhouette coefficient is used to find the optimal value of K. Eight personas are produced from the two data analyses. The pragmatic findings from this study make two contributions to the current literature. Firstly, the proposed DDPDM uses machine learning, specifically K-means clustering, to build data-driven personas. Secondly, the persona template is designed for university students, which supports the construction of data-driven personas. Future work will cover the second and third iterations. It will cover building SEFMs, building tailored interaction models for these personas and then evaluating them using chatbot technology.

MEASURING PERFORMANCE BY INTEGRATING K-MEDOIDS WITH DEA: MONGOLIAN CASE

Performance measurement encourages Decision Making Units (DMUs) to improve their level of performance by comparing their current financial positions with that of their peers. Data Envelopment Analysis (DEA) is a widely used approach to performance measurement, though it is susceptible when the data is heterogeneous. The main objective of this study is to examine the performance of Mongolian listed companies by combining DEA and a k-medoid clustering method. Clustering facilitates the characterization and patterns of data and identification of homogenous groups. This study applies the integration of k-medoids and performance measurement. The research used 89 Mongolian companies’ financial statements from 2012 to 2015 - obtained from the Mongolian Stock Exchange website. The companies are grouped by k-medoids clustering, and efficiency of each cluster is evaluated by DEA. According to the silhouette method, the companies are classified into two clusters which are considered first cluster as small and medium-sized (80), and second cluster as big (9) companies. Both clusters are analyzed and compared by financial ratios. The mean efficiency score of big companies’ is much higher than that of small and medium-sized companies. Integrated results show that cluster-specific efficiency provides better performance than pre-clustering efficiency results.

Examining Mexican-Heritage Mothers' Perceptions of Their Children's Weight: Comparison of Silhouette and Categorical Survey Methods.

Background: Failure to recognize children's overweight status by parents may contribute to children's risk for obesity. We examined two methods of measuring mothers' perceptions of children's weight and factors associated with weight perception inaccuracy. Methods: Cross-sectional analyses of clinical and self-report data from 287 Mexican-heritage mother-child dyads. Mothers identified their child's weight category using a scale (e.g., "normal/overweight/obese") and a visual silhouette scale (11 child gender-specific weight-varying images). Children's height and weight were measured to calculate body mass index (BMI). Chi-square tests examined associations between categorical, silhouette, and BMI percentile categories of children's weight. Bivariate logistic regression analyses examined factors associated with mothers' inaccuracy of their children's weight. Results: Only 13% of mothers accurately classified their child as obese using the categorical scale, while 78% accurately classified their child as obese using the silhouette scale. Mothers were more likely to underestimate their child's weight using BMI categories (62%) compared to using the silhouette scale (23%). Predictors of mothers' underestimation using the categorical method were child sex [female] (adjusted odds ratio [AOR] = 1.99; 95% CI: 1.02-3.86), child age [younger age] (AOR = 10.39; 95% CI: 4.16-25.92 for ages 5-6 years), and mother's weight status (overweight AOR = 2.99; 95% CI: 1.05-8.51; obese AOR = 5.19; 95% CI: 1.89-14.18). Child BMI was the only predictor of mothers' overestimation (AOR = 0.89; 95% CI: 0.85-0.94) using the silhouette method. Conclusions: Using silhouette scales to identify children's body weight may be a more accurate tool for clinicians and interventionists to activate parents' awareness of unhealthy weight in children compared to using traditional categorical weight-labeling methods.

A Clustering-Based Approach for Improving the Accuracy of UWB Sensor-Based Indoor Positioning System

There are several methods which can be used to locate an object or people in an indoor location. Ultra-wideband (UWB) is a specifically promising indoor positioning technology because of its high accuracy, resistance to interference, and better penetration. This study aims to improve the accuracy of the UWB sensor-based indoor positioning system. To achieve that, the proposed system is trained by using the K-means algorithm with an additional average silhouette method. This helps us to define the optimal number of clusters to be used by the K-means algorithm based on the value of the silhouette coefficient. Fuzzy c-means and mean shift algorithms are added for comparison purposes. This paper also introduces the impact of the Kalman filter while using the measured UWB test points as an input for the Kalman filter in order to obtain a better estimation of the position. As a result, the average localization error is reduced by 43.26% (from 16.3442 cm to 9.2745 cm) when combining the K-means algorithm with the Kalman filter in which the Kalman-filtered UWB-measured test points are used as an input for the proposed system.

