Besides predicting alternative central points for subsets, and consequently grouping alternative subset members, the number of clusters predicted can also vary depending on the algorithm selected. Whereas K-means and K-medoids require the number of clusters to be specified in advance, hierarchical clustering approaches automatically determine the number of clusters to group data points into without additional human intervention \cite{k-medoids_clustering,Dynamic_Time_Warping_Clustering}. Furthermore, as a form of unsupervised learning, clustering approaches will provide different group labels to subsets each time they are applied, even if the actual subset members remain unchanged, so a separate ‘subset mapping’ function based on ‘Hamming distance’ is required to ensure consistency in comparisons between generated clusters and expected groupings. Once again it is also worth noting that the definition of subsets using any clustering technique will only be valid if time series are being compared on comparative features rather than incomplete time series data. As such, time series segmentation based on shared features or imputation of missing data are again prerequisites for meaningful analysis, ensuring that only completed segments are used in defining subsets. Finally, if using feature-based distance measures as the basis for clustering (grouped into matrices of distance points relating each technology time series to every other time series) then it is generally suggested that either hierarchical clustering or the 'Partitioning Around Medoids’ (PAM) variant of K-Medoids are applied to the descriptive data \cite{k-medoids_clustering,Dynamic_Time_Warping_Clustering}.
Cross-validation techniques
To assess the predictive performance of any given combination of bibliometric indicators in practice it is necessary to determine how the classification results will generalise to an independent (i.e. unknown) data set. For this purpose, cross-validation techniques are commonly employed to provide an indication of model validity when considering out-of-sample predictions. This is accomplished by sequentially training and then generating test predictions from different subset decompositions of the original data, and using the average number of misclassified observations as a means to rank each predictor grouping. In doing so, cross-validation helps to address the risk of over-fitting models that are based on limited sample sizes, but equally provides a means to identify the most suitable predictor groupings to use for model building purposes based on their robustness to misclassifications. Cross-validation techniques are generally grouped into either exhaustive or non-exhaustive categories, as shown in Table \ref{table:cross-validation_techniques}.