alLearnMoreRel=paste0("<p>Determine the optimal number of clusters by inspecting ",
alLearnMoreRel=paste0("<p>Determine the optimal number of clusters by inspecting ",
"the average silhouette width and the total within cluster sum of squares (WSS) ",
"the average silhouette width and the total within cluster sum of squares (WSS) ",
"for a range of cluster numbers.</p>",
"for a range of cluster numbers.</p>",
"<p><b>Silhouette analysis</b> estimates the average distance between clusters. ",
"<p><b>Silhouette analysis</b> first computes how close each trajectory is with others in the cluster it is assigned to, ",
"Larger silhouette widths indicate better.<p>",
"this is then compared to closeness with trajectories in other clusters. ",
"Larger average silhouette widths usually indicate better clustering. To make sure averaging does not hide a locally bad",
"clustering, this should be inspected along with the silhouette plot in the \"Internal\" tab.<p>",
"<p><b>WSS</b> evaluates the compactness of clusters. ",
"<p><b>WSS</b> evaluates the compactness of clusters. ",
"Compact clusters achieve low WSS values. ",
"Compact clusters achieve low WSS values. ",
"Look for the <i>knee</i> in the plot of WSS as function of cluster numbers.</p>"),
"Look for the <i>elbow</i> in the plot of WSS as function of cluster numbers.</p>"),
alLearnMoreInt=paste0("<p>Evaluate the goodness of a clustering structure by inspecting ",
alLearnMoreInt=paste0("<p>Evaluate the goodness of a clustering structure by inspecting ",
"principle components, the dendrogram, ",
"principal components, the dendrogram, ",
"and the silhouette for a given number of clusters.</p>",
"and the silhouette for a given number of clusters.</p>",
"<p>Each point in the scatter plot of 2 principle components corresponds to a single time series. ",
"<p><b>Principal components:</b> Each point in the scatter plot corresponds to a single time series in the first 2 PCs space. ",
"Points are coloured by cluster numbers. Compact, well separated clusters ",
"Points are coloured by cluster numbers. Compact, well separated clusters ",
"indicate good partitioning.</p>",
"indicate good partitioning. The percentage of total variance carried by each PC is indicated.</p>",
"<p>The height of dendrogram branches indicates how well clusters are separated.</p>",
"<p><b>Dendrogram:</b> The height of branches indicates how well clusters are separated.</p>",
"<p>The silhouette plot displays how close each time series in one cluster ",
"<p><b>Silhouette plot:</b> The plot indicates for each series whether it is on average closer to series within its cluster ",
"is to time series in the neighboring clusters. ",
"or to series in other clusters. Each bar represents the <a href=https://en.wikipedia.org/wiki/Silhouette_(clustering) title=\"External link\">silhouette score</a> ",
"A large positive silhouette (Si) indicates time series that are well clustered.",
"(Si) for one series. The height of the bars varies ",
"A negative Si indicates time series that are closer to ",
"between 1 (the series is much closer to series in its cluster) and -1 (the series is much closer to series in an other cluster). ",
"a neighboring cluster, and are placed in the wrong cluster.</p>")
"Hence, large positive values of Si are usually associated with better clustering, while negative values are associated with worse clustering.")