Evaluating Stable Chronic Obstructive Pulmonary Disease by Ultrasound.

Background and Aim The purpose of the study was to evaluate the relationship between COPD severity and the diaphragmatic function measured by point-of-care US in patients with stable COPD. Method A total of 61 patients with COPD and 40 healthy subjects who had been admitted to Ufuk University Hospital between December 2018 and May 2019 were enrolled. Point-of-care US was performed, and lung silhouette and anterior, right, and left hemidiaphragm method in M-mode were used to evaluate the diaphragm. Results The point-of-care US measurements, lung silhouette method right (Lung Sil R), lung silhouette method left (Lung Sil L), right hemidiaphragm US method in B-mode (Ant B-Mode R), and right hemidiaphragm US method in M-mode (Ant M-Mode R), were significantly different among groups (P < 0.001 for each). FEV1 was strongly correlated with Lung Sil R, Lung Sil L, Ant B-Mode R, and Ant M-Mode R (r = 0.963, P < 0.001; r = 0.956, P < 0.001; r = 0.953, P < 0.001; and r = 0.917, and P < 0.001, respectively). Negative correlations were detected between the number of exacerbations per year and Lung Sil R and the number of exacerbations per year and Ant M-Mode R (r = −0.599, P < 0.001 and r = −0.587, and P < 0.001, respectively). Conclusion In this study, FEV1 and annual number of exacerbations turned out to be strongly correlated US findings. The use of US in COPD patients could help to support clinical decision, but further clinical studies are necessary to confirm those findings.

Reality mining and predictive analytics for building smart applications

BackgroundMobile phone and sensors have become very useful to understand and analyze human lifestyle because of the huge amount of data they can collect every second. This triggered the idea of combining benefits and advantages of reality mining, machine learning and big data predictive analytics tools, applied to smartphones/sensors real time. The main goal of our study is to build a system that interacts with mobile phones and wearable healthcare sensors to predict patterns.MethodsWearable healthcare sensors (heart rate sensor, temperature sensor and activity sensor) and mobile phone are used for gathering real time data. All sensors are managed using IoT systems; we used Arduino for collecting data from health sensors and Raspberry Pi 3 for programming and processing. Kmeans clustering algorithm is used for patterns prediction and predicted clusters (partitions) are transmitted to the user in his front-end interface in the mobile application. Real world data and clustering validation statistics (Elbow method and Silhouette method) are used to validate the proposed system and assess its performance and effectiveness. All data management and processing tasks are conducted over Apache Spark Databricks.ResultsThis system relies on real time gathered data and can be applied to any prediction case making use of sensors and mobile generated data. As a proof of concept, we worked on predicting miscarriages to help pregnant women make quick decisions in case of miscarriage or probable miscarriage by creating a real time system prediction of miscarriage using wearable healthcare sensors, mobile tools, data mining algorithms and big data technologies. 9 risk factors contribute vastly in prediction, the Elbow method asserts that the optimal number of cluster is 2 and we achieve a higher value (0, 95) of Silhouette width that validates the good matching between clusters and observations. K-means algorithm gives good results in clustering the data.

Classification of Collegiate Athletes Based on Their Injury History

Sports-related injuries can have a significant impact on an athlete’s performance and career. While some injuries are inevitable, many can be prevented. Cluster analysis is a useful statistical technique that can assign individuals into groups (i.e., latent subgroups) based on common characteristics. PURPOSE: To utilize cluster analysis to 1) identify the latent subgroups based on athletes’ injury history; and 2) examine the characteristics of latent subgroups among athletes. METHODS: A total of 1,538 college athletes competing in the South Eastern Conference in NCAA division I were segmented by three criteria; 1) Injury parts indicate the body part sustaining the injury, 2) Injury types describe the detail of their injury status such as strain, contusion or tendonitis. 3) Injury duration refers to how long the athlete was unable to participate in training. K-means clustering analysis with the Euclidean similarity of injury log vectors was conducted to label players. The number of groups(k) was determined by applying the average silhouette method. The characteristics of clusters were analyzed descriptively, and the sports were allocated to each group followed by the athlete clusters. RESULTS: Five clusters were identified by the maximum average silhouette coefficient (0.153) among coefficients for randomly drawn k’s between 2 to 20. The first group, mainly baseball, men’s basketball, and men’s tennis, had injury to their ankle, arm, and hamstring for contusion and strain for a few weeks. The second group was mostly from football, with injury to their ankle, knee, and shoulder with the most extended injury durations. The third group, mostly football or track and field, were the athletes likely to have knee inflammation, and the duration was nearly half of a year. The injured body parts of the fourth group were back, finger, and hamstring, and the types of injuries were fracture and tendonitis. This cluster was mainly women’s basketball and track and field athletes. The members of the last group had head injury (e.g., concussion), and were soccer, softball or volleyball athletes. CONCLUSION: This study may help practitioners in recognizing the likelihood of an athletes’ injury according to their sport. Additionally, coaches could also consider this information in daily practices.

