Silhouettes: a graphical aid to the interpretation and validation of cluster analysis

By Peter J. Rousseeuw. 1987

A new graphical display is proposed for partitioning techniques. Each cluster is represented by a so-called silhouette, which is based on the comparison of its tightness and separation. This silhouette shows which objects lie well within their cluster, and which ones are merely somewhere in between clusters. The entire clustering is displayed by combining the silhouettes into a single plot, allowing an appreciation of the relative quality of the clusters and an overview of the data configuration. The average silhouette width provides an evaluation of clustering validity, and might be used to select an ‘appropriate’ number of clusters.

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Benchmark and Survey of Automated Machine Learning Frameworks (2019, methodology): “To assess the quality of the resulting clusters—and therefore also the overall configuration similarity—, the silhouette coefficient (Rousseeuw, 1987) is computed.”
Survey on Automated Machine Learning (2019, methodology): “out. 1971) is used as the distance metric between two congurations. To assess the quality of the resulting clusters|and therefore also the overall conguration similarity|, the silhouette coecient (Rousseeuw, 1987) is computed. Figure 14 shows the silhouette coecient versus number of instances per cl”
Deep Graph Infomax (2018, background): “The projection obtains a Silhouette score [22] of 0.”
Scaling Multi-Agent Reinforcement Learning with Selective Parameter Sharing (2021, methodology): “The elbow method (Thorndike, 1953), the silhouette method (Rousseeuw, 1987), or the Davies–Bouldin index (Davies & Bouldin, 1979), all could be used to determine the number of clusters since our method tends to produce well-separated values.”
Making AI Forget You: Data Deletion in Machine Learning (2019, background): “Silhouette Coefﬁcient [72]: This coefﬁcient measures a type of correlation (between -1 and +1) that captures how dense each cluster is and how well-separated different clusters are.”
Sensing spatial distribution of urban land use by integrating points-of-interest and Google Word2Vec model (2017, methodology): “The average silhouette value can be used as a criterion to determine the number of POI clusters K (Rousseeuw 1987, Yuan et al .”
Uncovering Prognosis-Related Genes and Pathways by Multi-Omics Analysis in Lung Cancer (2020, methodology): “Based on the result depicted by the elbow method, we performed further analysis, to obtain the optimal number of clusters, using the Silhouette index [16] and Calinski–Harabasz criterion [17].”
An Evolutionary Approach to Multiobjective Clustering (2007, methodology): “On those data sets containing spherically shaped clusters, it does not perform quite as well as the Silhouette Width, but its performance is still high and extends to the Long and Smile data sets.”
Discovering Urban Functional Zones Using Latent Activity Trajectories (2015, methodology): “The number of clusters can be predefined according to the needs of an application or determined using the average silhouette value as the criterion [15].”
Cluster validation techniques for genome expression data (2003, methodology): “Cluster validity techniques include the Silhouette method [7], Dunn’s based index [8,9], Davies-Bouldin index [10] and the C-index [11].”
Density-Based Clustering Validation (2014, background): “5.1 Real Datasets Results for real datasets are shown in Tables 1 and 2, for which the best values for each dataset are highlighted.”
Large-scale genotyping of complex DNA (2003, methodology): “We evaluated the quality of classification by calculating the average silhouette width, s”
Deciphering Signatures of Mutational Processes Operative in Human Cancer (2013, unknown): “The average silhouette width (Rousseeuw, 1987) of the N clusters is used as a measure of reproducibility for the whole solution.”
Cluster Quality Analysis Using Silhouette Score (2020, methodology): “We choose the more direct method of analyzing the silhouette scores [5] which measure the quality of clusters.”
Analysing Lexical Semantic Change with Contextualised Word Representations (2020, methodology): “For each word independently, we automatically select the number of clusters K that maximises the silhouette score (Rousseeuw, 1987), a metric of cluster quality which favours intra-cluster coherence and penalises inter-cluster similarity, without the need for gold labels.”