Silhouette Index as Clustering Evaluation Tool

Dudek, Andrzej

doi:10.1007/978-3-030-52348-0_2

Cited by 52 publications

(18 citation statements)

References 7 publications

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“…For the optimal estimate of the k-medoids (and therefore of the k clusters), we used the analysis of the silhouette that allows us to graphically visualize the quality of the clustering. The silhouette index is generally used to identify the optimal number of groups in a hierarchical cluster and as a synthetic indicator to evaluate the overall quality of clustering [27]. Its advantage is the low computational complexity and the simple rules of interpretation.…”

Section: Discussionmentioning

confidence: 99%

Sentinel Lymph Node Metastasis on Clinically Negative Patients: Preliminary Results of a Machine Learning Model Based on Histopathological Features

et al. 2021

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The reported incidence of node metastasis at sentinel lymph node biopsy is generally low, so that the majority of women underwent unnecessary invasive axilla surgery. Although the sentinel lymph node biopsy is time consuming and expensive, it is still the intra-operative exam with the highest performance, but sometimes surgery is achieved without a clear diagnosis and also with possible serious complications. In this work, we developed a machine learning model to predict the sentinel lymph nodes positivity in clinically negative patients. Breast cancer clinical and immunohistochemical features of 907 patients characterized by a clinically negative lymph node status were collected. We trained different machine learning algorithms on the retrospective collected data and selected an optimal subset of features through a sequential forward procedure. We found comparable performances for different classification algorithms: on a hold-out training set, the logistics regression classifier with seven features, i.e., tumor diameter, age, histologic type, grading, multiplicity, in situ component and Her2-neu status reached an AUC value of 71.5% and showed a better trade-off between sensitivity and specificity (69.4 and 66.9%, respectively) compared to other two classifiers. On the hold-out test set, the performance dropped by five percentage points in terms of accuracy. Overall, the histological characteristics alone did not allow us to develop a support tool suitable for actual clinical application, but it showed the maximum informative power contained in the same for the resolution of the clinical problem. The proposed study represents a starting point for future development of predictive models to obtain the probability for lymph node metastases by using histopathological features combined with other features of a different nature.

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Section: Discussionmentioning

confidence: 99%

Sentinel Lymph Node Metastasis on Clinically Negative Patients: Preliminary Results of a Machine Learning Model Based on Histopathological Features

et al. 2021

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“…, 12. The number of clusters is selected by using the silhouette index (SI index [86]; see also References [87,88]. The highest value of SI index indicates the best division.…”

Section: Methodsmentioning

confidence: 99%

Changes in Electricity Production from Renewable Energy Sources in the European Union Countries in 2005–2019

Matuszewska‐Janica

Żebrowska‐Suchodolska

Ala-Karvia

et al. 2021

Energies

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The policy related to the use of renewable sources is a key element of the energy policy executed in the European Union (EU). One of the targets set for 2050 is to increase the share of electricity in energy consumption to 50%, and 80% of electricity is to be generated from low-carbon sources. In recent years, the EU economies have significantly modified their electricity production, which raises the question of the scale of these changes. The aim of the presented analysis is to assess changes in the use of renewable sources for electricity production in the EU countries in 2005–2019. Gini coefficient and k-mean are applied in the analysis. The conducted research shows that EU countries, in line with the energy policy assumptions, have both increased the share of renewable sources in energy production, especially in electricity production, as well as increased the diversity of used renewable sources. The results also indicate a vast diversity in terms of the use of such sources for the production of renewable electricity in the EU. This indicates that the energy transition is being implemented by EU countries with individual country-level approaches. Nonetheless, a variety of the EU’s both support and restrictive measures are of considerable importance for the ongoing energy transition.

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“…Negative values, on the other hand, reflect the possibility of erroneous assignment of data points to clusters. The silhouette index has become widely recognised and valued in the field primarily because of its intuitive interpretation and its effectiveness in accommodating diverse cluster shapes and densities [32][33][34][35]. The silhouette index can be derived by utilising Equation (3).…”

Section: Silhouette Indexmentioning

confidence: 99%

Regional Clustering Based on Types of Non-Communicable Diseases Using k-Means Algorithm

Munandar,

Yunizar Yusuf Pratama

2024

matrik

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Noncommunicable diseases (NCDs) have become a global threat to public health, necessitating a comprehensive understanding of their geographic and epidemiological distribution in order to devise appropriate interventions. The objective of this study is to clustering areas of Banten Province based on NCDS profiles using the unsupervised learning technique. The method used in this study is the k-means algorithm for grouping types of non-communicable diseases based on region. The processing and normalisation of NCDS prevalence data from various health sources preceded cluster analysis using the k-means clustering algorithm. This research is categorised into two scenarios: the first involves the clustering of data obtained from outlier analysis, while the second scenario excludes any outliers. The objective is to observe disparities in regional clustering outcomes by categorising non-communicable diseases according to these two scenarios. The silhouette index is used to determine the validity of cluster results. These findings are analysed in depth to determine the geographic and socioeconomic patterns associated with each cluster's NCDS profile. Based on the mean silhouette index value of 0.812, the results indicate that the sum of k = 2 in the k-means algorithm is the optimal cluster result in this case. Five non-communicable diseases, namely diabetes, hypertension, obesity, stroke, and cataracts, necessitate significant focus in the first cluster (C1), where 202 regions were grouped. Six regions belong to the second cluster (C2), which includes areas that are not only susceptible to the five non-communicable diseases in cluster C1 but also to breast cancer, cervical cancer, heart disease, chronic obstructive pulmonary disease (COPD), and congenital deafness.

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Silhouette Index as Clustering Evaluation Tool

Cited by 52 publications

References 7 publications

Sentinel Lymph Node Metastasis on Clinically Negative Patients: Preliminary Results of a Machine Learning Model Based on Histopathological Features

Sentinel Lymph Node Metastasis on Clinically Negative Patients: Preliminary Results of a Machine Learning Model Based on Histopathological Features

Changes in Electricity Production from Renewable Energy Sources in the European Union Countries in 2005–2019

Regional Clustering Based on Types of Non-Communicable Diseases Using k-Means Algorithm

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