Using random projection, a method to speed up both kernel k-means and centroid initialization with k-means++ is proposed. We approximate the kernel matrix and distances in a lower-dimensional space ${\mathbb{R}}^d$ before the kernel k-means clustering motivated by upper error bounds. With random projections, previous work on bounds for dot products and an improved bound for kernel methods are considered for kernel k-means. The complexities for both kernel k-means with Lloyd’s algorithm and centroid initialization with k-means++ are known to be $O\left(nkD\right)$ and $\Theta \left(nkD\right)$, respectively, with n being the number of data points, the dimensionality of input feature vectors D and the number of clusters k. The proposed method reduces the computational complexity for the kernel computation of kernel k-means from $O\left(n^{2}D\right)$ to $O\left(n^{2}d\right)$ and the subsequent computation for k-means with Lloyd’s algorithm and centroid initialization from $O\left(nkD\right)$ to $O\left(nkd\right)$. Our experiments demonstrate that the speed-up of the clustering method with reduced dimensionality $d=200$ is 2 to 26 times with very little performance degradation (less than one percent) in general.

Behavioral theory assumes that leaders can be identified by their daily behaviors. Social network analysis helps to understand behavioral patterns within their social networks. This work considers leaders as the managerial personnel of the organization and differentiates managements from non-managerial staff by their behavior with five different types of interactions with PageRank and their attributes in modern organizations. PageRank and word embedding using word2vec with phrases from features are adopted to extract new features for the identification of managerial staff. Both traditional machine learning methods and graph neural networks are utilized with real-world data from an Austrian IT company called Knapp System Integration. Our experimental results show that the proposed new features extracted using PageRank with different types of interactions and word2vec with phrases significantly improve the identification accuracy. We also propose to use graph neural networks as an effective learning algorithm to identify managers from organizations. Our approach can identify managerial staff with an accuracy of around 80%, which demonstrates that managers could be identified through social network analysis. By analyzing the behaviors of members, the proposed method is effective as a performance appraisal tool for organizations. The study facilitates sustainable management by helping organizations to retain managerial talents or to invite potential talents to join the management team.

Over the past few decades, the study of leadership theory has expanded across various disciplines, delving into the intricacies of human behavior and defining the roles of individuals within organizations. Its primary objective is to identify leaders who play significant roles in the communication flow. In addition, behavioral theory posits that leaders can be distinguished based on their daily conduct, while social network analysis provides valuable insights into behavioral patterns. Our study investigates five and six types of social networks frequently observed in different organizations. This study is conducted using datasets we collected from an IT company and public datasets collected from a manufacturing company for the thorough evaluation of prediction performance. We leverage PageRank and effective word embedding techniques to obtain novel features. State-of-the-art performance is obtained using various statistical machine learning methods, graph convolutional networks (GCN), automated machine learning (AutoML), and explainable artificial intelligence (XAI). More specifically, our approach can achieve state-of-the-art performance with an accuracy close to $90\%$ for leaders identification with data from projects of different types. This investigation contributes to the establishment of sustainable leadership practices by aiding organizations in retaining their leadership talent.