Application of K-Means Clustering for Designing Power Distribution Network

Installation of independent power distribution network with central generation using solar power plant is a trending solution to meet the demands of electricity of energy starved rural areas. In this paper, application of K-means clustering is proposed for designing power distribution network which segregates the houses in suitable number of clusters and all the clusters centroids are connected to the central location of solar power plant. Total number of clusters is selected by application of three methods like Elbow method, CH index method and Average Silhouette method. This paper can act as a useful tool for planning and designing the distribution network while optimizing the distribution losses and installation cost of the network.

Demand Response Strategy Applied to Residential Electric Water Heaters Using Dynamic Programming and K-Means Clustering

Previous studies have shown that electric water heaters (EWHs) have strong potential in demand-side management applications more precisely because they offer energy storage capability, so, can be employed as shift loads. However, the challenge of EWH curtailment strategies is to minimize the impact on the hot water availability while shaving the peak of consumption during critical periods. The success of such strategies depends highly on the knowledge of the consumption behavior of each user. Thus, appropriated modeling and consumption analysis could yield better management strategies. This study proposes an electric water heater control strategy based on the dynamic programming and power consumption profile classification. An adaptive clustering process allows recognizing the clients who contribute to the highest power consumption during the peak periods. The analysis and simulation indicate that an appropriate control on the group of users could be implemented to reduce the peak demand and to meet the hot water demand. A k-means clustering algorithm has been used for cluster analysis. The silhouette method has been applied to estimate the appropriate number of clusters.

Representing local shape geometry from multi-view silhouette perspective: A distinctive and robust binary 3D feature

Local geometry description is of central importance in 3D computer vision and robotics, while the design of a distinctive and robust binary descriptor still remains a challenge at present. This paper tackles this problem by proposing to utilize the silhouette cue from multiple viewpoints to represent local shape geometry, forming a new binary feature called rotational silhouette maps (RSM). Key to the RSM descriptor are the leverage of multi-view information for comprehensive characterization paired with the silhouette method for binary and robust feature encoding. Specifically, an RSM is computed for the radius neighbors of a keypoint, at which a local reference frame (LRF) is first constructed to attain rotation invariance. Then, the local shape is rotated in the LRF multiple times to capture the multi-view information. For each view, a silhouette map is generated via projection. By concatenating all the silhouette maps, the RSM feature is computed. Extensive experiments are deployed on three standard datasets, where descriptiveness and robustness with respect to Gaussian noise, shot noise, varying mesh resolutions, the number of keypoints, keypoint localization errors, clutter and occlusion are assessed based on a comparison with nine state-of-the-art descriptors. The results reveal the overall superiority of the proposed descriptor in terms of distinctiveness and robustness.

Research on social data by means of cluster analysis

This paper presents a data mining study and cluster analysis of social data obtained on small producers and family farmers from six country cities in Ceará state, northeast Brazil. The analyzed data involve demographic, economic, agriculture and food insecurity information. The goal of the study is to establish profiles for the small producer families that reside in the region and to identify relevant features which differentiate these profiles. Moreover, we provide an efficient data mining methodology for analysis of social data sets which is capable of handling its natural challenges, such as mixed variables and abundance of null values. We use the Silhouette method for the estimation of the best number of natural groups within the data, along with the Partitioning Around Medoids clustering algorithm in order to compute the profiles. The Correlation-Based Feature Selection method is used to identify which social criteria are the most important to differentiate the families from each profile. Classification models based on support vector machines, multilayer perceptron and decision trees were developed aiming to predict in which of the identified clusters an arbitrary family would be best fit. We obtained a good separation of the families into two clusters, and a multilayer perceptron model with approximately 93.5% prediction accuracy.