Graphical Summaries of Circular Data with Outliers Using Python Programming Language

Graph in statistics is used to summarise and visualise the data in pictorial form. Graphical summary enables us to visualise the data in a more simple and meaningful way so that the interpretation will be easier to understand. The graphical summaries of circular data with outliers is discussed in this study. Most of the time, people use linear data in real life applications. Other than linear data, there is another data type that has a direction which refers to circular data and it is different from linear data in many aspects such as in descriptive statistics and statistical modeling. Unfortunately, the availability of statistical software specialises in analysing circular data is very limited. In this study, the graphical summaries of circular data are plotted using the in-demand programming language, Python. The Python code for generating graphical summaries of circular data such as circular dot plot and rose diagram is proposed. The historical circular data is used to illustrate the graphical summaries with the existence of outliers. This study will be helpful for those who are started exploring circular data and choose Python as an analysis tool

A synthetic data generation procedure for univariate circular data with various outliers scenarios using Python programming language

Synthetic data is artificial data that is created based on the statistical properties of the original data. The aim of this study is to generate a synthetic or simulated data for univariate circular data that follow von Mises (VM) distribution with various outliers scenario using Python programming language. The procedure of formulation a synthetic data generation is proposed in this study. The synthetic data is generated from various combinations of seven sample size, n and five concentration parameters, K. Moreover, a synthetic data will be generated by formulating a data generation procedure with different condition of outliers scenarios. Three outliers scenarios are proposed in this study to introduce the outliers in synthetic dataset by placing them away from inliers at a specific distance. The number of outliers planted in the dataset are fixed with three outliers. The synthetic data is randomly generated by using Python library and package which are 'numpy', 'random' and von Mises'. In conclusion, the synthetic data of univariate circular data from von Mises distribution is generated and the outliers are successfully introduced in the dataset with three outliers scenarios using Python. This study will be valuable for those who are interested to study univariate circular data with outliers and choose Python as an analysis tool

The effect of different similarity distance measures in detecting outliers using single-linkage clustering algorithm for univariate circular biological data

Clustering algorithms can be used to create an outlier detection procedure in univariate circular data. The circular distance between each point of angular observation in circular data is used to calculate the similarity measure to appropriately group observations. In this paper, we present a clustering-based procedure for detecting outliers in univariate circular biological data using various similarity distance measures. Three circular similarity distance measures; Satari distance, Di distance and Chang-chien distance were used to detect outliers using a single-linkage clustering algorithm. Satari distance and Di distance are two similarity measures that have similar formulas for univariate circular data. This study aims to develop and demonstrate the effectiveness of the proposed clustering-based procedure with various similarity distance measures in detecting outliers. The circular similarity distance of SL-Satari/Di and other similarity measures, including SL-Chang, were compared at various dendrogram cutting points. It is found that a clustering-based procedure using a single-linkage algorithm with various similarity distances is a practical and promising approach to detect outliers in univariate circular data, particularly for biological data. According to the results, the SL-Satari/Di distance outperformed the SL-Chang distance for certain data conditions

Cranial morphology associated with syndromic craniosynostosis: A potential detection of abnormality in patient's cranial growth using angular statistics

Introduction: Apert, Crouzon, and Pfeiffer syndromes are common genetic syndromes related to syndromic craniosynostosis (SC), whereby it is a congenital defect that occurs when the cranial growth is distorted. Identifying cranial angles associated with these 3 syndromes may assist the surgical team to focus on a specific cranial part during the intervention planning, thus optimizing surgical outcomes and reducing potential morbidity. Objective: The aim of this study is to identify the cranial angles, which are associated with Apert, Crouzon, and Pfeiffer syndromes. Methods: The cranial computed tomography scan images of 17 patients with SC and 22 control groups aged 0 to 12 years who were treated in the University Malaya Medical Centre were obtained, while 12 angular measurements were attained using the Mimics software. The angular data were then divided into 2 groups (patients aged 0 to 24 months and >24 months). This work proposes a 95% confidence interval (CI) for angular mean to detect the abnormality in patient's cranial growth for the SC syndromes. Results: The 95% CI of angular mean for the control group was calculated and used as an indicator to confirm the abnormality in patient's cranial growth that is associated with the 3 syndromes. The results showed that there are different cranial angles associated with these 3 syndromes. Conclusions: All cranial angles of the patients with these syndromes lie outside the 95% CI of angular mean of control group, indicating the reliability of the proposed CI in the identification of abnormality in the patient's cranial growth

The Effect of Different Similarity Distance Measures in Detecting Outliers Using Single-Linkage Clustering Algorithm for Univariate Circular Biological Data

The procedure of outliers detection in univariate circular data can be developed using clustering algorithm. In clustering, it is necessary to calculate the similarity measure in order to cluster the observations into their own group. The similarity measure in circular data can be determined by calculating circular distance between each point of angular observation. In this paper, clustering-based procedure for outlier detection in univariate circular biological data with different similarity distance measures will be developed and the performance will be investigated. Three different circular similarity distance measures are used for the outliers detection procedure using single-linkage clustering algorithm. However, there are two similarity measures namely Satari distance and Di distance that are found to have similarity in formula for univariate circular data. The aim of this study is to develop and demonstrate the effectiveness of proposed clustering-based procedure with different similarity distance measure in detecting outliers. Therefore, in this study the circular similarity distance of SL-Satari/Di and another similarity measure namely SL-Chang will be compared at certain cutting rule. It is found that clustering-based procedure using single-linkage algorithm with different similarity distances are applicable and promising approach for outlier detection in univariate circular data, particularly for biological data. The result also found that at a certain condition of data, the SL-Satari/Di distance seems to overperform the performance of SL-Chang distance

Cranial morphology associated with syndromic graniosynostosis: A potential detection of abnormality in patient’s cranial growth using angular statistics

Introduction: Apert, Crouzon, and Pfeiffer syndromes are common genetic syndromes related to syndromic craniosynostosis (SC), whereby it is a congenital defect that occurs when the cranial growth is distorted. Identifying cranial angles associated with these 3 syndromes may assist the surgical team to focus on a specific cranial part during the intervention planning, thus optimizing surgical outcomes and reducing potential morbidity. Objective: The aim of this study is to identify the cranial angles, which are associated with Apert, Crouzon, and Pfeiffer syndromes. Methods: The cranial computed tomography scan images of 17 patients with SC and 22 control groups aged 0 to 12 years who were treated in the University Malaya Medical Centre were obtained, while 12 angular measurements were attained using the Mimics software. The angular data were then divided into 2 groups (patients aged 0 to 24 months and >24 months). This work proposes a 95% confidence interval (CI) for angular mean to detect the abnormality in patient’s cranial growth for the SC syndromes. Results: The 95% CI of angular mean for the control group was calculated and used as an indicator to confirm the abnormality in patient’s cranial growth that is associated with the 3 syndromes. The results showed that there are different cranial angles associated with these 3 syndromes. Conclusions: All cranial angles of the patients with these syndromes lie outside the 95% CI of angular mean of control group, indicating the reliability of the proposed CI in the identification of abnormality in the patient’s cranial growth